Gr 10 Math Nov P1 Easy

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Which set of numbers includes all positive integers starting from 1?

Natural Numbers (correct)

Rational Numbers

Integers

Whole Numbers

What distinguishes whole numbers from natural numbers?

Whole numbers include fractions

Whole numbers include negative numbers

Whole numbers include zero (correct)

Whole numbers start from negative integers

Which of the following is an example of an irrational number?

0.75

π (correct)

−3

2

Which symbol represents the set of integers?

Z Signup and view all the answers

Rational numbers can be expressed in which form?

Fractions of two integers Signup and view all the answers

Which of the following best describes irrational numbers?

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

What is the definition of imaginary numbers?

Numbers that have negative square roots Signup and view all the answers

Which subset of the real number system includes rational and irrational numbers?

Real Numbers Signup and view all the answers

Which statement correctly describes irrational numbers?

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

How would you convert the terminating decimal 0.75 into a rational number?

0.75 is represented as $\frac{3}{4}$. Signup and view all the answers

What is a key characteristic of a recurring decimal?

It can be expressed as a fraction with a sequence of repeating digits. Signup and view all the answers

Which of the following is an example of a surd?

$\sqrt{2}$ Signup and view all the answers

What is the first step in rounding off a decimal number?

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

What is a monomial?

A mathematical expression consisting of a single term. Signup and view all the answers

In multiplying two binomials, what is the correct resulting form?

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

What is the role of coefficients in a mathematical expression?

They represent the numerical factor of terms. Signup and view all the answers

Which of the following correctly identifies a term in an expression?

A constant combined with a variable. Signup and view all the answers

What can be concluded about non-terminating decimals?

Non-terminating decimals can only be irrational numbers. Signup and view all the answers

What is the result of multiplying the binomial extit{(A + B)} by 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 mathematical terms?

A numerical value without a variable Signup and view all the answers

What identity is used to factor a difference of two squares?

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

Which operation is used for simplifying the fraction rac{a}{b} imes rac{c}{d}?

Multiply numerators and denominators together Signup and view all the answers

In the expression extit{(ax + b)(cx + d)}, what does the term extit{acx^2} represent?

The leading term in the product Signup and view all the answers

What is the first step in the general procedure for factorising a trinomial?

Identify any common factors Signup and view all the answers

For the sum of two cubes, which of the following is the correct factorization?

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

What does the term 'equation' refer to in mathematics?

A statement that two expressions are equal Signup and view all the answers

Which law states that $a^m \times a^n = a^{m+n}$?

Product of Exponents Law Signup and view all the answers

What is the outcome when you simplify the algebraic fraction rac{2x^2}{4x}?

x Signup and view all the answers

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

One solution Signup and view all the answers

Which of the following is NOT a step in solving linear equations?

Divide by common factors Signup and view all the answers

What is the form of a standard quadratic equation?

ax^2 + bx + c = 0 Signup and view all the answers

How can solutions for simultaneous equations be found using substitution?

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

Which method in solving simultaneous equations involves eliminating one variable by adjusting coefficients?

Elimination Signup and view all the answers

What characteristic distinguishes quadratic equations from linear equations?

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

Which of the following is a necessary step after factoring a quadratic equation?

Set each factor equal to zero Signup and view all the answers

In solving an equation, what must always be maintained?

The equality of both sides of the equation Signup and view all the answers

Which approach can also be used to solve simultaneous equations apart from algebraic methods?

Graphical method Signup and view all the answers

What is the result of applying the zero exponent rule?

Any base raised to the power of zero equals one. Signup and view all the answers

Which property is used to simplify the expression rac{a^m}{a^n}?

Division of Exponents with the Same Base Signup and view all the answers

What happens to the number of equations when solving for two unknown variables?

You need two equations Signup and view all the answers

What form is used to express the equation if both sides are equal with the same base?

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

How can you simplify a complex fraction with exponential terms?

By changing all terms to prime bases and cancelling common terms. Signup and view all the answers

Which of the following best describes rational exponents?

They represent roots and can be expressed as fractions. Signup and view all the answers

What does the property (ab)^n = a^n b^n illustrate?

Raising a Product to a Power Signup and view all the answers

Which step should be taken first when solving an exponential equation using logarithms?

Convert the exponential equation to a logarithmic form. Signup and view all the answers

When simplifying the expression a^{m/n}, what should you do if m and n share a common factor?

Factor out the common factor in both m and n. Signup and view all the answers

What is the result of (a^{m/n})^{p/q}?

a^{mp/nq} Signup and view all the answers

How do you express a negative exponent, such as a^{-n}?

As 1/a^n. Signup and view all the answers

What do the coordinates of the solution represent in a system of simultaneous equations?

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

Which of the following is the first step when solving a word problem?

Determine what we are asked to solve for Signup and view all the answers

How do you isolate an unknown variable in a literal equation?

By asking how it is linked to other variables Signup and view all the answers

What is the key difference when solving linear inequalities compared to linear equations?

The inequality sign is flipped when multiplying or dividing by a negative Signup and view all the answers

What does the term 'common difference' refer to in a linear sequence?

The difference between any term and the term before it Signup and view all the answers

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

The common difference between terms Signup and view all the answers

What method would you use to solve a literal equation involving a variable in the denominator?

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

What does the general term $T_n$ indicate in a sequence?

Any specific term in the sequence Signup and view all the answers

Which of the following describes a linear inequality?

The largest exponent of a variable is 1 Signup and view all the answers

What do we do to verify the solution to an equation after solving it?

Substitute it back into the original equation Signup and view all the answers

What occurs to the graph of a function as the value of 'a' increases when 'a' is greater than zero?

The graph becomes narrower. Signup and view all the answers

What is the range of a parabolic function when 'a' is less than zero?

(−∞; q] Signup and view all the answers

What shape does the graph of a function take when 'a' is less than zero?

Frown. Signup and view all the answers

For the function of the form y = ax^2 + q, where is the axis of symmetry located?

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

What is the y-intercept for the function y = ax^2 + q?

q Signup and view all the answers

What kind of asymptote does the hyperbolic function y = a/x + q have horizontally?

y = q Signup and view all the answers

What happens to the graph of a hyperbolic function as the value of 'a' becomes negative?

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

What is true about the range of the hyperbolic function y = a/x + q?

It excludes q. Signup and view all the answers

How is the y-intercept determined for the function y = a/x + q?

The function does not have a y-intercept. Signup and view all the answers

What does a positive value of 'q' do to the graph of the hyperbola y = a/x + q?

