Gr 10 Math Nov P1 Mix

Which of the following sets includes only non-negative numbers?

Natural Numbers (correct)

Rational Numbers

Integers

Imaginary Numbers

What is the correct symbol for the set of whole numbers?

N0 (correct)

N

Q

Z

Which of the following numbers is considered irrational?

sqrt{2} (correct)

0.75

1/3

3

Which statement about integers is true?

They include both positive and negative numbers. Signup and view all the answers

Which subset of real numbers can be represented as a fraction?

Rational Numbers Signup and view all the answers

What characterizes irrational numbers?

Their decimal expansions are non-repeating and non-terminating. Signup and view all the answers

What is the symbol for rational numbers?

Q Signup and view all the answers

Which of the following numbers is classified as imaginary?

sqrt{-1} Signup and view all the answers

What is the product of the binomial extit{(A + B)} and the trinomial extit{(C + D + E)}?

A(C + D + E) + B(C + D + E) Signup and view all the answers

Which of the following describes a constant in algebra?

A term without a variable Signup and view all the answers

What is the formula for multiplying two binomials extit{(ax + b)(cx + d)}?

acx^2 + adx + bcx + bd Signup and view all the answers

What is the identity used for factorising the difference of two squares?

a^2 - b^2 = (a + b)(a - b) Signup and view all the answers

Which of the following correctly simplifies the expression extit{a/b × c/d}?

<pre><code>extit{ac/bd} </code></pre> Signup and view all the answers

What does the term 'exponent' refer to?

A number raised to a power Signup and view all the answers

Which process involves grouping terms with common factors?

Factorising by grouping Signup and view all the answers

In the context of equations, what does it mean for two expressions to be equal?

Both expressions represent the same quantity Signup and view all the answers

What is the first step in simplifying an algebraic fraction?

Identify and factor out common factors Signup and view all the answers

What is the resulting form of the difference of two cubes, represented by extit{x^3 - y^3}?

x^3 - y^3 = (x - y)(x^2 - xy + y^2) Signup and view all the answers

Which statement best defines an irrational number?

A number with a non-repeating, non-terminating decimal expansion. Signup and view all the answers

What is the first step in converting a terminating decimal into a rational number?

Identify the integer part. Signup and view all the answers

When rounding a number, if the digit after the required decimal place is less than 5, what should be done?

Leave the last digit unchanged. Signup and view all the answers

Which expression represents the process of multiplying two linear binomials?

acx^2 + adx + bcx + bd Signup and view all the answers

What type of number is \sqrt{4}?

Rational number Signup and view all the answers

How can an irrational number be represented more simply?

By rounding it off. Signup and view all the answers

What is the correct definition of a binomial?

An expression with two terms. Signup and view all the answers

What should you identify first when estimating surds?

Perfect squares or cubes Signup and view all the answers

Which of the following is an example of a terminating decimal?

2.75 Signup and view all the answers

What do you call the numerical factor in a term?

Coefficient Signup and view all the answers

What is one method used to solve linear equations?

Expanding all brackets Signup and view all the answers

How many solutions can a linear equation have?

At most one solution Signup and view all the answers

Which is true about quadratic equations?

They can have at most one or two solutions Signup and view all the answers

What is the first step in solving simultaneous equations using substitution?

Express one variable in terms of the other Signup and view all the answers

What is a necessary condition for solving quadratic equations effectively?

The equation must be balanced Signup and view all the answers

Which of the following is not a step in the method for solving quadratic equations?

Combine like terms Signup and view all the answers

When solving by elimination, what is the first step?

Make the coefficients of a variable the same Signup and view all the answers

What does it mean if a quadratic equation has no solutions?

The quadratic does not intersect the x-axis Signup and view all the answers

Which step involves ensuring the quadratic is in the correct form?

Rewriting the equation Signup and view all the answers

Which of the following is true regarding solving equations?

Operations must be performed on both sides to maintain balance Signup and view all the answers

What does the solution of a system of simultaneous linear equations represent?

The intersection point of the graphs Signup and view all the answers

Which step is NOT part of the problem solving strategy for word problems?

Translate the words into a graphical representation Signup and view all the answers

What is a literal equation?

An equation with several letters or variables Signup and view all the answers

When solving the inequality $2x + 2 e 1$, what happens if both sides are multiplied by -1?

The inequality is reversed Signup and view all the answers

In the formula for a linear sequence $T_n = dn + c$, what does the variable $d$ represent?

The common difference between terms Signup and view all the answers

To find the common difference $d$ in a sequence, you calculate $T_n - T_{n-1}$. What does $T_n$ denote?

The $n$th term in the sequence Signup and view all the answers

When rearranging a literal equation to isolate an unknown variable, which principle is applied?

Perform the opposite operation on both sides Signup and view all the answers

What is the primary method used to solve linear inequalities?

Using similar operations as linear equations Signup and view all the answers

What term describes an ordered list of items, usually numbers?

Sequence Signup and view all the answers

What is the result of $(a^m)^n$ according to the power of a power rule?

$a^{mn}$ Signup and view all the answers

In the equation $v = \frac{D}{t}$, what does $v$ represent?

Speed Signup and view all the answers

Which expression is equivalent to $a^{m/n} \times a^{p/q}$ using the multiplication of exponents rule?

$a^{m/n + p/q}$ Signup and view all the answers

If $a^{m/n} = a^{p/q}$, what does it imply if the bases are the same?

$m/n = p/q$ Signup and view all the answers

What is a linear sequence defined by?

The constant difference between successive terms Signup and view all the answers

Which of the following represents the zero exponent law?

$a^0 = 1$ for any $a$ Signup and view all the answers

What is the simplified form of $rac{a^m}{a^n}$ using the division of exponents rule?

$a^{m-n}$ Signup and view all the answers

What does the constant 'm' represent in the equation of a straight line?

The gradient of the graph Signup and view all the answers

Which method is typically used to solve exponential equations when bases cannot easily be made the same?

Logarithms Signup and view all the answers

How does the value of 'c' affect a straight line graph?

It shifts the graph vertically Signup and view all the answers

What is the domain of a linear function of the form y = mx + c?

All real numbers Signup and view all the answers

When simplifying $\left(\frac{a}{b}\right)^n$, which exponent law is applied?

Raising a quotient to a power Signup and view all the answers

How do you calculate the y-intercept of a straight-line graph?

Set x = 0 Signup and view all the answers

Which expression represents the prime factorization of an exponential expression?

Express each base as a prime number Signup and view all the answers

What effect does a positive value of 'a' have on a parabola?

The graph opens upwards Signup and view all the answers

What does a negative exponent indicate for a number $a$?

$a^{-n} = \frac{1}{a^n}$ Signup and view all the answers

When rewriting an expression with fractional exponents like $\sqrt[n]{a}$, what is the correct conversion?

$a^{1/n}$ Signup and view all the answers

What happens to the graph of the function y = ax^2 + q when q < 0?

The graph shifts downwards Signup and view all the answers

What kind of points are needed to sketch a straight-line graph effectively?

The x-intercept and the y-intercept Signup and view all the answers

What is the range of a linear function of the form f(x) = mx + c?

All real numbers Signup and view all the answers

What occurs when 'm' is set to 0 in the equation of a straight line?

The line becomes horizontal Signup and view all the answers

What happens to the graph of a parabola as the value of $a$ increases beyond 1?

The graph gets narrower. Signup and view all the answers

For which value of $a$ will the graph of the parabola open downwards?

Any negative value of $a$ Signup and view all the answers

Where is the y-intercept of the function $y = ax^2 + q$ calculated?

By substituting $x = 0$ Signup and view all the answers

If $q < 0$, what can be concluded about the range of the parabola when $a > 0$?

The range is $[q; ext{infinity})$. Signup and view all the answers

In the function $y = rac{a}{x} + q$, what is the domain of the function?

$ ext{All real numbers except } x=0$ Signup and view all the answers

Which statement accurately describes the turning point of the quadratic function $f(x) = ax^2 + q$ when $a < 0$?

The turning point is a maximum. Signup and view all the answers

How is the horizontal asymptote defined in the hyperbolic function $y = rac{a}{x} + q$?

At $y = q$ Signup and view all the answers

What effect does a negative value of $a$ have on the hyperbola $y = rac{a}{x} + q$?

The graph lies in the second and fourth quadrants. Signup and view all the answers

Which of the following best describes the axis of symmetry for the function $f(x) = ax^2 + q$?

The line $x = 0$ Signup and view all the answers

What does the parameter $q$ determine in trigonometric functions?

The vertical shift Signup and view all the answers

Which formula represents accumulated amount with simple interest?

$A = P(1 + in)$ Signup and view all the answers

In which scenario is compound interest MORE beneficial than simple interest?

Investing money over time Signup and view all the answers

What key variable is needed to calculate simple interest?

Principal amount Signup and view all the answers

How does inflation affect prices over time?

Inflation increases the price of goods and services Signup and view all the answers

What is the primary effect of compound interest on an investment?

Causes exponential growth Signup and view all the answers

What is required to identify asymptotes in functions like tangents?

Setting the denominator to zero Signup and view all the answers

What does the principal amount represent in the context of loans and investments?

The original amount invested or borrowed Signup and view all the answers

Which of these scenarios would utilize the compound interest formula?

Calculating the future value of a savings account Signup and view all the answers

What is meant by the term 'currency strength'?

The value of a currency in relation to another Signup and view all the answers

What is the general form of a function representing exponential growth?

y = ab^x + q, where b > 1 Signup and view all the answers

Which characteristic is true for the sine function?