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

What is the formula used to calculate the amount in a new currency?

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

What does a probability of 0.5 signify?

The event occurs half the time, or 1 time out of every 2 Signup and view all the answers

Which of the following describes relative frequency?

The number of occurrences of an event compared to the total number of trials Signup and view all the answers

In a Venn diagram, what does the union of two sets represent?

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

What does the intersection of two sets contain?

Elements that are in both set A and set B Signup and view all the answers

How is probability defined?

It is a real number between 0 and 1 Signup and view all the answers

What does a probability of 1 imply?

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

What is the result of conducting more trials in an experiment regarding relative frequency?

It tends to get closer to theoretical probability Signup and view all the answers

Which of the following accurately describes a Venn diagram?

A graphical representation of relationships between sets Signup and view all the answers

What does the symbol $P(A igcup B)$ represent?

The probability of the union of events A and B Signup and view all the answers

What is a necessary condition for two events to be considered mutually exclusive?

Their intersection is the empty set Signup and view all the answers

What is the key characteristic of the vertical asymptote for the function of the form $y = \frac{a}{x} + q$?

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

What effect does a positive value of $q$ have on the graph of an exponential function $y = ab^x + q$?

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

What is the correct formula for the probability of the union of two mutually exclusive events?

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

How do you find the y-intercept of the function $y = ab^x + q$?

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

What is the complement of an event A denoted as?

A' Signup and view all the answers

What statement correctly identifies the relationship between an event and its complement?

Their union equals the sample space Signup and view all the answers

What determines whether the graph of an exponential function curves upwards or downwards?

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

In the sine function $y = a \sin \theta + q$, what does a negative value for $a$ indicate?

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

If event A occurs, what is the probability of event A not occurring?

$1 - P(A)$ Signup and view all the answers

Which of the following can be concluded about the probabilities of any event and its complement?

They add up to 1 Signup and view all the answers

What is the range of the sine function $y = \sin \theta$?

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

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

Their intersection is empty Signup and view all the answers

For an exponential function where $b > 1$, what type of growth does it represent?

Exponential growth. Signup and view all the answers

What is the common difference in a linear sequence?

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

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

It determines the y-intercept of the graph Signup and view all the answers

What does the expression $P(A igcup A')$ equal?

$P(S)$ Signup and view all the answers

Which statement is true about the domain of the sine function $y = a \sin \theta + q$?

The domain is $[0°; 360°]$. Signup and view all the answers

What is the x-intercept of the cosine function $y = \cos \theta$?

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

Which statement is true regarding a linear function when 'm' is positive?

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

Which visual representation best depicts mutually exclusive events?

Two separate, non-overlapping circles Signup and view all the answers

What is the domain of the function represented by the equation 'y = mx + c'?

All real numbers for x Signup and view all the answers

What characterizes the maximum turning point of the sine function $y = \sin \theta$?

Occurs at (90°, 1) Signup and view all the answers

What happens to the parabola of the function 'y = ax^2 + q' when 'q' is greater than zero?

It shifts vertically upwards Signup and view all the answers

Which statement correctly describes the effect of 'a' in the equation 'y = ax^2 + q'?

It determines whether the parabola opens upwards or downwards Signup and view all the answers

What is the correct formula to determine the x-intercept of a linear function?

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

How is the gradient of a line defined?

The ratio of horizontal change to vertical change Signup and view all the answers

What does a negative value of 'm' represent in a straight-line equation?

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

When sketching a graph of the form 'y = mx + c', which two points are easiest to use?

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

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

The vertical shift of the function Signup and view all the answers

How is the y-intercept calculated for a function?

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

In the simple interest formula $A = P(1 + in)$, what does the variable $i$ represent?

The interest rate as a decimal Signup and view all the answers

Why is compound interest generally more favorable for investments than simple interest?

It accumulates interest on both the principal and accumulated interest Signup and view all the answers

What is the definition of inflation?

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 calculated?

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

What is a key characteristic of the compound interest formula?

It compounds interest earned onto the principal amount Signup and view all the answers

How can population growth be calculated?

Using the compound interest formula Signup and view all the answers

What impact do exchange rates have on international trade?

They determine how much one currency is worth in terms of another Signup and view all the answers

What is the significance of identifying domain and range in functions?

They help define the limits of input and output values for the function Signup and view all the answers

What is the range of the function in the form $y = a \cos \theta + q$ when $a > 0$?

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

Which of the following correctly describes the asymptotes of the tangent function?

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

To determine the equation of a parabola, how do you identify the value of $q$?

Using the y-intercept point $(0; y)$ Signup and view all the answers

What effect does increasing the value of $a$ have on the graph of $y = a \tan \theta + q$?

It increases the steepness of the graph branches Signup and view all the answers

When interpreting trigonometric graphs, what is the first step in determining the equation?

Identify the type of trigonometric graph and note vertical shifts Signup and view all the answers

Which characteristic is true for the sine and cosine functions concerning their graphs?

Their graphs can be shifted to overlap each other Signup and view all the answers

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

180° Signup and view all the answers

What is a key characteristic of the equation of a hyperbola $y = \frac{a}{x} + q$?

The sign of $a$ affects the direction of the hyperbola's branches. Signup and view all the answers

Which statement is true regarding the x-intercepts of the tangent function?

They occur at every multiple of 180° Signup and view all the answers

What does the direction of a parabola indicate when examining its sketch?

It indicates whether $a$ is positive or negative. Signup and view all the answers

Which set of numbers includes all integers?

Integers Signup and view all the answers

What characterizes rational numbers specifically?

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

Which of the following best describes imaginary numbers?

They are numbers that cannot be expressed on the number line. Signup and view all the answers

Which statement is true regarding whole numbers?

They include all integers except for negative ones. Signup and view all the answers

Which of the following is a characteristic of irrational numbers?

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

How would you classify the number $rac{5}{0}$?

Undefined Signup and view all the answers

What type of numbers comprise the set of real numbers?

Both rational and irrational numbers Signup and view all the answers

Which of the following examples is NOT a rational number?

$rac{5}{0}$ Signup and view all the answers

Which of the following statements is true regarding irrational numbers?

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

What must be done first when converting a recurring decimal into a rational number?

Align the recurring pattern by multiplying by a power of 10. Signup and view all the answers

In the process of rounding off a decimal number, what action should be taken if the digit after the required decimal place is 9?

Change the last digit to 0 and round up the preceding digit. Signup and view all the answers

Which of the following best describes a surd?

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

What does the general formula $(ax + b)(cx + d)$ yield when multiplied?

A quadratic expression that combines like terms. Signup and view all the answers

Which characteristic defines rational numbers in decimal form?

They are either terminating or repeating. Signup and view all the answers

What is the result of rounding off the number 3.5678 to two decimal places?

3.57 Signup and view all the answers

How should the expression $(2x + 3)(x + 4)$ be distributed?

By applying the distributive law twice. Signup and view all the answers

Which of the following expressions cannot be categorized simply as a term?

x + y Signup and view all the answers

What is a necessary characteristic of a number to be classified as a surd?

It cannot be simplified to a rational number. 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

Which step is NOT part of the method for solving linear equations?

Divide by zero Signup and view all the answers

When solving simultaneous equations using the elimination method, what is the goal?

To make coefficients of one variable the same Signup and view all the answers

What must always be maintained when solving equations?

The left side should always equal the right side Signup and view all the answers

What is the first step in solving a quadratic equation in standard form?

Rewrite the equation in standard form Signup and view all the answers

Which of the following describes the solution to a linear equation?

It is called a root of the equation Signup and view all the answers

What distinguishes a quadratic equation from a linear equation?

Quadratic equations involve exponent higher than 1 Signup and view all the answers

When would a quadratic equation have no solutions?

If the discriminant is negative Signup and view all the answers

What is the result of multiplying a monomial and a binomial?

It results in an expression with two terms. Signup and view all the answers

What method involves expressing one variable in terms of another when solving simultaneous equations?

Substitution Signup and view all the answers

Which of the following expressions represents the result of $(A + B)(C + D + E)$?

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

Which identity can be applied when factorizing a difference of two squares?

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

Which operation must be performed equally on both sides of the equation?

Any operation performed Signup and view all the answers

Which step is NOT part of the general procedure for factorizing a trinomial?

Write down an equation. Signup and view all the answers

How is the sum of two cubes expressed when factorized?

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

Which operation describes the multiplication of two fractions?

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

What characterizes a term in a mathematical expression?

It is a single mathematical entity. Signup and view all the answers

What does simplifying a complex fraction typically involve?

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

In the expression $(ab)^n$, what does this property express?

It means $a^n b^n$. Signup and view all the answers

Which term refers to a numerical factor in a term?

Coefficient Signup and view all the answers

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

$x^{6}$ Signup and view all the answers

Which property is exemplified by the expression $rac{a^5}{a^2}$?

Division of Exponents Signup and view all the answers

In the expression $(3x^2)^4$, how is the exponent distributed?

The exponent is multiplied with both base and variable Signup and view all the answers

What does the expression $a^{-3}$ simplify to?

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

When solving the equation $a^x = a^3$, what is the next step under the principles of exponential equations?

Set $x$ equal to $3$ Signup and view all the answers

Which of the following is NOT a step in simplifying expressions with rational exponents?

Ignore the bases Signup and view all the answers

How can the expression $a^{1/2}$ be interpreted?

Square root of $a$ Signup and view all the answers

What is the first step to take when given the exponential equation $2^{x+1} = 8$?

Write $8$ as $2^3$ Signup and view all the answers

Which expression corresponds to the application of raising a product to a power?

$(ab)^n = a^{n} b^{n}$ Signup and view all the answers

Which step should be taken to check for extraneous solutions in an exponential equation?

Verify solutions in the original equation Signup and view all the answers

What represents the solution to a system of simultaneous equations?

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

Which step should be taken first when addressing a word problem?

Read the whole question thoroughly Signup and view all the answers

What does the common difference in a linear sequence refer to?

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

When solving literal equations, what is the main goal?

To isolate the variable in the equation Signup and view all the answers

Which of the following statements about the gradient (m) of a straight-line graph is true?

If m < 0, the graph slopes downwards from left to right Signup and view all the answers

What is a linear inequality?

An expression representing a range of values Signup and view all the answers

What does the term 'common difference' refer to in a sequence?

The difference between consecutive terms in a linear sequence Signup and view all the answers

What is the effect of the y-intercept (c) in the equation y = mx + c?

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

When determining the x-intercept of a linear equation, what must you set y to?

Zero Signup and view all the answers

How is the general term of a linear sequence expressed?

As $T_n = dn + c$ Signup and view all the answers

What must be done if a negative number is used to multiply or divide both sides of a linear inequality?

The inequality sign must be switched Signup and view all the answers

In the equation y = ax² + q, what does the parameter a influence?

The direction and width of the parabola Signup and view all the answers

What characterizes a positive value for the coefficient a in a quadratic function?

The graph opens upwards and has a minimum point Signup and view all the answers

Which of the following formulas represents the area of a circle?

A = πr^2 Signup and view all the answers

What do we need to do to check the solution of a word problem?

Verify that the solution makes sense in context Signup and view all the answers

How do you calculate the y-intercept when given the equation y = mx + c?

Let x equal zero Signup and view all the answers

What does a negative value for q indicate in the equation y = ax² + q?

The parabola shifts vertically downwards Signup and view all the answers

What is the first characteristic to determine when sketching the graph of y = mx + c?

The sign of m Signup and view all the answers

What is the range of the function if the parameter $a$ is greater than 0?

[q; , \infty) Signup and view all the answers

Which statement is true regarding the y-intercept of a parabolic graph?

It is found by setting $x=0$. Signup and view all the answers

What effect does the parameter $q$ have on the graph of the function?

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

For which range of $a$ does the graph of $f(x)$ have a maximum turning point?

$a < 0$ 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

What is the general behavior of the graph of $y = \frac{a}{x} + q$ as $x$ approaches zero?

It approaches the y-axis. Signup and view all the answers

How are the axes of symmetry for the function $y = \frac{a}{x} + q$ characterized?

The lines $y = x + q$ and $y = -x + q$. Signup and view all the answers

What determines the shape of the graph of a hyperbola with respect to parameter $a$?

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

If $a < 0$, what can be expected of the turning point of the graph?

It will be a maximum point at $(0; q)$. Signup and view all the answers

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

The constant $q$ Signup and view all the answers

For the exponential function $y = ab^x + q$, what happens when $q < 0$?

The horizontal asymptote moves downwards. Signup and view all the answers

In the sine function $y = a ext{sin} heta + q$, how does $|a| > 1$ affect the graph?

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

What is the x-intercept of the function $y = a ext{sin} heta + q$?

The points where $y = 0$. Signup and view all the answers

Which of the following correctly describes the domain of the cosine function $y = ext{cos} heta$?

[0°, 360°] Signup and view all the answers

What characteristics define the exponential function $y = b^x$?