The x-intercepts are located at (180°, 0) Signup and view all the answers

What effect does a positive value of q have on the graph of an exponential function?

It shifts the graph vertically upward. Signup and view all the answers

In the function y = a sin θ + q, what does the parameter a determine?

The amplitude of the wave Signup and view all the answers

For the function y = ab^x + q, what does the value of b represent?

The growth or decay factor Signup and view all the answers

What is the range of the sine function?

[-1, 1] Signup and view all the answers

Which type of asymptote do exponential functions have?

Horizontal asymptote at y = q Signup and view all the answers

What happens to the graph of y = ab^x + q when a is negative?

The graph curves downwards. Signup and view all the answers

In functions of the form y = cos θ, where are the maximum turning points located?

(0°, 1) and (360°, 1) Signup and view all the answers

What are the x-intercepts of the cosine function?

(90°, 0) and (270°, 0) Signup and view all the answers

What does the probability of the union of two events, A and B, account for?

It sums the probabilities of both events plus their intersection. Signup and view all the answers

What is the probability of two mutually exclusive events occurring together?

0 Signup and view all the answers

Which statement is true about complementary events?

Their probabilities sum to 1. Signup and view all the answers

What does the identity P(A ∪ B) = P(A) + P(B) - P(A ∩ B) correct?

It subtracts the overlap of two events. Signup and view all the answers

What is the visual representation for mutually exclusive events?

Two separate circles. Signup and view all the answers

Which statement is a consequence of complementary events?

They cannot co-occur. Signup and view all the answers

What is represented by the area outside event A in a Venn diagram of sample space S?

The complement of event A, denoted as A'. Signup and view all the answers

What is the probability relationship for two mutually exclusive events A and B?

P(A ∪ B) = P(A) + P(B) Signup and view all the answers

Which identity demonstrates that the union of an event and its complement covers the sample space?

A ∪ A' = S Signup and view all the answers

What can be inferred if two events A and B have a probability of intersection equal to zero?

They are mutually exclusive events. Signup and view all the answers

What is the period of the cosine function?

360° Signup and view all the answers

What effect does a negative value of the coefficient 'a' have on the parabola's graph?

It changes the graph from a smile to a frown. Signup and view all the answers

What is the range of the tangent function, y = tan θ?

All real numbers Signup and view all the answers

Which statement about the y-intercept of the tangent function is correct?

It can be found by solving y = a tan(0°) + q. Signup and view all the answers

How can the cosine graph be related to the sine graph?

The cosine graph is a phase shift of the sine graph by 90°. Signup and view all the answers

What effect does the value of 'q' have on the tangent function graph?

It shifts the graph vertically. Signup and view all the answers

What is the correct expression for the domain of the tangent function, y = a tan θ + q?

{θ : 0° ≤ θ ≤ 360°, θ ≠ 90°, 270°} Signup and view all the answers

How can the value of 'a' in the parabola equation y = ax² + q affect its shape?

It dictates the direction and width of the parabola. Signup and view all the answers

In a hyperbola, which statement is true regarding the variable 'a'?

It influences the shape and direction of the hyperbola. Signup and view all the answers

How do you determine the value of 'q' when finding the equation of a parabola?

By identifying the y-intercept point. Signup and view all the answers

What is the relationship between local purchasing and the economy?

It strengthens the local currency. Signup and view all the answers

What does a probability of 1 represent?

An event will occur every time. Signup and view all the answers

How can probabilities be represented?

As a real number, percentage, or fraction. Signup and view all the answers

What does relative frequency measure?

How often an event occurs in experimental trials. Signup and view all the answers

Which statement is true about the union of two sets?

It contains elements that are in at least one of the two sets. Signup and view all the answers

What is the formula for calculating theoretical probability?

$ P(E) = \frac{n(E)}{n(S)} $ Signup and view all the answers

What does a probability of 0 indicate?

An event will never occur. Signup and view all the answers

Which definition applies to the intersection of two sets?

All elements that are in both sets. Signup and view all the answers

What key concept does a Venn diagram illustrate?

Relationships between sets. Signup and view all the answers

What does the formula ( f = \frac{p}{t} ) signify?

The probability of an event occurring based on trials. Signup and view all the answers

What defines a rational number?

A number that can be expressed as a fraction of two integers Signup and view all the answers

Which of the following sets includes all natural numbers and zero?

Whole Numbers Signup and view all the answers

Which number set does not include any negative numbers?

Natural Numbers Signup and view all the answers

Which of the following statements about irrational numbers is true?

Irrational numbers have non-repeating, non-terminating decimals. Signup and view all the answers

What is the relationship between rational and irrational numbers in the real number system?

Real numbers include both rational and irrational numbers. Signup and view all the answers

In the real number hierarchy, which set is immediately below the set of integers?

Whole Numbers Signup and view all the answers

Which of the following would be classified as an irrational number?

π Signup and view all the answers

What type of number is represented by the symbol $rac{-5}{2}$?

Rational Number Signup and view all the answers

What characterizes a rational number in decimal form?

It can be expressed as a fraction with integer numerator and denominator. Signup and view all the answers

Which step is essential when converting a recurring decimal into a rational number?

Multiply by a power of 10 that matches the length of the repeating cycle. Signup and view all the answers

What happens to an irrational number when it is rounded off?

It becomes a rational number with a decimal expansion. Signup and view all the answers

When estimating surds, what is the first step?

Identify the perfect powers surrounding the surd. Signup and view all the answers

What is crucial for identifying when to round a number up?

If the next digit is 5 or greater. Signup and view all the answers

Which expression represents the general formula for multiplying two linear binomials?

(ax + b)(cx + d) = acx^2 + adx + bcx + bd Signup and view all the answers

What defines a surd?

The n-th root of a number that cannot be simplified to a rational number. Signup and view all the answers

In the rounding process, what adjustment is necessary if the digit being rounded is 9?

Change it to 0 and increase the preceding digit by 1. Signup and view all the answers

Which of the following is true about irrational numbers compared to rational numbers?

Irrational numbers cannot be expressed as fractions. Signup and view all the answers

What is the maximum number of solutions for a linear equation?

One solution Signup and view all the answers

Which step is NOT part of solving a linear equation?

Divide by variable terms Signup and view all the answers

When solving a quadratic equation, what form should it be rewritten in first?

Form with zero on one side Signup and view all the answers

What characterizes a quadratic equation compared to a linear equation?

Can have two solutions Signup and view all the answers

In the method of solving simultaneous equations by substitution, what is the first action taken?

Express one variable in terms of another Signup and view all the answers

Which of the following methods is used to simplify two equations to find values for two variables?

Using elimination or substitution Signup and view all the answers

What is the purpose of checking the answer after solving an equation?

To verify the solution satisfies the original equation Signup and view all the answers

What happens when operations are performed on one side of an equation?

It must be done on the other side too Signup and view all the answers

What is a common feature of quadratic equations with no solutions?

The discriminant is negative Signup and view all the answers

When solving by elimination, what is the goal regarding the coefficients?

Make the coefficients the same Signup and view all the answers

What is the first term in the expansion of the binomial extit{(A + B)(C + D + E)}?

A(C + D + E) Signup and view all the answers

What does the identity для factorising the difference of two squares state?

$a^2 - b^2 = (a + b)(a - b)$ Signup and view all the answers

Which of the following steps is NOT part of simplifying an algebraic fraction?

Identify the greatest common divisor Signup and view all the answers

When multiplying two binomials extit{(ax + b)(cx + d)}, what term represents the middle term of the expansion?

$adx + bcx$ Signup and view all the answers

Which expression correctly represents the sum of two cubes?

$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$ Signup and view all the answers

What is a key step in factorising a quadratic trinomial of the form $ax^2 + bx + c$?

Generate all possible pairs of factors for $a$ and $c$ Signup and view all the answers

What is the result of multiplying the fractions $rac{a}{b} imes rac{c}{d}$?

$rac{ac}{bd}$ Signup and view all the answers

To simplify the expression $rac{x^2 + 2x}{x}$, which of the following is the first step?

Factor the numerator Signup and view all the answers

What is the equivalent expression for extit{(A + B)(C + D + E)}?

$AC + AD + AE + BC + BD + BE$ Signup and view all the answers

What does the solution of a system of simultaneous equations represent in graphical terms?

The coordinates of the intersecting point Signup and view all the answers

In solving linear inequalities, what happens to the inequality sign when both sides are divided by a negative number?

The sign is switched Signup and view all the answers

Which of the following steps is NOT part of the problem-solving strategy for word problems?

Estimate a solution Signup and view all the answers

What does the variable 'd' represent in the general formula for a linear sequence $T_n = dn + c$?

The common difference between terms Signup and view all the answers

To change the subject of the formula in a literal equation effectively, what is the initial action you perform?

Add or subtract terms to isolate the variable Signup and view all the answers

What is the outcome of taking the square root of both sides of an equation involving a variable?

There will be both positive and negative answers Signup and view all the answers

In a linear sequence, if the common difference is 5, what will be the value of the third term $T_3$ if the first term $T_1$ is 10?

20 Signup and view all the answers

When isolating an unknown variable that appears in two or more terms of a literal equation, what should be performed?

Factor out the variable Signup and view all the answers

How do you determine the common difference in a linear sequence?

By calculating $T_n$ minus $T_{n-1}$ Signup and view all the answers

In the context of solving linear equations, what does it mean when two expressions are said to be equal?

They give the same solution Signup and view all the answers

What is the result of simplifying the expression $(ab)^{m/n}$?

$a^{m/n} b^{m/n}$ Signup and view all the answers

Which exponent law applies when dividing two expressions with the same base?

Division of Exponents Signup and view all the answers

When simplifying the expression $rac{a^3}{a^5}$, what is the result?

$a^{-2}$ Signup and view all the answers

Which of the following represents the rule for simplifying an expression with a zero exponent?

$a^0 = 1$ for any $a eq 0$ Signup and view all the answers

What is the first step in solving the exponential equation $5^x = 5^3$?

Set the exponents equal to each other Signup and view all the answers

To simplify the expression $rac{(a^2b^3)^4}{(ab)^5}$, what is the first action you should take?

Use the power of a product rule Signup and view all the answers

Which method can be used to solve the exponential equation $2^x = 8$?

Equating the exponents by rewriting 8 as a power of 2 Signup and view all the answers

What transformation is needed for the expression $rac{1}{a^{-3}}$ to express it with a positive exponent?

Convert negative exponent to positive Signup and view all the answers

In rational exponents, what is the value of $a^{1/2}$?

$ ext{sqrt}(a)$ Signup and view all the answers

What does the coefficient 'm' represent in a linear function of the form $y = mx + c$?

The slope of the graph Signup and view all the answers

How does the value of 'c' affect the graph of a linear function?

It shifts the graph vertically Signup and view all the answers

What characteristic is used to find the x-intercept of a linear function?

Set $y$ to 0 Signup and view all the answers

In a linear sequence, what does the term 'common difference' refer to?

The constant difference between successive terms Signup and view all the answers

When $a < 0$ in a quadratic function $y = ax^2 + q$, what shape does the graph take?

It opens downwards like an upside-down U Signup and view all the answers

What does the term $T_n$ represent in the general formula for a linear sequence $T_n = dn + c$?

The nth term in the sequence Signup and view all the answers

If the value of $m$ in the function $y = mx + c$ equals 0, what is the nature of the graph?

A line that is horizontal Signup and view all the answers

Which of the following describes the effect of $q$ in the quadratic function $y = ax^2 + q$?

It acts as a vertical shift Signup and view all the answers

What are the two points needed to plot a straight-line graph using the dual intercept method?

X-intercept and y-intercept Signup and view all the answers

What does a positive value of 'm' indicate about the linear graph $y = mx + c$?

The graph slopes upwards to the right Signup and view all the answers

What happens to the graph of a parabola when the value of ( a ) is negative?

The graph opens downwards with a maximum turning point. Signup and view all the answers

How does the value of ( q ) affect the graph of the parabola ( y = ax^2 + q )?

It determines the vertical shift of the graph. Signup and view all the answers

What is the range of the function ( f(x) = ax^2 + q ) when ( a > 0 )?

[q, ∞) Signup and view all the answers

Which of the following describes the y-intercept of the function ( y = ax^2 + q )?

It is located at ( (0, q) ). Signup and view all the answers

What are the asymptotes of the hyperbolic function ( y = \frac{a}{x} + q )?

Horizontal asymptote at ( y = q ) and vertical asymptote at ( x = 0 ). Signup and view all the answers

For the hyperbolic function ( y = \frac{a}{x} + q ), which of the following statements is true when ( a < 0 )?

The graph lies in the second and fourth quadrants. Signup and view all the answers

What is the domain of the hyperbolic function ( y = \frac{a}{x} + q )?

{x: x \in \mathbb{R}, x \neq 0} Signup and view all the answers

In the context of parabolic graphs, what is indicated by the sign of ( a )?

The direction of the graph opening. Signup and view all the answers

Which characteristic is true for all parabolic functions in the form ( y = ax^2 + q )?

They all possess an axis of symmetry. Signup and view all the answers

What characterizes the range of exponential functions when the constant $a$ is greater than zero?

The range is greater than $q$. Signup and view all the answers

Which statement about the y-intercept of the function $y = ab^x + q$ is true?

The y-intercept is found by letting $x = 0$. Signup and view all the answers

What is the effect of a negative value of $a$ on the graph of the function $y = a imes ext{sin}( heta) + q$?

The graph reflects about the x-axis. Signup and view all the answers

For the function represented as $y = rac{a}{x} + q$, how is the vertical asymptote defined?

It is the line $x = 0$. Signup and view all the answers

How does the value of $b$ affect the function $y = ab^x + q$?

It affects the rate of growth or decay. Signup and view all the answers

What is the domain of the sine function defined as $y = ext{sin}( heta)$?

The interval $[0°, 360°]$. Signup and view all the answers

When the function is represented as $y = a imes ext{cos}( heta) + q$, what is true about the amplitude when $|a| > 1$?

The amplitude experiences vertical stretch. Signup and view all the answers

What will the vertical asymptote be in the function $y = rac{a}{x} + q$?

At $x = 0$. Signup and view all the answers

For an exponential function $y = ab^x + q$, if $b$ is between 0 and 1, what type of behavior does the function exhibit?

Exponential decay. Signup and view all the answers

What is the proper definition of theoretical probability?

A real number between 0 and 1 representing event likelihood Signup and view all the answers

Which of the following statements about relative frequency is true?

It is calculated by the formula \ f = \frac{p}{t} Signup and view all the answers

How is the union of two sets represented?

A ( A \cup B ) Signup and view all the answers

What characterizes the intersection of two events in probability?

Outcomes that are in both sets Signup and view all the answers

In the context of probability, what does a probability of 0 indicate?

The event will never occur Signup and view all the answers

What do Venn diagrams help to represent in probability?

The relationships between different sets Signup and view all the answers

What aspect of a trigonometric function does the variable $q$ influence?

Vertical shift Signup and view all the answers

Which formula correctly represents the calculation of accumulated amount using simple interest?

$A = P(1 + in)$ Signup and view all the answers

If an event has a theoretical probability of 0.5, what can be inferred about its occurrence?

It will occur half the time Signup and view all the answers

What is the primary difference between simple interest and compound interest?

Simple interest earns interest only on the principal, while compound interest earns interest on both the principal and the accumulated interest. Signup and view all the answers

What does the sample space consist of in probability theory?

The list of all outcomes that can occur in a random experiment Signup and view all the answers

Considering the conversion formula, what does 'Amount in new currency' represent?

Original currency divided by exchange rate Signup and view all the answers

When calculating the y-intercept of a function, what must you set $x$ equal to?

0 Signup and view all the answers

What is the outcome of an experiment with a probability of 1?

The event is certain to occur Signup and view all the answers

Which of the following statements about inflation is true?

Inflation is the average annual increase in the price of goods and services. Signup and view all the answers

In a hire purchase agreement, how is interest typically calculated?

At a simple interest rate on the remaining amount after the initial deposit. Signup and view all the answers

Which of the following explains how population growth is calculated?

By using the compound interest formula, similar to investments. Signup and view all the answers

What do asymptotes indicate in functions like hyperbolas and tangents?

They are lines that the curve approaches but never touches. Signup and view all the answers

Which variable influences the amplitude and reflection in trigonometric functions?

$a$ Signup and view all the answers

What does the identity $P(A \u222A B) = P(A) + P(B) - P(A \cap B)$ help to correct?

It removes double-counting in probabilities. Signup and view all the answers

Which statement is true about mutually exclusive events?

Their union is the sum of individual probabilities. Signup and view all the answers

What is the complement of an event A, represented as A'?

The set containing all outcomes not in A. Signup and view all the answers

What happens to the probabilities of complementary events?

They always sum to 1. Signup and view all the answers

If events A and B are mutually exclusive, what is true about their intersection?

It is empty. Signup and view all the answers

In the context of Venn diagrams, what does the area of overlap represent?

The joint probability of A and B. Signup and view all the answers

What is the graphical representation of the union of two events A and B?

The combined area of both circles A and B, including the overlap. Signup and view all the answers

Which identity correctly describes the relationship between complementary events and the sample space?

A / A' = S. Signup and view all the answers

What does the notation P(S) = 1 signify in probability?

It indicates the total probability of all events occurring. Signup and view all the answers

Why is it necessary to subtract P(A \cap B) from the equation for the union of two events?

To correct for double counting of shared outcomes. Signup and view all the answers

What is the period of the cosine and sine functions?

360° Signup and view all the answers

What effect does a positive value of $q$ have in the function $y = a an heta + q$?

It shifts the graph upwards. Signup and view all the answers

Which of the following describes the domain of the tangent function $y = an heta$?

{ \theta : 0° \leq \theta \leq 360°, \theta \neq 90° } Signup and view all the answers

How can the equation of a parabola in the form $y = ax^2 + q$ be determined?

By obtaining both $a$ and $q$ from the y-intercept. Signup and view all the answers

What is the range of the tangent function $y = an \theta$?

{ f(\theta) : f(\theta) \in \mathbb{R} } Signup and view all the answers

What occurs when the graph of the cosine function is shifted to the right by 90°?

It becomes a sine function. Signup and view all the answers

When determining the equation of a hyperbola, what is the first step?

Identify the direction of the hyperbola. Signup and view all the answers

Which characteristic is true for the y-intercept of the function $y = a an \theta + q$?

It is equal to $q$. Signup and view all the answers

What defines the range of a parabola represented by $y = ax^2 + q$?

The value of $a$ determines the minimum or maximum y-value. Signup and view all the answers

What is the significance of asymptotes in the function $y = a \tan \theta + q$?

They signify where the function will never touch or cross. Signup and view all the answers

Which of the following statements about natural numbers is false?