It is defined for all real numbers. Signup and view all the answers

What effect does a negative value of $a$ have on the exponential graph $y = ab^x + q$?

It curves the graph downwards. Signup and view all the answers

In the sine function, how does a positive value of $q$ affect the graph?

It shifts the graph upward by $q$ units. Signup and view all the answers

What are the x-intercepts of the sine function defined between 0° and 360°?

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

What is one characteristic of the range of the function $y = a ext{sin} heta + q$ when $a > 0$?

It depends on the value of $q$. Signup and view all the answers

What is the correct expression for the probability of the union of two events A and B?

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

What does it mean for two events to be mutually exclusive?

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

What is the correct formula to convert an amount from one currency to another?

$ ext{Amount in new currency} = rac{ ext{Amount in original currency}}{ ext{Exchange rate}}$ Signup and view all the answers

Which identity describes the relationship between complementary events A and A'?

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

Which of the following describes a probability of exactly 1?

The event will always occur Signup and view all the answers

What is the result of the probability of two mutually exclusive events A and B?

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

How is the theoretical probability of an event denoted mathematically?

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

What does the union of two sets represent?

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

What does P(A ∩ B) equal for mutually exclusive events A and B?

0 Signup and view all the answers

Which of the following statements about relative frequency is true?

It may vary each time an experiment is conducted Signup and view all the answers

Which of the following can be inferred about two events A and A'?

They are complementary events. Signup and view all the answers

In a Venn diagram representing two events with partial overlap, what does the section of overlap signify?

Elements belonging to both sets Signup and view all the answers

How do you visually represent the probability relationship for the union of two events using a Venn diagram?

By showing overlapping circles. Signup and view all the answers

What does the complement of event A indicate?

All elements in sample space not in event A Signup and view all the answers

What happens to the relative frequency as more trials are conducted?

It stabilizes around the theoretical probability Signup and view all the answers

Which probability situation corresponds to a probability of 0?

An impossible event Signup and view all the answers

What would happen if you added the probabilities of two events A and B that are not mutually exclusive?

The calculation will double-count the intersection. Signup and view all the answers

If event A occurs 30 times out of 100 trials, what is the relative frequency of A?

Both A and C Signup and view all the answers

What is the relationship between the probabilities of an event and its complement?

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

What is the primary characteristic of a sample space in probability?

It contains all possible outcomes of an experiment 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 does the parameter $q$ do in the function $y = a \tan \theta + q$?

Introduces a vertical shift Signup and view all the answers

What is the x-intercept of the function $y = \tan \theta$?

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

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

180 Signup and view all the answers

How can the sign of $a$ in the equation $y = ax^2 + q$ affect the parabola?

It affects whether the parabola opens upwards or downwards Signup and view all the answers

Which of the following points is a vertical asymptote for the function $y = \tan \theta$?

270 Signup and view all the answers

To find the equation of a hyperbola in the form $y = \frac{a}{x} + q$, what is a key step?

Examine the sketch for sign determination Signup and view all the answers

What is the best method for calculating the y-intercept of a parabola defined by $y = ax^2 + q$?

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

What determines the steepness of the branches in the function $y = a \tan \theta + q$?

The value of $a$ Signup and view all the answers

Which characteristic applies to both sine and cosine functions within their overall graphs?

They can be shifted to overlap each other Signup and view all the answers

Which variable determines the vertical shift in trigonometric functions?

q Signup and view all the answers

How is the accumulated amount calculated using simple interest?

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

What distinguishes compound interest from simple interest?

Interest is calculated on both the principal and accumulated interest. Signup and view all the answers

What causes the growth of an investment to be exponential with compound interest?

Interest compounds over time, earning interest on itself. Signup and view all the answers

In a hire purchase agreement, how is interest charged?

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

What does the variable 'P' represent in financial formulas?

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

How is the future price calculated considering inflation?

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

What happens to a currency when it strengthens?

More money is invested in that country. Signup and view all the answers

What does the term 'domain' refer to in functions?

The inputs that can be used in the function. Signup and view all the answers

What indicates the presence of asymptotes in a function?

Setting the denominator to zero. Signup and view all the answers

Which of the following sets includes all integers?

Integers Signup and view all the answers

What distinguishes rational numbers from irrational numbers?

Rational numbers have repeating decimals. Signup and view all the answers

Which of the following defines whole numbers?

All natural numbers including zero. Signup and view all the answers

Which of the following is an example of an imaginary number?

√-1 Signup and view all the answers

What does the symbol R represent in the real number system?

Real Numbers Signup and view all the answers

What type of numbers does the set of natural numbers (N) include?

Positive integers only. Signup and view all the answers

Which of the following statements is correct regarding rational numbers?

They can be written in the form a/b, where b is not zero. 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 a key property of irrational numbers?

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

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

Multiply the decimal by a power of 10. Signup and view all the answers

Which type of decimal is considered rational?

Terminating decimals. Signup and view all the answers

What is the correct process to round off a decimal number when the next digit is 5 or greater?

Round up the last digit. Signup and view all the answers

What determines whether a decimal expansion is irrational?

If it has a non-terminating and non-repeating form. Signup and view all the answers

How can surds be expressed?

In the form $ oot{n}{a}$. Signup and view all the answers

What is the outcome when you round a number like 9.89 to one decimal place?

9.9 Signup and view all the answers

When multiplying two binomials $(ax + b)(cx + d)$, the resulting term $bd$ represents which component?

The constant term. Signup and view all the answers

Which of the following correctly identifies the role of coefficients in an algebraic expression?

They are the numerical factors in terms. Signup and view all the answers

What describes the significant characteristic of a monomial?

It is an expression with one term. Signup and view all the answers

What is the result of applying the rule extit{(a^m)^n = a^{mn}}?

a^{mn} Signup and view all the answers

Which operation is used to simplify the expression rac{a^m}{a^n}?

Subtraction of exponents Signup and view all the answers

What does the zero exponent rule state?

a^0 = 1 Signup and view all the answers

Which of the following correctly describes the purpose of rational exponents?

To represent roots through fractional exponents Signup and view all the answers

What is the primary method for solving exponential equations when bases can be made the same?

Equating the exponents Signup and view all the answers

What does the solution to a system of simultaneous equations represent when the graphs of the equations are drawn?

The coordinates of intersection Signup and view all the answers

What is the outcome when simplifying the expression (ab)^{n}?

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

How can complex fractions with exponential terms be simplified?

By converting to prime bases and cancelling common terms Signup and view all the answers

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

Ignore the whole question Signup and view all the answers

When simplifying an expression involving a negative exponent, such as a^{-n}, what is the proper expression?

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

What is necessary to isolate an unknown variable in a literal equation?

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

Which step should be taken first when applying the laws of exponents to combine like terms?

Identify the base Signup and view all the answers

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

By subtracting any term from the term that follows it Signup and view all the answers

What does the expression rac{a^{m/n}}{b^{p/q}} simplify to when using exponent rules?

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

What happens to the inequality sign when both sides of an inequality are divided by a negative number?

It changes to a less than sign Signup and view all the answers

Which formula represents the area of a circle?

A = ext{π}r^2 Signup and view all the answers

What is the general term of a linear sequence expressed as?

T_n = dn + c Signup and view all the answers

In solving linear inequalities, what should you do if you multiply both sides by a negative number?

Flip the inequality sign Signup and view all the answers

What does the term 'sequence' refer to in mathematics?

An ordered list of items, usually numbers Signup and view all the answers

What must be true about the coefficients in a linear sequence?

They indicate the difference between terms Signup and view all the answers

What is the process called when breaking down an expression into simpler expressions?

Factorisation Signup and view all the answers

Which of the following correctly represents the identity for the difference of two squares?

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

In the multiplication of a monomial and a binomial, which expression represents the correct operation?

$a(x + y) = ax + ay$ Signup and view all the answers

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

Two solutions Signup and view all the answers

What is the first step in solving a linear equation?

Expand all brackets Signup and view all the answers

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

Identify common factors Signup and view all the answers

Which method involves setting each factor equal to zero?

Factoring method Signup and view all the answers

Which law is used for simplifying expressions of the form $rac{a^m}{a^n}$?

Exponent Law Signup and view all the answers

What must be maintained while solving equations?

The balance of the equation Signup and view all the answers

What is obtained when multiplying a binomial $(A + B)$ by a trinomial $(C + D + E)$?

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

What does the expression $(x + y)(x^2 - xy + y^2)$ represent?

Sum of two cubes Signup and view all the answers

How many equations are needed to solve for three unknown variables?

Three equations Signup and view all the answers

What is required to simplify the algebraic fraction $rac{2x^2}{4x}$?

Divide both terms by 2 Signup and view all the answers

Which step follows after grouping like terms in a linear equation?

Isolate the variable Signup and view all the answers

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

To verify both sides of the equation are equal Signup and view all the answers

What is the correct expression for the sum of two cubes?

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

In simplifying complex fractions, what is the first action you should take?

Factorise all terms Signup and view all the answers

In solving simultaneous equations by elimination, what is the main goal?

To eliminate one variable Signup and view all the answers

What characterizes a quadratic equation compared to a linear equation?

It can have two solutions Signup and view all the answers

What is the primary method for solving quadratic equations?

Factorisation Signup and view all the answers

What is the definition of a common difference in a linear sequence?

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

What effect does an increase in the constant 'm' have on the graph of a linear function?

It increases the slope. Signup and view all the answers

Which statement accurately describes the y-intercept of a straight line?

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

How is the x-intercept of a straight-line graph calculated?

By setting $y = 0$ in the equation. Signup and view all the answers

What effect does a positive 'a' have on the graph of a quadratic function?

The graph has a minimum turning point. 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

Which of the following correctly describes the range of a linear function?

It can take on any real value. Signup and view all the answers

What does the term 'gradient' refer to in the context of straight line graphs?

The slope of the graph. Signup and view all the answers

What does the value of 'q' affect in a quadratic function?

The turning point of the graph. Signup and view all the answers

In the equation $y = mx + c$, what does 'c' represent?

The y-intercept of the line. Signup and view all the answers

What happens to the graph of an exponential function when the constant q is positive?

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

Which of the following describes the effect of a negative constant a in the equation y = a sin θ + q?

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

How is the x-intercept calculated for the function y = ab^x + q?

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

What is the range of the function y = a cos θ + q when a > 0?

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

Which statement is true for the function y = b^x when 0 < b < 1?

It represents exponential decay. Signup and view all the answers

What is the effect of a vertical shift q on the horizontal asymptote of the function y = ab^x + q?

It shifts by q units. Signup and view all the answers

In the function y = a sin θ + q, how is the period affected by changes in a?

It remains constant regardless of a. Signup and view all the answers

What are the x-intercepts for the sine function y = sin θ within the range [0°, 360°]?

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

For the function y = ab^x + q, which parameter primarily influences the growth or decay rate of the function?

b Signup and view all the answers

When sketching the graph of y = a/x + q, which characteristic must be determined?

The x and y intercepts. Signup and view all the answers

What is the range of a cosine function in the form of $y = a \cos \theta + q$ when $a > 0$?

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

Which of the following describes the characteristics of the tangent function $y = \tan \theta$?

It has asymptotes at $\theta = 90°$ and $\theta = 270°$. Signup and view all the answers

How does the parameter $q$ affect the graph of a function of the form $y = a \tan \theta + q$?

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

To determine the equation of a parabola, which characteristic indicates the direction of the parabola?

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

Which statement correctly describes the effect of the value of $a$ in a hyperbola defined as $y = \frac{a}{x} + q$?

It determines the steepness of the branches. Signup and view all the answers

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

180° Signup and view all the answers

Which method is correct for determining the equation of a trigonometric function?

Identify the graph type and then solve for $a$ and $q$. Signup and view all the answers

What is the x-intercept of the tangent function $y = \tan \theta$?

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

In a hyperbola represented by $y = \frac{a}{x} + q$, which parameter indicates the vertical shift of the graph?

The constant $q$. Signup and view all the answers

How can the y-intercept of a function of the form $y = a \sin \theta + q$ be determined?

By substituting $\theta = 0$ into the equation. Signup and view all the answers

What does the variable $q$ determine in the equations for trigonometric functions?

Vertical shift Signup and view all the answers

In the formula for simple interest, which variable represents the initial amount of money invested?

P Signup and view all the answers

What advantage does compound interest have over simple interest?

It can generate interest on both the principal and accumulated interest. Signup and view all the answers

How is the final accumulated amount ($A$) in both simple and compound interest usually calculated?

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

What is the primary calculation method for hire purchase agreements?

Interest is calculated at a simple interest rate on the remaining loan amount. Signup and view all the answers

What does the inflation rate in the formula for future price represent?

The average increase in the price of goods and services. Signup and view all the answers

Which of the following statements is true regarding population growth calculations?

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

How can currency strength be characterized?