Natural numbers include zero. Signup and view all the answers

What is a defining characteristic of irrational numbers?

They cannot be expressed as a simple fraction. Signup and view all the answers

Which of the following sets does not belong to the real number system?

Imaginary Numbers Signup and view all the answers

Which of the following is an example of a rational number?

$rac{2}{5}$ Signup and view all the answers

Which statement best describes the relationship between whole numbers and integers?

Whole numbers include all integers except negative ones. Signup and view all the answers

Which of the following is true about the set of rational numbers?

Rational numbers can be expressed as the quotient of two integers. Signup and view all the answers

Which of the following examples is not a real number?

$rac{2}{0}$ Signup and view all the answers

How are natural numbers classified within the real number system?

They are a subset of rational numbers. Signup and view all the answers

What characterizes rational numbers when expressed as decimals?

They include both terminating and repeating decimals. Signup and view all the answers

Which of the following best describes a surd?

The n-th root of a number that cannot be simplified to a rational number. Signup and view all the answers

Which method accurately describes converting a recurring decimal into a rational number?

Multiply the decimal by a power of ten to align the repeating part. Signup and view all the answers

What is the first step to round off a decimal number to a specific decimal place?

Identify the required decimal place and the next digit. Signup and view all the answers

In multiplying two binomials, what does the term 'ad' represent?

One of the cross-products in the expansion. Signup and view all the answers

What is the outcome when rounding off a digit that is 9?

The preceding digit increases by 1, and the 9 becomes 0. Signup and view all the answers

Which of the following is true about irrational numbers?

They have non-repeating, non-terminating decimal expansions. Signup and view all the answers

When estimating the value of a surd, what should be identified first?

The nearest perfect squares or cubes surrounding the surd. Signup and view all the answers

What distinguishes a decimal from an irrational number?

Rational numbers are represented as fractions. Signup and view all the answers

In which situations will rounding off a decimal results in a loss of precision?

When rounding irrational numbers. Signup and view all the answers

What is the result of applying the power of a power rule to $(3^2)^4$?

3^{12} Signup and view all the answers

What expression simplifies to $a^m imes a^n$ according to the multiplication of exponents rule?

a^{m+n} Signup and view all the answers

Which of the following represents the correct simplification of $rac{a^3}{a^5}$ using the division of exponents rule?

a^{-2} Signup and view all the answers

How can the expression $(xy)^3$ be expressed using the raising a product to a power rule?

x^3y^3 Signup and view all the answers

In which scenario can logarithms be used to solve an exponential equation?

When the bases are different Signup and view all the answers

What is the correct expression for the zero exponent rule?

a^0 = 1 Signup and view all the answers

What must be the same for the exponents to be equated in an exponential equation?

The bases must be equal Signup and view all the answers

Which of the following is a step in simplifying an expression with rational exponents?

Use prime factorization where necessary Signup and view all the answers

Which of the following statements about negative exponents is true?

They indicate fractions Signup and view all the answers

Which expression corresponds to the law of rational exponents for powering a power?

a^{(m/n) imes (p/q)} Signup and view all the answers

What does the solution to a system of simultaneous linear equations represent?

The coordinates of the intersection point of the two graphs Signup and view all the answers

What is the first step when using a problem-solving strategy for word problems?

Read the whole question Signup and view all the answers

In the context of literal equations, what is meant by changing the subject of the formula?

Rearranging an equation to isolate a specific variable Signup and view all the answers

When solving linear inequalities, what must be done if both sides are divided by a negative number?

The inequality sign is reversed Signup and view all the answers

What does the variable 'd' represent in the formula for a linear sequence $T_n = dn + c$?

The difference between consecutive terms Signup and view all the answers

Which of the following correctly defines a linear inequality?

An inequality with variables where the highest exponent is 1 Signup and view all the answers

What is the formula for the common difference 'd' in a linear sequence?

$d = T_n - T_{n-1}$ Signup and view all the answers

When rearranging a literal equation, which technique helps isolate the unknown variable?

Performing opposite operations on both sides Signup and view all the answers

What does the term 'term' refer to in the context of sequences?

An individual item in the sequence Signup and view all the answers

In a linear equation, what does the solution represent geometrically?

The coordinates of a point Signup and view all the answers

What will be the result of multiplying a monomial by a binomial represented by the equation $a(x + y)$?

ax + ay Signup and view all the answers

What is the correct expression to factorize a trinomial of the form $ax^2 + bx + c$?

$(x + m)(x + n)$ where $mn = c$ and $m + n = b$. Signup and view all the answers

What identity is used to factorize the difference of two cubes $x^3 - y^3$?

$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$ Signup and view all the answers

Which method involves grouping terms with common factors to simplify an expression?

Factorising by pairs Signup and view all the answers

When multiplying two binomials $(ax + b)(cx + d)$, which components do you derive from $ad$ in the expansion?

The constant term of the resulting polynomial Signup and view all the answers

Which of the following describes the correct procedure for simplifying the algebraic fraction $rac{a}{b} imes rac{c}{d}$?

Multiply the numerators and denominators independently Signup and view all the answers

For the expression $(A + B)(C + D + E)$, what does the result look like using the distributive property?

$AC + AD + AE + BC + BD + BE$ Signup and view all the answers

To determine the common factors in the expression $3x^2 + 6x$, which of these is primarily extracted?

$3x$ Signup and view all the answers

When applying the laws of exponents, what is the result of $a^m imes a^n$?

$a^{m+n}$ Signup and view all the answers

In factorisation, what does the term 'common factor' refer to?

A factor shared by all terms in an expression Signup and view all the answers

What is the effect of the parameter $q$ in the function $y = ab^x + q$?

It causes a vertical shift in the graph. Signup and view all the answers

Which of the following describes the x-intercepts of the function $y = a imes ext{sin}( heta) + q$?

They are found by setting $y = a imes ext{sin}( heta) + q$ to zero. Signup and view all the answers

How is the vertical shift of the sine function determined when the function is represented as $y = a imes ext{sin}( heta) + q$?

By the value of $q$ alone. Signup and view all the answers

What characterizes the horizontal asymptote of the exponential function $y = ab^x + q$?

It is given by the line $y = q$. Signup and view all the answers

For the function $y = a imes ext{cos}( heta) + q$, what happens when $a < 0$?

The graph is reflected about the x-axis. Signup and view all the answers

What describes the rate of growth or decay in the function $y = ab^x$ when $b > 1$?

It grows exponentially. Signup and view all the answers

In the sine function $y = a imes ext{sin}( heta) + q$, what effect does $|a| > 1$ have?

It stretches the graph vertically. Signup and view all the answers

Which option best describes the domain of the exponential function $y = ab^x + q$?

It encompasses all real values of $x$. Signup and view all the answers

For the sine function, what are the specific x-intercepts within the interval $[0°, 360°]$?

At $0°, 180°, and 360°$. Signup and view all the answers

What is the maximum number of solutions a quadratic equation can have?

Two Signup and view all the answers

What is the first step in solving linear equations?

Expand all brackets Signup and view all the answers

When using substitution to solve simultaneous equations, what is typically done first?

Express one variable in terms of the other Signup and view all the answers

What method is commonly used to solve quadratic equations when they can be factored?

Factorisation Signup and view all the answers

What is a necessary condition for solving a quadratic equation effectively?

It must be balanced Signup and view all the answers

In solving simultaneous equations by elimination, what should be done to the coefficients of one variable?

They should be made the same Signup and view all the answers

What is the last step in solving a quadratic equation?

Check the solution Signup and view all the answers

Which process is used to reduce the number of unknown variables in simultaneous equations?

Substitution Signup and view all the answers

When rearranging an equation, what principle must always be followed?

Both sides must remain equal Signup and view all the answers

What distinguishes a linear equation from a quadratic equation?

Linear equations have one solution; quadratic can have two. Signup and view all the answers

What is the general formula for a linear sequence?

T_n = dn + c Signup and view all the answers

What effect does a positive value of 'm' have on the graph of a linear function?

The graph slopes upwards from left to right. Signup and view all the answers

What happens to a graph when the value of 'c' is negative?

The graph shifts vertically downward. Signup and view all the answers

How is the y-intercept of a linear function calculated?

By setting x = 0. Signup and view all the answers

What is the shape of the graph when 'a' in the equation y = ax^2 + q is greater than zero?

The graph is a parabola that opens upward. Signup and view all the answers

What defines the vertical shift of a parabola in the function y = ax^2 + q?

The value of 'q'. Signup and view all the answers

Which of these points is essential for sketching a straight-line graph using the gradient and y-intercept method?

Y-intercept. Signup and view all the answers

What would be the result of a negative value of 'a' in the equation y = ax^2 + q?

The graph opens downwards. Signup and view all the answers

What is the effect of varying the value of 'm' in a linear function's equation y = mx + c?

It affects the slope of the graph. Signup and view all the answers

What does the variable $q$ affect in the trigonometric functions?

Vertical shift of the function Signup and view all the answers

What is the primary difference between simple interest and compound interest?

Simple interest is calculated only on the principal amount. Signup and view all the answers

How is the y-intercept of a function calculated?

By setting $x = 0$ Signup and view all the answers

In the context of hire purchase agreements, how is interest calculated?

On the remaining balance after the deposit Signup and view all the answers

What does the interest rate represent in the formula for simple interest?

The percentage earned or paid per year Signup and view all the answers

How can the domain of a function be determined?

By identifying all possible $x$ values Signup and view all the answers

Which statement is true regarding inflation calculations?

It is calculated using the compound interest formula. Signup and view all the answers

What does a strong currency indicate about a country's economy?

Increased foreign investment Signup and view all the answers

Which formula is used for calculating the accumulated amount in simple interest?

$A = P(1 + in)$ Signup and view all the answers

What happens to interest in the context of compound interest over multiple periods?

It grows exponentially due to interest on interest. Signup and view all the answers

What is the theoretical probability of an event that occurs once in a total of 4 possible outcomes?

0.25 Signup and view all the answers

Given two events A and B that have partial overlap, the intersection of A and B represents what?

Elements in both A and B Signup and view all the answers

What happens to the relative frequency as the number of trials increases?

It tends to converge to theoretical probability Signup and view all the answers

Which formula would you use to convert an amount from dollars to euros if the exchange rate is 0.85 euros per dollar?

Amount in new currency = Amount in original currency / Exchange rate Signup and view all the answers

When is the probability of an event equal to 0?

When it is impossible for the event to occur Signup and view all the answers

Which statement about the union of two sets A and B is correct?

It includes all elements that are in either A or B Signup and view all the answers

If the probability of an event occurring is 0.5, what can be inferred about its outcomes?

It will occur half the time in a series of trials Signup and view all the answers

What is represented by a Venn diagram?

Relationships between different sets Signup and view all the answers

How is the relative frequency of an event defined in an experimental scenario?

The number of times the event occurs divided by the total trials Signup and view all the answers

What is the probability identity used to calculate the union of two events?

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) Signup and view all the answers

Which of the following statements is true about mutually exclusive events?

Their union equals the sum of their individual probabilities. Signup and view all the answers

What is the probability relationship for two mutually exclusive events A and B?

P(A ∪ B) = P(A) + P(B) Signup and view all the answers

Which of the following best defines the complement of a set A?

All elements that are not in A. Signup and view all the answers

Which statement is true about complementary events?

They are mutually exclusive events. Signup and view all the answers

What is the sum of the probabilities of an event A and its complement A'?

1 Signup and view all the answers

Which of the following correctly represents the intersection of event A and its complement A'?

P(A ∩ A') = 0 Signup and view all the answers

When combining events A and B, what happens if they are not mutually exclusive?

You subtract the intersection of A and B. Signup and view all the answers

In the context of Venn diagrams, what does the area where two events overlap represent?

The probability of both events occurring. Signup and view all the answers

Which of the following describes the relationship between the sample space S and the complement of event A?

A ∪ A' = S Signup and view all the answers

What happens to the graph of a parabola as the value of 'a' increases while 'a' is greater than 0?

The graph becomes narrower. Signup and view all the answers

What happens to the graph of a function when the value of 'a' is greater than 0?

The graph becomes narrower as 'a' approaches infinity. Signup and view all the answers

For the parabola defined by the equation $y = ax^2 + q$, what does the variable 'q' represent?

The vertical shift of the graph. Signup and view all the answers

How is the range of the function $y = ax^2 + q$ determined when 'a' is less than 0?

The range is from negative infinity to 'q'. Signup and view all the answers

What are the axes of symmetry for the parabolas in the form of $y = ax^2 + q$?

The line $x = 0$. Signup and view all the answers

What is true about the behavior of the graph of a hyperbolic function when 'a' is less than 0?

It lies in the second and fourth quadrants. Signup and view all the answers

What is true regarding the domain of the function $y = \frac{a}{x} + q$?

It includes all real numbers except x = 0. Signup and view all the answers

How do changes in the coefficient 'q' affect the hyperbolic function $y = \frac{a}{x} + q$?

They shift the graph vertically by 'q' units. Signup and view all the answers

What is the range of hyperbolic functions of the form $y = \frac{a}{x} + q$?

All real numbers except for 'q'. Signup and view all the answers

When finding the x-intercept of the function $y = ax^2 + q$, what condition must be satisfied?

Set 'y' equal to 0. Signup and view all the answers

How do the vertical asymptotes of the hyperbola behave?

The vertical asymptote is the line x = 0. Signup and view all the answers

What is the range of the function defined by the equation $y = a \cos \theta + q$ for $a > 0$?

[q - |a|, q + |a|] Signup and view all the answers

What is the period of the tangent function $y = a \tan \theta + q$?

180 Signup and view all the answers

What is the maximum number of solutions that a quadratic equation can have?

Two Signup and view all the answers

Which step is NOT part of solving linear equations?

Remember the Pythagorean theorem Signup and view all the answers

When solving simultaneous equations by substitution, what is the first action typically taken?

Express one variable in terms of the other Signup and view all the answers

What must always be true about an equation when performing operations on it?

Both sides must balance Signup and view all the answers

Which method can be used to solve quadratic equations?

Graphing Signup and view all the answers

In solving quadratic equations, when you factor into the form ((rx + s)(ux + v) = 0), what is the next step?

Find the roots Signup and view all the answers

Which statement best describes a linear equation?

It includes constants and can only have one solution Signup and view all the answers

What method can simplify solving simultaneous equations?

Elimination of a variable by equalizing coefficients Signup and view all the answers

What is the importance of checking the solution after solving an equation?

It ensures the values satisfy the original equation Signup and view all the answers

What is the result of applying the power of a power rule to the expression $(x^2)^3$?

x^6 Signup and view all the answers

What does the negative exponent rule state for the expression $a^{-m}$?

$rac{1}{a^m}$ Signup and view all the answers

In simplifying the expression $rac{a^{3/4}}{a^{1/2}}$, what is the simplified result?

a^{1/4} Signup and view all the answers

When raising a product to a power, what is the correct form of $(xy)^m$?

$x^m imes y^m$ Signup and view all the answers

What happens when solving the exponential equation $3^x = 3^4$?

$x = 4$ Signup and view all the answers

How can the expression $rac{(x^2y)^3}{x^4y^2}$ be simplified?

x^{-2}y^{3} Signup and view all the answers

What is the value of $a^0$ for any nonzero $a$?

1 Signup and view all the answers

What can be concluded when $x^2 = 16$?

$x = 4$ Signup and view all the answers

Which method can be used when the bases are different in an exponential equation?

Use logarithms Signup and view all the answers

Which of the following sets includes all positive integers starting from 1?

Natural Numbers (N) Signup and view all the answers

What is the primary distinction between whole numbers and natural numbers?

Whole numbers include zero. Signup and view all the answers

Which of the following is true about rational numbers?

They can be expressed as a fraction of two integers. Signup and view all the answers

Which numbers fall under the category of integers?

Whole numbers and their negative counterparts. Signup and view all the answers

What characterizes irrational numbers compared to rational numbers?

They cannot be expressed as a simple fraction. Signup and view all the answers

What is the correct set symbol for irrational numbers?

Q' Signup and view all the answers

Which of the following statements is true about real numbers?

Real numbers can be either positive or negative. Signup and view all the answers

What defines imaginary numbers?

They have a negative square root. Signup and view all the answers

What happens to the graph of a parabola as the value of $a$ increases beyond 1?

The graph gets narrower and stretches upward. Signup and view all the answers

For the standard form of a hyperbola $y = \frac{a}{x} + q$, which of the following describes the domain?

All real numbers except zero. Signup and view all the answers

What is the x-intercept of the function represented by the equation $y = \frac{a}{x} + q$?

It can be found by setting $y = 0$. Signup and view all the answers

If $a < 0$ in the equation $y = ax^2 + q$, what type of turning point does the graph have?

A maximum turning point. Signup and view all the answers

What characterizes the graph of a parabola when $q < 0$?

The turning point is below the x-axis. Signup and view all the answers

How does the value of $q$ affect a hyperbolic function's graph?

It shifts the graph vertically. Signup and view all the answers

What is the range of the function represented by $f(x) = ax^2 + q$ when $a > 0$?

[q, ∞) Signup and view all the answers

What type of shape does the graph exhibit when $a < 0$?

It resembles a parabola opening downwards. Signup and view all the answers

What is the axis of symmetry for the functions of the form $f(x) = ax^2 + q$?

The y-axis (line $x = 0$). Signup and view all the answers

What does the term 'variable' represent in algebra?

A symbol representing an unknown quantity. Signup and view all the answers

Which identity is used to factorise the sum of two cubes?

$x^3 + y^3 = (x + y)(x^2 + xy + y^2)$ Signup and view all the answers

Which of the following statements correctly describes a coefficient?

The numerical factor in a term. Signup and view all the answers

What is the first step when simplifying an algebraic fraction?

Factorise the numerator and the denominator. Signup and view all the answers

In the equation $a^m imes a^n$, what is the result according to the exponent laws?

$a^{m+n}$ Signup and view all the answers

What is the correct formulation for multiplying a monomial and a binomial?

$ax + ay$ Signup and view all the answers

When factorising a quadratic trinomial $ax^2 + bx + c$, what is the general first step?

Identify the values of a, b, and c. Signup and view all the answers

What is the formula for finding the difference of two squares?

$a^2 - b^2 = (a - b)(a + b)$ Signup and view all the answers

Which of these is a valid step in the process of factorisation by grouping?

Group terms that share a common factor. Signup and view all the answers

What distinguishes irrational numbers from rational numbers?

Irrational numbers have non-terminating, non-repeating decimal expansions. Signup and view all the answers

Which of the following correctly converts a terminating decimal into a rational number?

Using the formula: integer part + $rac{ ext{decimal digits}}{10^n}$ where $n$ is the position of the last digit. Signup and view all the answers

When rounding a decimal number, what should be done if the next digit is exactly 5?