It strengthens as more investment enters the economy. Signup and view all the answers

What is the impact of compound interest on investments over time?

It allows the investment to grow exponentially. Signup and view all the answers

Which aspect of a trigonometric function is affected by the variable $a$?

Amplitude and reflection Signup and view all the answers

What does a probability of 0 represent?

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

Which of the following correctly represents the probability of an event occurring?

The ratio of favorable outcomes to total outcomes Signup and view all the answers

What is represented by the intersection of two sets A and B?

Elements that are common to both sets Signup and view all the answers

If the exchange rate is 2:1 and you have $10, how much will you have in the new currency?

$20 Signup and view all the answers

What does relative frequency provide as a measure?

An experimental probability Signup and view all the answers

Which of the following statements about theoretical probability is true?

It is based on the ratio of favorable outcomes to possible outcomes Signup and view all the answers

What is the formula for calculating relative frequency?

f = p / t Signup and view all the answers

In a Venn diagram, what does the area outside a set represent?

Elements that do not belong to the set Signup and view all the answers

If an event has a theoretical probability of 0.5, how can it be expressed as a percentage?

50% Signup and view all the answers

What does the union of two sets A and B include?

All elements in both A and B Signup and view all the answers

What is the formula for calculating the probability of the union of two events?

P(A ext{ or } B) = P(A) + P(B) - P(A ext{ and } B) Signup and view all the answers

Which statement accurately describes mutually exclusive events?

The probability of their intersection is zero. Signup and view all the answers

What happens to the probabilities of two mutually exclusive events when calculated together?

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

What does the complement of an event A represent?

All elements in sample space except those in A. Signup and view all the answers

What is the relationship between an event and its complement?

They are mutually exclusive. Signup and view all the answers

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

The probabilities of complementary events. Signup and view all the answers

If events A and B are mutually exclusive, what is P(A ext{ and } B)?

0 Signup and view all the answers

Which of the following statements is true regarding the union of two events?

P(A ext{ or } B) = P(A) + P(B) - P(A ext{ and } B) Signup and view all the answers

What is indicated by the formula P(A ext{ and } A') = 0?

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

In a Venn diagram illustrating event A and its complement, what does the shaded area represent?

Only the outcomes of event A'. Signup and view all the answers

What happens to the graph of a function when the coefficient $a$ in $y = ax^2 + q$ is greater than 0?

The graph is a 'smile' with a minimum turning point. Signup and view all the answers

What is the range of the function $y = ax^2 + q$ if $a < 0$?

(-$ ightarrow$; q] Signup and view all the answers

For the equation $y = ax^2 + q$, where is the vertex or turning point located?

(0, q) Signup and view all the answers

What is the effect of changing the value of $q$ in the function $y = rac{a}{x} + q$?

It affects the horizontal asymptote. Signup and view all the answers

What is the nature of the x-intercept in the function $y = rac{a}{x} + q$?

It cannot exist since the function is undefined at $x = 0$. Signup and view all the answers

What describes the domain of the function $y = rac{a}{x} + q$?

{$x : x eq 0}$ Signup and view all the answers

What does a negative coefficient $a$ signify in the function $y = ax^2 + q$?

The graph is a 'frown' with a maximum turning point. Signup and view all the answers

What is the vertical shift determined by in the hyperbolic function $y = rac{a}{x} + q$?

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

What are the characteristics of the hyperbolic functions defined by $y = rac{a}{x} + q$?

They have both horizontal and vertical asymptotes. Signup and view all the answers

What happens to the graph of $f(x) = ax^2 + q$ as the value of $a$ approaches 0 from the positive side?

The graph widens. Signup and view all the answers

Which number set includes zero and all positive integers?

Whole Numbers Signup and view all the answers

What is the primary characteristic of irrational numbers?

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

How are rational numbers defined in the number system?

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

Which of the following numbers is classified as irrational?

$ ext{pi}$ Signup and view all the answers

Which subset of the real number system does not include negative numbers?

Natural Numbers Signup and view all the answers

Which statement is true about integers?

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

What is the set of numbers that includes all rational and irrational numbers?

Real Numbers Signup and view all the answers

Which of the following best describes a characteristic of rational numbers?

They must have a non-zero denominator. Signup and view all the answers

Which of the following represents a key characteristic of irrational numbers?

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

What is the correct method to convert a terminating decimal into a rational number?

Add the integer part and a fraction of the decimal digits. Signup and view all the answers

In rounding off a decimal number, what determines if you round up the last digit?

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

What is the process to estimate the value of a surd?

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

When multiplying a monomial by a binomial, which term is incorrect in the expression?

You only add the two terms after multiplication. Signup and view all the answers

Which of the following decimal forms represents a rational number?

0.7 (terminating) Signup and view all the answers

Which of the following operations is part of converting recurring decimals into rational numbers?

Subtracting the original from a multiplied equation. Signup and view all the answers

What is an example of a surd?

√5 Signup and view all the answers

What can be concluded about the decimal representation of irrational numbers?

They are non-terminating and non-repeating. Signup and view all the answers

What must be adjusted in the rounding process when rounding up a number ending in 9?

The preceding digit is increased by 1. 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

Which step is NOT part of the method for solving linear equations?

Graph the equations Signup and view all the answers

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

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

What forms must a quadratic equation be rewritten into before solving?

ax^2 + bx + c = 0 Signup and view all the answers

Which of the following methods does NOT involve eliminating a variable from simultaneous equations?

Graphical method Signup and view all the answers

Which algebraic method is typically used to simplify a quadratic expression?

Factoring Signup and view all the answers

What is a key characteristic of linear equations compared to quadratic equations?

Linear equations have at most one solution. Signup and view all the answers

What is the importance of keeping an equation balanced when solving?

It ensures equivalence between both sides. Signup and view all the answers

When solving equations, what should be checked after determining a solution?

The accuracy by substituting back into the original equation Signup and view all the answers

How do quadratic equations differ from linear equations in terms of solutions?

Quadratic equations may have multiple (two) solutions. Signup and view all the answers

What is the result of multiplying a binomial by a trinomial?

Each term of the binomial is multiplied with the trinomial separately Signup and view all the answers

In the expression \( a(x + y) \, what does 'a' represent?

The coefficient in the expression Signup and view all the answers

Which of the following describes the identity used to factor a difference of two squares?

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

Which steps are essential in simplifying algebraic fractions?

Factoring the numerator and denominator and cancelling common factors Signup and view all the answers

Which is the proper factorization of the sum of two cubes?