Always round up the last digit in the required position. Signup and view all the answers

What is a key characteristic of surds?

Surds cannot be expressed as a simple fraction. Signup and view all the answers

Which of the following statements about the method of converting recurring decimals to rational numbers is correct?

You should multiply by a sufficiently high power of 10 to line up the repeating digits. Signup and view all the answers

Which expression best describes how to compare the sizes of two surds, $ oot{n}{a}$ and $ oot{n}{b}$?

$ oot{n}{a} > oot{n}{b}$ if $a > b$. Signup and view all the answers

What method is typically used to multiply a monomial by a binomial?

Distribute the monomial across each term in the binomial. Signup and view all the answers

What is the primary purpose of estimating surds?

To determine bounds using perfect squares or cubes. Signup and view all the answers

In which scenario would a number like $rac{1}{3}$ be considered irrational?

When approximated to two decimal places. Signup and view all the answers

What is the key characteristic of the horizontal asymptote for the function of the form $y = ab^x + q$?

It is given by the equation $y = q$. Signup and view all the answers

For the function $y = rac{a}{x} + q$, how is the x-intercept calculated?

By letting $y = 0$ and solving for $x$. Signup and view all the answers

What determines whether a graph of $y = ab^x + q$ curves upwards or downwards?

The sign of $a$. Signup and view all the answers

What is the range of an exponential function $y = ab^x + q$ when $a > 0$?

$orall y : y > q$. Signup and view all the answers

Which of the following statements about the domain of the function $y = a an heta + q$ is accurate?

The domain includes all real numbers except where the function is undefined. Signup and view all the answers

What does the parameter $q$ affect in the function $y = a an heta + q$?

The vertical shift of the graph. Signup and view all the answers

Which statement is true about the characteristics of the sine function $y = rac{1}{2} an heta + q$?

Its y-intercept varies with $q$. Signup and view all the answers

In the context of trigonometric functions, what is typically the y-intercept of the cosine function $y = rac{3}{2} an heta + q$?

At $(0°, 1)$. Signup and view all the answers

What does the sign of $b$ signify in an exponential function of the form $y = ab^x + q$?

The direction of exponential growth or decay. Signup and view all the answers

What effect does having $|a| > 1$ in the function $y = a an heta + q$ have on the graph?

It stretches the graph vertically. Signup and view all the answers

What effect does the parameter $q$ have in trigonometric functions such as sine, cosine, and tangent?

It determines the vertical shift of the function. Signup and view all the answers

Which formula is used to calculate accumulated amount in simple interest?

$A = P (1 + in)$ Signup and view all the answers

How does compound interest differ from simple interest?

Compound interest is earned on both the principal and accumulated interest. Signup and view all the answers

What is the main characteristic of a hire purchase agreement?

It involves paying for a product in installments with simple interest on the remaining amount. Signup and view all the answers

Which factors contribute to the strength of a currency?

Increasing investments in the country. Signup and view all the answers

What does the range of a function represent?

The set of all outputs that the function can produce. Signup and view all the answers

How is inflation measured in terms of price increases over time?

Using the compound interest formula. Signup and view all the answers

Which of the following formulas is applied in population growth calculations?

$A = P(1 + i)^n$ Signup and view all the answers

What defines the domain of a function?

The set of all values that can be inputted into the function. Signup and view all the answers

In the context of finance, what does the term 'principal' refer to?

The initial amount of money invested or borrowed. Signup and view all the answers

What does the variable $c$ represent in the equation of a linear function $y = mx + c$?

The y-intercept of the graph Signup and view all the answers

What is the effect of a negative value of $m$ in the equation $y = mx + c$?

The graph slopes downwards from left to right Signup and view all the answers

In the context of a linear sequence, what is a common difference?

The constant difference between successive terms Signup and view all the answers

How does an increase in the value of $c$ affect the graph of a linear function?

The graph shifts vertically upwards Signup and view all the answers

What characteristic of the graph is determined by the value of $a$ in the equation of the form $y = ax^2 + q$?

The direction in which the parabola opens Signup and view all the answers

Which of the following methods is used to determine the graph of $y = mx + c$?

Calculating and plotting both the x-intercept and y-intercept. Signup and view all the answers

What is the domain and range of a linear function $f(x) = mx + c$?

Domain: all real numbers, Range: all real numbers Signup and view all the answers

What is the effect of the value of $q$ in a parabolic function $y = ax^2 + q$?

It shifts the graph vertically up or down. Signup and view all the answers

What do you calculate to find the x-intercept of a linear function?

Set $y = 0$ and solve for $x$ Signup and view all the answers

In which scenario will a parabola open upwards?

When $a > 0$ Signup and view all the answers

What is the formula for converting an amount from one currency to another?

Amount in new currency = Amount in original currency / Exchange rate Signup and view all the answers

If an event has a probability of 0, what does it indicate about the event?

The event will never occur Signup and view all the answers

In the context of probability, what does the ratio $P(E) = \frac{n(E)}{n(S)}$ represent?

The likelihood of event E occurring Signup and view all the answers

What does a probability of 0.5 indicate about an event?

The event will occur half the time Signup and view all the answers

What is a Venn diagram primarily used for in probability?

To illustrate the relationships between different sets Signup and view all the answers

What does the term 'union' denote in set theory?

Elements in at least one of the sets Signup and view all the answers

Relative frequency provides what type of probability?

Empirical probability Signup and view all the answers

If two events A and B have no overlap, what can be said about their intersection?

A ∩ B is empty Signup and view all the answers

As the number of trials increases, relative frequency tends to approach which form of probability?

Theoretical probability Signup and view all the answers

What does a probability of 1 indicate about an event?

The event will always occur Signup and view all the answers

What is the range of the function defined by the equation $y = a \cos \theta + q$ for $a > 0$?

[q - |a|, q + |a|] Signup and view all the answers

What is the period of the cosine and sine functions?

360° Signup and view all the answers

What is the range of the tangent function $y = \tan \theta$?

[f(\theta) : f(\theta) \in \mathbb{R}] Signup and view all the answers

How does changing the value of $q$ in the equation $y = a \tan \theta + q$ affect the graph?

It shifts the graph vertically. Signup and view all the answers

To find the equation of a parabola, which point is specifically used to calculate the value of $q$?

The y-intercept. Signup and view all the answers

What effect does changing the value of $a$ have on the graph of the function $y = \frac{a}{x} + q$?

It stretches or compresses the branches. Signup and view all the answers

What are the x-intercepts of the tangent function $y = \tan \theta$?

(0°, 0), (180°, 0), (360°, 0) Signup and view all the answers

What are the asymptotes of the tangent function defined by $y = \tan \theta$?

At $\theta = 90°$ and $\theta = 270°$ Signup and view all the answers

What defines the direction in which a parabola opens?

The sign of $a$. Signup and view all the answers

Which statement accurately reflects the relationship between sine and cosine functions?

The cosine graph can be shifted left by 90° to overlap with the sine graph. Signup and view all the answers

What is the correct expression to calculate the probability of the union of two events?

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) Signup and view all the answers

What defines mutually exclusive events?

Events that cannot occur at the same time. Signup and view all the answers

Which statement is true regarding the probabilities of complementary events?

P(A) + P(A') = P(S) Signup and view all the answers

In a Venn diagram, which representation indicates mutually exclusive events?

Two circles that do not touch. Signup and view all the answers

What is the intersection of two mutually exclusive events?

The empty set. Signup and view all the answers

How can the probability of the union of two mutually exclusive events be calculated?

By adding their individual probabilities. Signup and view all the answers

What is the complement of event A as represented?

All outcomes not in event A. Signup and view all the answers

What does the identity P(A) + P(A') = 1 signify?

The combined probability of complementary events. Signup and view all the answers

What happens if you add the probabilities of events A and B without recognizing their intersection?

You double-count the intersection area. Signup and view all the answers

What is indicated by the notation P(A ∩ B) = ∅?

Events A and B are mutually exclusive. Signup and view all the answers

What do the coordinates of the intersection point represent in a system of linear equations?

The solution to the system of equations Signup and view all the answers

Which of the following is a key step in solving word problems mathematically?

Assigning variables to unknown quantities Signup and view all the answers

What is the result when multiplying both sides of an inequality by a negative number?

The inequality must be switched Signup and view all the answers

In the formula for a linear sequence, what does the term $c$ represent?

The constant term Signup and view all the answers

Which principle is essential for isolating an unknown variable in a literal equation?

Performing the same operation to both sides Signup and view all the answers

What is the common difference in a linear sequence denoted by?

d Signup and view all the answers

How is the common difference $d$ calculated in a sequence?

By subtracting $T_{n-1}$ from $T_n$ Signup and view all the answers

When changing a literal equation to isolate a variable in the denominator, what operation is usually performed?

Multiply both sides by the lowest common denominator Signup and view all the answers

Which of the following sequences is classified as a linear sequence?

2, 4, 6, 8 Signup and view all the answers

What characterizes surds?

They are the n-th root of numbers that cannot simplify to rational numbers. Signup and view all the answers

When converting a recurring decimal to a rational number, what is the first step?

Multiply by a power of 10 before defining the recurring pattern. Signup and view all the answers

How can rounding off an irrational number be interpreted?

As obtaining a rational approximation. Signup and view all the answers

Which of the following describes the nature of rational numbers?

They encompass variations of both terminating and repeating decimals. Signup and view all the answers

In the context of estimating surds, what is the role of identifying perfect powers?

It provides boundaries for comparison to better estimate the value. Signup and view all the answers

What type of decimal numbers qualify as rational numbers?

Only repeating and terminating decimals. Signup and view all the answers

What happens if the digit to be rounded in a decimal is 9?

It converts to 0 and increases the previous digit by one. Signup and view all the answers

Which statement best describes the procedure for multiplying a monomial by a binomial?

You distribute the monomial across both terms of the binomial. Signup and view all the answers

What does the expression $(ax + b)(cx + d)$ expand to?

$acx^2 + (ad + bc)x + bd$ Signup and view all the answers

Which statement accurately describes the set of rational numbers?

They can be expressed as a quotient of two integers. Signup and view all the answers

What distinguishes irrational numbers from rational numbers?

Irrational numbers have non-terminating decimal expansions. Signup and view all the answers

Which of the following numbers is classified as a natural number?

7 Signup and view all the answers

In the context of the real number system, which of the following subsets contains negative values?

Integers Signup and view all the answers

Which example best represents an irrational number?

√2 Signup and view all the answers

What is the relationship between rational numbers and real numbers?

All rational numbers are also real numbers. Signup and view all the answers

Which of the following statements about imaginary numbers is true?

They are defined as numbers with negative square roots. Signup and view all the answers

What is the complete set of real numbers represented by?

R Signup and view all the answers

What is the result of applying the power of a power rule to the expression $(x^3)^4$?

$x^{12}$ Signup and view all the answers

If $a^m = 2$ and $a^n = 8$ for positive values of $a$, what is the relationship between $m$ and $n$?

$m = n/3$ Signup and view all the answers

How would you simplify the expression $rac{a^{5/2}}{a^{3/2}}$ using the laws of exponents?

$a^{1/2}$ Signup and view all the answers

What does the expression $(rac{2}{3})^{2/3}$ simplify to?

$rac{2^{2/3}}{3^{2/3}}$ Signup and view all the answers

If $a > 0$ and $a^{-2}$ is present in an expression, how is it equivalently expressed?

$rac{1}{a^2}$ Signup and view all the answers

In solving the equation $3^x = 27$, which method would you use to isolate $x$?

Equating exponents Signup and view all the answers

What is the equivalent expression for $(ab)^{3/4}$?

$a^{3/4}b^{3/4}$ Signup and view all the answers

Which of the following is NOT a correct application of the zero exponent rule?

$0^0 = 0$ Signup and view all the answers

When simplifying the expression $(x^4y^2)^3$, which step is first?

Use the power of a power rule Signup and view all the answers

Which statement best describes how to handle a negative exponent in the expression $a^{-3}$?

It becomes $rac{1}{a^3}$ Signup and view all the answers

What do the coordinates of the intersection point of two linear equations represent?

The solution to the system of equations Signup and view all the answers

In the equation $v = \frac{D}{t}$, what does $D$ represent?

Distance Signup and view all the answers

What is the common difference in the linear sequence defined by $T_n = 3n + 5$?

3 Signup and view all the answers

When converting the equation $4x - 2 > 10$ into an inequality solution, what is the first step?

Add 2 to both sides Signup and view all the answers

In the context of solving literal equations, what does 'changing the subject of the formula' mean?

Isolating any variable in the formula Signup and view all the answers

When solving the inequality $2 - x \geq 3$, what is the resulting inequality after isolation of $x$?

x \leq -1 Signup and view all the answers

In a linear sequence, if $d$ is not positive, what can we conclude about the sequence?

The terms are decreasing Signup and view all the answers

How do you find the value of $d$ in a linear sequence defined by the general term $T_n = 7n - 2$?

By identifying the coefficient of $n$ Signup and view all the answers

If the linear equation $y = 3x + 2$ intersects the x-axis at a certain point, what is the x-coordinate of that point?

-2/3 Signup and view all the answers

What is the maximum number of solutions a quadratic equation can possess?

2 Signup and view all the answers

Which step is essential to verify the accuracy of a solution in both linear and quadratic equations?

Substituting the solution back into the original equation Signup and view all the answers

What process is employed to eliminate a variable when solving simultaneous equations?

Elimination Signup and view all the answers

When rearranging terms in a linear equation, what is primarily moved to one side?

All variables Signup and view all the answers

Which of the following statements is true regarding the factorisation of a quadratic equation?

It can sometimes yield a single repeated factor. Signup and view all the answers

In the method for solving linear equations, what is the purpose of expanding all brackets?

To simplify both sides of the equation Signup and view all the answers

What is the first step when using the substitution method for solving simultaneous equations?

Isolating one variable in equation Signup and view all the answers

What must be true about the balance of an equation when performing operations?

Both sides must be altered equally Signup and view all the answers

In what scenario can a quadratic equation have no real solutions?

When the discriminant is negative Signup and view all the answers

What does the term 'factorisation' refer to in algebra?

Breaking down an expression into simpler expressions that multiply to give the original. Signup and view all the answers

Which of the following represents the correct expansion of the product of a binomial and a trinomial?

A(C + D + E) + B(C + D + E) Signup and view all the answers

When simplifying the fraction $rac{a}{b} + rac{c}{b}$, what is the simplest form of the expression?

$rac{a + c}{b}$ Signup and view all the answers

Which equation correctly represents the factorisation of a difference of squares?

$a^2 - b^2 = (a + b)(a - b)$ Signup and view all the answers

What is the first step in the general procedure for factorising a trinomial of the form $ax^2 + bx + c$?

Identify any common factors. Signup and view all the answers

Which identity is used for factorising the sum of two cubes?

$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$ Signup and view all the answers

When multiplying two binomials, which form does the result take?

$acx^2 + (ad + bc)x + bd$ Signup and view all the answers

What is the resulting form of the difference of two cubes represented by the expression $x^3 - y^3$?

$(x - y)(x^2 - xy + y^2)$ Signup and view all the answers

In the operation of multiplying a binomial by a trinomial, what does each term of the binomial get multiplied by?

Each term of the trinomial. Signup and view all the answers

What represents the y-intercept in a linear equation of the form $y = mx + c$?

It is the point where the graph crosses the y-axis. Signup and view all the answers

How does the value of $m$ affect the graph of a linear function?

It determines the slope and direction of the graph. Signup and view all the answers

In the quadratic function $y = ax^2 + q$, what aspect of the graph is significantly influenced by the value of $q$?

The vertical position of the turning point. Signup and view all the answers

What does a negative value for $a$ in the quadratic function $y = ax^2 + q$ indicate about the graph?

The graph opens downwards, producing a maximum turning point. Signup and view all the answers

What is the domain of linear functions represented by $f(x) = mx + c$?

All real numbers. Signup and view all the answers

What role does the y-intercept ($c$) play when $c < 0$ in the graph of a linear function?

It shifts the entire graph downwards. Signup and view all the answers

What are the three characteristics needed to sketch the graph of a linear function $f(x) = mx + c$?

The sign of $m$, the y-intercept, and the x-intercept. Signup and view all the answers

What is the defining characteristic of a linear sequence?

The elements change at a constant rate. Signup and view all the answers

In the equation $m = \frac{\text{change in } y}{\text{change in } x}$, what does $m$ represent?

The rate of change of the function. Signup and view all the answers

What happens to the graph of a parabola when the value of $a$ is decreased while being less than zero?

The graph becomes wider as it approaches zero. Signup and view all the answers

How does the function $y = ax^2 + q$ behave when $a$ is positive?

The graph is a parabola that opens upwards with a minimum turning point. Signup and view all the answers

Which statement accurately describes the domain and range for the hyperbolic function $y = \frac{a}{x} + q$?

Domain: all real numbers except for $0$; Range: all values except for $q$. Signup and view all the answers

What is the effect of choosing $q$ to be less than zero in the hyperbola $y = \frac{a}{x} + q$?

The graph shifts vertically downwards by $|q|$ units. Signup and view all the answers

What characteristic of the parabola is defined by the value of $q$?

It sets the vertical shift of the graph. Signup and view all the answers

Which statement is true about the turning points of the graph $y = ax^2 + q$ when $a < 0$?

The maximum turning point occurs at $(0, q)$. Signup and view all the answers

What happens to the hyperbolic graph's shape when $a$ is negative?

The graph lies in the second and fourth quadrants. Signup and view all the answers

What is the result of evaluating the x-intercept for the function $y = \frac{a}{x} + q$?

It can be found by setting $y$ equal to $0$. Signup and view all the answers

Which statement about the axes of symmetry of the parabolic function $y = ax^2 + q$ is correct?

The axis of symmetry is always at the line $x = 0$. Signup and view all the answers

What is the range of the cosine function expressed in terms of parameters a and q?

[q - |a|, q + |a|] Signup and view all the answers

For the tangent function, what are the specified asymptotes within the range of 0° to 360°?

theta = 90° and theta = 270° Signup and view all the answers

In the context of the parabola, what does a negative value of a indicate?

The parabola opens downward. Signup and view all the answers

When determining the equation of a hyperbola, what is the first step in the process?

Examine the sketch to determine the sign of a. Signup and view all the answers

If q in the tangent function is greater than 0, what effect does this have on the graph?

The graph shifts upward by q units. Signup and view all the answers

What does the process of calculating intercepts involve for parabolas and lines?

Setting y to 0 to find x-intercepts and x to 0 for the y-intercept. Signup and view all the answers

How do the graphs of sine and cosine functions relate to each other?

The cosine graph can be achieved by shifting the sine graph to the left by 90°. Signup and view all the answers

What primary factor influences the steepness of the branches in the tangent function?

The value of a. Signup and view all the answers

What is the period of the tangent function?