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

What is one method of factorizing a quadratic trinomial?

Finding two binomials that produce the original trinomial when multiplied Signup and view all the answers

Which property describes what happens when you multiply two terms with the same base and different exponents?

You add the exponents Signup and view all the answers

In the expression \( a^m \, what does 'a' represent?

The base being raised to a power Signup and view all the answers

Which operation is performed when dividing fractions?

Multiply the numerator by the reciprocal of the denominator Signup and view all the answers

Which step is typically the first in factorizing a trinomial?

Look for common factors Signup and view all the answers

What is the outcome when you apply the zero exponent rule to a non-zero number?

The result is 1 Signup and view all the answers

Which of the following applies when dividing exponents with the same base?

Subtract the exponents Signup and view all the answers

What happens when two exponential expressions with the same base are equal, specifically when the base is greater than zero and not equal to one?

The exponents must be equal Signup and view all the answers

How would you express a negative exponent, such as $a^{-n}$?

It is equal to $1/a^n$ Signup and view all the answers

In which situation would you apply logarithms to solve an exponential equation?

When bases are not easily made the same Signup and view all the answers

What is the first step to take when simplifying a fraction with rational exponents?

Convert roots to fractional exponents Signup and view all the answers

Which of the following statements about the multiplication of exponents is correct?

The bases must be the same and the exponents add Signup and view all the answers

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

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

When simplifying an expression like $(ab)^n$, which of the following properly describes the result?

It equals $a^n b^n$ Signup and view all the answers

In the factorization of an exponential expression, what does common factor refer to?

The greatest common factor of the coefficients Signup and view all the answers

What defines a linear sequence?

It has a constant difference between successive terms. Signup and view all the answers

What effect does the coefficient 'm' have in the linear function equation $y = mx + c$?

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

In the equation $y = mx + c$, what does 'c' represent?

The y-intercept of the line. Signup and view all the answers

What happens to the graph of a linear function if 'c' is greater than 0?

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

How can the x-intercept of a linear function be determined?

Set $y$ equal to zero in the equation. Signup and view all the answers

What does the sign of 'a' indicate in the quadratic function $y = ax^2 + q$?

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

In a quadratic function $y = ax^2 + q$, what does 'q' control?

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

Which method requires knowing the gradient and y-intercept for plotting a straight line?

Slope Intercept Method. Signup and view all the answers

What is the general form of a parabolic function?

$y = ax^2 + q$ Signup and view all the answers

What do the coordinates of the solution represent in a system of simultaneous equations?

The point where the two graphs intersect Signup and view all the answers

What is the first step to take when solving a word problem?

Read the whole question Signup and view all the answers

What is a literal equation?

An equation with multiple variables Signup and view all the answers

What should you do if you need to isolate the unknown variable in a literal equation?

Ask how the variable is connected and perform the opposite operation Signup and view all the answers

Which of the following is true about solving linear inequalities compared to linear equations?

The method remains the same, but inequalities reverse when divided by a negative Signup and view all the answers

What does the common difference in a linear sequence represent?

The difference between any term and the term before it Signup and view all the answers

Which equation represents the general formula for a linear sequence?

$T_n = dn + c$ Signup and view all the answers

How do you calculate the common difference $d$ in a sequence?

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

Which approach can be used for solving simultaneous equations apart from substitution?

Graphical method Signup and view all the answers

What condition must be met when both sides of a linear inequality are divided by a negative number?

The inequality sign is switched Signup and view all the answers

What does a probability of 0 signify?

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

How is relative frequency defined?

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

What does the union of two sets represent?

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

How can a probability of 0.5 be best interpreted?

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

What is a primary use of Venn diagrams?

To visually show relationships between sets. Signup and view all the answers

What does the theoretical probability formula P(E) = n(E) / n(S) illustrate?

The ratio of successful outcomes to all possible outcomes. Signup and view all the answers

What does a probability of 1 indicate about an event?

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

Which type of frequency approaches theoretical probability with more trials?

Relative frequency. Signup and view all the answers

What does the intersection of two sets contain?

Elements common to both sets. Signup and view all the answers

How does the graph of a parabola change when the value of $a$ is greater than 1?

It narrows and stretches vertically upwards. Signup and view all the answers

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

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

What describes the turning point of a parabola when $a < 0$?

It has a maximum turning point. Signup and view all the answers

What happens to the graph of a parabola as the value of $a$ approaches 0 from the positive side?

It gets wider. Signup and view all the answers

What is the range of a parabola when $a < 0$?

(-∞, q) Signup and view all the answers

What describes the y-intercept of the function $y = ax^2 + q$?

It is found by letting $x = 0$. Signup and view all the answers

Which statement is true about the vertical asymptote of the hyperbolic function $y = \frac{a}{x} + q$?

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

What effect does the value of $q$ have on the graph of the hyperbola?

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

What is the axis of symmetry for a parabola defined by $f(x) = ax^2 + q$?

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

What is the correct method to find the x-intercept of a function of the form $y = \frac{a}{x} + q$?

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

Which of the following changes would cause the graph of an exponential function to shift downward?

Setting $q < 0$ Signup and view all the answers

For which value of $b$ does the function $y = ab^x + q$ represent exponential growth?

$b > 1$ Signup and view all the answers

What is the range of an exponential function when $a > 0$?

${f(x) : f(x) > q}$ Signup and view all the answers

What is the y-intercept for the function $y = a \sin \theta + q$?

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

What does the effect of $a < 0$ signify in the function $y = a \cos \theta + q$?

Reflection about the x-axis Signup and view all the answers

What characteristic defines the horizontal asymptote of the function $y = ab^x + q$?

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

How would the graph of the sine function change if $a > 1$?

It would undergo vertical stretch Signup and view all the answers

Which of the following is true about the domain and range of the cosine function $y = \cos \theta$?

Domain: $[0°, 360°]$, Range: $[-1, 1]$ Signup and view all the answers

What will the x-intercepts of the sine function $y = a \sin \theta + q$ be when $q = 0$ and $a > 0$?

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

What is the identity used 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 effect does the variable $q$ have on trigonometric functions?

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

What defines mutually exclusive events?

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

In calculating simple interest, what does the variable $P$ represent?

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

For mutually exclusive events, how is the probability of their union calculated?

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

What is the complement of a set A, denoted as A', comprised of?

Elements not in set A Signup and view all the answers

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

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

What financial concept uses the formula $A = P(1 + i)^n$ for calculating future values?

Population growth. Signup and view all the answers

What is true about the union of an event and its complement?