180° Signup and view all the answers

What does a probability of 0 indicate about an event?

The event is impossible. Signup and view all the answers

When describing probability as a fraction, which represents a probability of 0.5?

$rac{1}{2}$ Signup and view all the answers

Which formula correctly defines the theoretical probability of an event?

$P(E) = rac{n(E)}{n(S)}$ Signup and view all the answers

How does relative frequency differ from theoretical probability?

It is determined through experimental trials. Signup and view all the answers

In relation to Venn diagrams, which of the following correctly represents 'A and B'?

A ∩ B Signup and view all the answers

What is represented by a probability that approaches 1 as more trials are conducted?

The relative frequency is becoming constant. Signup and view all the answers

Which of the following statements about union and intersection is incorrect?

Union is always a subset of both sets. Signup and view all the answers

Which of the following situations describes 'complete containment' in the context of Venn diagrams?

Set B contains all elements of A. Signup and view all the answers

What is the range of values for probability?

From 0 to 1 Signup and view all the answers

When calculating the amount in a new currency, which component clearly indicates the conversion involved?

Divide the amount in the original currency by the exchange rate. Signup and view all the answers

How does the variable $q$ affect the sine function $y = a an \theta + q$?

It determines the vertical shift of the graph. Signup and view all the answers

What characterizes the difference between simple interest and compound interest?

Compound interest is calculated on both the principal and the accumulated interest. Signup and view all the answers

In the context of hyperbolas, how can asymptotes be identified?

By finding the values that make the denominator equal to zero. Signup and view all the answers

Which formula accurately represents the accumulated amount with simple interest?

$A = P(1 + in)$ Signup and view all the answers

What is the defining characteristic of the population growth formula compared to simple interest?

It uses the same compound interest formula as for financial contexts. Signup and view all the answers

What component is crucial in determining the vertical shift of the cosine function?

The constant $q$. Signup and view all the answers

When calculating the accumulated amount from inflation, which variable plays the same role as the principal in other financial contexts?

$P$, signifying the current price. Signup and view all the answers

What is a key factor that distinguishes a hire purchase agreement from other loan types?

Simple interest is applied on the remaining balance. Signup and view all the answers

What effect does an increase in the interest rate have on the accumulated amount for both simple and compound interest?

It increases the final amount for both simple and compound interest. Signup and view all the answers

Which statement best describes the impact of foreign exchange rates on international trade?

They can either inflate or deflate international prices. Signup and view all the answers

What is the probability relationship for mutually exclusive events?

P(A ∪ B) = P(A) + P(B) Signup and view all the answers

In a Venn diagram representing two events A and B, which area corresponds to the probability of their intersection?

Only the overlapping area of A and B Signup and view all the answers

If event A has a probability of 0.4, what must the probability of its complement A' be?

0.6 Signup and view all the answers

Which identity correctly expresses the relationship between the probabilities of complementary events?

P(A) + P(A') = 1 Signup and view all the answers

Which statement correctly describes mutually exclusive events?

They cannot have any outcomes in common. Signup and view all the answers

Which of the following statements about the probability of unions of two events is true?

P(A ∪ B) requires knowing P(A ∩ B) to avoid double counting. Signup and view all the answers

In the context of unions and intersections, what does the notation P(A ∩ B) represent?

The probability that both A and B occur simultaneously Signup and view all the answers

What does the symbol P(S) signify in probability theory?

The probability of the sample space Signup and view all the answers

What is one consequence of events A and B being mutually exclusive?

P(A ∪ B) = P(A) + P(B) Signup and view all the answers

What does the sign of the constant $a$ determine in the graph of the function $y = ab^x + q$?

The direction of the curve of the graph Signup and view all the answers

In the function $y = ab^x + q$, what is the impact of $b$ when $b > 1$?

The function represents exponential growth Signup and view all the answers

What is the range of the function $y = a ext{sin}( heta) + q$ when $a < 0$ and $q = 2$?

[2 - |a|, 2] Signup and view all the answers

For the sine and cosine functions, how do their y-intercepts differ at $x = 0$?

Sine has a y-intercept of 0, while cosine has 1 Signup and view all the answers

What defines the period of the sine and cosine functions?

The interval over which the function repeats Signup and view all the answers

Which characteristic is specific to the x-intercepts of the sine function?

They are located at specific multiples of $180°$ Signup and view all the answers

What effect does a negative value of $a$ have on a function of the form $y = a ext{cos}( heta) + q$?

It reflects the graph about the x-axis Signup and view all the answers

What is the domain restriction for the sine function described?

$[0°, 360°]$ Signup and view all the answers

How is the y-intercept of the exponential function defined mathematically?

$y = ab^0 + q$ Signup and view all the answers

In the context of exponential functions, what happens to the graph when $q < 0$?

The graph shifts down by $q$ units Signup and view all the answers

Gr 10 Math Nov P1 Mix

Questions and Answers

Which of the following sets includes only non-negative numbers?

What is the correct symbol for the set of whole numbers?

Which of the following numbers is considered irrational?

Which statement about integers is true?

Which subset of real numbers can be represented as a fraction?

What characterizes irrational numbers?

What is the symbol for rational numbers?

Which of the following numbers is classified as imaginary?

What is the product of the binomial extit{(A + B)} and the trinomial extit{(C + D + E)}?

Which of the following describes a constant in algebra?

What is the formula for multiplying two binomials extit{(ax + b)(cx + d)}?

What is the identity used for factorising the difference of two squares?

Which of the following correctly simplifies the expression extit{a/b × c/d}?

What does the term 'exponent' refer to?

Which process involves grouping terms with common factors?

In the context of equations, what does it mean for two expressions to be equal?

What is the first step in simplifying an algebraic fraction?

What is the resulting form of the difference of two cubes, represented by extit{x^3 - y^3}?

Which statement best defines an irrational number?

What is the first step in converting a terminating decimal into a rational number?

When rounding a number, if the digit after the required decimal place is less than 5, what should be done?

Which expression represents the process of multiplying two linear binomials?

What type of number is \sqrt{4}?

How can an irrational number be represented more simply?

What is the correct definition of a binomial?

What should you identify first when estimating surds?

Which of the following is an example of a terminating decimal?

What do you call the numerical factor in a term?

What is one method used to solve linear equations?

How many solutions can a linear equation have?

Which is true about quadratic equations?

What is the first step in solving simultaneous equations using substitution?

What is a necessary condition for solving quadratic equations effectively?

Which of the following is not a step in the method for solving quadratic equations?

When solving by elimination, what is the first step?

What does it mean if a quadratic equation has no solutions?

Which step involves ensuring the quadratic is in the correct form?

Which of the following is true regarding solving equations?

What does the solution of a system of simultaneous linear equations represent?

Which step is NOT part of the problem solving strategy for word problems?

What is a literal equation?

When solving the inequality $2x + 2 e 1$, what happens if both sides are multiplied by -1?

In the formula for a linear sequence $T_n = dn + c$, what does the variable $d$ represent?

To find the common difference $d$ in a sequence, you calculate $T_n - T_{n-1}$. What does $T_n$ denote?

When rearranging a literal equation to isolate an unknown variable, which principle is applied?

What is the primary method used to solve linear inequalities?

What term describes an ordered list of items, usually numbers?

What is the result of $(a^m)^n$ according to the power of a power rule?

In the equation $v = \frac{D}{t}$, what does $v$ represent?

Which expression is equivalent to $a^{m/n} \times a^{p/q}$ using the multiplication of exponents rule?

If $a^{m/n} = a^{p/q}$, what does it imply if the bases are the same?

What is a linear sequence defined by?

Which of the following represents the zero exponent law?

What is the simplified form of $ rac{a^m}{a^n}$ using the division of exponents rule?

What does the constant 'm' represent in the equation of a straight line?

Which method is typically used to solve exponential equations when bases cannot easily be made the same?

How does the value of 'c' affect a straight line graph?

What is the domain of a linear function of the form y = mx + c?

When simplifying $\left(\frac{a}{b}\right)^n$, which exponent law is applied?

How do you calculate the y-intercept of a straight-line graph?

Which expression represents the prime factorization of an exponential expression?

What effect does a positive value of 'a' have on a parabola?

What does a negative exponent indicate for a number $a$?

When rewriting an expression with fractional exponents like $\sqrt[n]{a}$, what is the correct conversion?

What happens to the graph of the function y = ax^2 + q when q < 0?

What kind of points are needed to sketch a straight-line graph effectively?

What is the range of a linear function of the form f(x) = mx + c?

What occurs when 'm' is set to 0 in the equation of a straight line?

What happens to the graph of a parabola as the value of $a$ increases beyond 1?

For which value of $a$ will the graph of the parabola open downwards?

Where is the y-intercept of the function $y = ax^2 + q$ calculated?

If $q < 0$, what can be concluded about the range of the parabola when $a > 0$?

In the function $y = rac{a}{x} + q$, what is the domain of the function?

Which statement accurately describes the turning point of the quadratic function $f(x) = ax^2 + q$ when $a < 0$?

How is the horizontal asymptote defined in the hyperbolic function $y = rac{a}{x} + q$?

What effect does a negative value of $a$ have on the hyperbola $y = rac{a}{x} + q$?

Which of the following best describes the axis of symmetry for the function $f(x) = ax^2 + q$?

What does the parameter $q$ determine in trigonometric functions?

What is the simplified form of $rac{a^m}{a^n}$ using the division of exponents rule?

What type of number is represented by the symbol $rac{-5}{2}$?