It covers the entire sample space. Signup and view all the answers

When identifying asymptotes for a function, what is the main step to take?

Set the denominator equal to zero. Signup and view all the answers

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

The relationship between an event and its complement. Signup and view all the answers

What does inflation represent in economic terms?

The average annual increase in prices of goods and services. Signup and view all the answers

In a Venn diagram, how do mutually exclusive events appear?

They are separate and do not intersect. Signup and view all the answers

In the context of financing, what is the outcome of a hire purchase agreement?

Payments are made over time, including interest on the remaining balance. Signup and view all the answers

What is the relationship represented by P(A ∩ A')?

Equal to the empty set Signup and view all the answers

If P(A) = 0.3, what is P(A')?

0.7 Signup and view all the answers

What does the variable $i$ signify in financial formulas for interest calculations?

The interest rate expressed as a decimal. Signup and view all the answers

How does compound interest differ from simple interest?

Compound interest accumulates on both the principal and previously earned interest. Signup and view all the answers

Which of the following statements about probabilities is incorrect?

The intersection of two mutually exclusive events is non-empty. Signup and view all the answers

What indicates the strength of a currency in the foreign exchange market?

The amount of investment in the country relative to other currencies. Signup and view all the answers

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

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

In which direction does a parabola open if the value of $a$ in the equation $y = ax^2 + q$ is negative?

It opens downwards. Signup and view all the answers

What determines the steepness of the graph branches for the function $y = a \tan \theta + q$?

The absolute value of $a$ Signup and view all the answers

At which degrees does the tangent function have asymptotes?

90° and 270° Signup and view all the answers

Which of the following correctly represents the y-intercept of the function $y = a \tan \theta + q$?

(0, q) Signup and view all the answers

How does a vertical shift of $q > 0$ affect the graph of $y = a \tan \theta + q$?

It shifts the graph up by $q$ units. Signup and view all the answers

What characterizes the periods of sine and cosine functions?

Both have a period of 360°. Signup and view all the answers

How can the equations of trigonometric functions like $y = a \sin \theta + q$ be determined?

By examining sketches and substituting points into the equation. Signup and view all the answers

What is the relationship between the sine and cosine graphs?

The sine graph is the same as the cosine graph shifted right by 90°. Signup and view all the answers

When determining the equation of a hyperbola in the form $y = \frac{a}{x} + q$, what signifies the vertical shift?

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

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Questions and Answers

Which set of numbers includes all positive integers starting from 1?

What distinguishes whole numbers from natural numbers?

Which of the following is an example of an irrational number?

Which symbol represents the set of integers?

Rational numbers can be expressed in which form?

Which of the following best describes irrational numbers?

What is the definition of imaginary numbers?

Which subset of the real number system includes rational and irrational numbers?

Which statement correctly describes irrational numbers?

How would you convert the terminating decimal 0.75 into a rational number?

What is a key characteristic of a recurring decimal?

Which of the following is an example of a surd?

What is the first step in rounding off a decimal number?

What is a monomial?

In multiplying two binomials, what is the correct resulting form?

What is the role of coefficients in a mathematical expression?

Which of the following correctly identifies a term in an expression?

What can be concluded about non-terminating decimals?

What is the result of multiplying the binomial extit{(A + B)} by the trinomial extit{(C + D + E)}?

Which of the following describes a constant in mathematical terms?

What identity is used to factor a difference of two squares?

Which operation is used for simplifying the fraction rac{a}{b} imes rac{c}{d}?

In the expression extit{(ax + b)(cx + d)}, what does the term extit{acx^2} represent?

What is the first step in the general procedure for factorising a trinomial?

For the sum of two cubes, which of the following is the correct factorization?

What does the term 'equation' refer to in mathematics?

Which law states that $a^m \times a^n = a^{m+n}$?

What is the outcome when you simplify the algebraic fraction rac{2x^2}{4x}?

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

Which of the following is NOT a step in solving linear equations?

What is the form of a standard quadratic equation?

How can solutions for simultaneous equations be found using substitution?

Which method in solving simultaneous equations involves eliminating one variable by adjusting coefficients?

What characteristic distinguishes quadratic equations from linear equations?

Which of the following is a necessary step after factoring a quadratic equation?

In solving an equation, what must always be maintained?

Which approach can also be used to solve simultaneous equations apart from algebraic methods?

What is the result of applying the zero exponent rule?

Which property is used to simplify the expression rac{a^m}{a^n}?

What happens to the number of equations when solving for two unknown variables?

What form is used to express the equation if both sides are equal with the same base?

How can you simplify a complex fraction with exponential terms?

Which of the following best describes rational exponents?

What does the property (ab)^n = a^n b^n illustrate?

Which step should be taken first when solving an exponential equation using logarithms?

When simplifying the expression a^{m/n}, what should you do if m and n share a common factor?

What is the result of (a^{m/n})^{p/q}?

How do you express a negative exponent, such as a^{-n}?

What do the coordinates of the solution represent in a system of simultaneous equations?

Which of the following is the first step when solving a word problem?

How do you isolate an unknown variable in a literal equation?

What is the key difference when solving linear inequalities compared to linear equations?

What does the term 'common difference' refer to in a linear sequence?

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

What method would you use to solve a literal equation involving a variable in the denominator?

What does the general term $T_n$ indicate in a sequence?

Which of the following describes a linear inequality?

What do we do to verify the solution to an equation after solving it?

What occurs to the graph of a function as the value of 'a' increases when 'a' is greater than zero?

What is the range of a parabolic function when 'a' is less than zero?

What shape does the graph of a function take when 'a' is less than zero?

For the function of the form y = ax^2 + q, where is the axis of symmetry located?

What is the y-intercept for the function y = ax^2 + q?

What kind of asymptote does the hyperbolic function y = a/x + q have horizontally?

What happens to the graph of a hyperbolic function as the value of 'a' becomes negative?

What is true about the range of the hyperbolic function y = a/x + q?

How is the y-intercept determined for the function y = a/x + q?

What does a positive value of 'q' do to the graph of the hyperbola y = a/x + q?

What is the formula used to calculate the amount in a new currency?

What does a probability of 0.5 signify?

Which of the following describes relative frequency?

In a Venn diagram, what does the union of two sets represent?

What does the intersection of two sets contain?

How is probability defined?

What does a probability of 1 imply?

What is the result of conducting more trials in an experiment regarding relative frequency?

What does the symbol $P(A igcup B)$ represent?

What does the expression $P(A igcup A')$ equal?

How would you classify the number $rac{5}{0}$?