Gr 10 Math June P1 Easy

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Which set includes only positive integers starting from 1?

Integers (Z)

Rational Numbers (Q)

Natural Numbers (N) (correct)

Whole Numbers (N0)

Which of the following sets includes zero?

Natural Numbers (N)

Integers (Z)

Whole Numbers (N0) (correct)

Irrational Numbers (Q')

What distinguishes rational numbers from irrational numbers?

Rational numbers have repeating decimal expansions.

Rational numbers can be expressed as a fraction of two integers. (correct)

Rational numbers are always whole numbers.

Rational numbers cannot be negative.

Which of the following represents irrational numbers?

π and √2 Signup and view all the answers

What is included in the set of real numbers?

Both rational and irrational numbers Signup and view all the answers

Which of the following statements about imaginary numbers is true?

They are not part of the real number system. Signup and view all the answers

What is a rational number?

A number that can be expressed in the form of ( \frac{a}{b} ), where ( a ) and ( b ) are integers and ( b \neq 0 ). Signup and view all the answers

Which of the following is a characteristic of irrational numbers?

They cannot be expressed as fractions with integer numerator and denominator. Signup and view all the answers

How can you convert a terminating decimal into a rational number?

By identifying the integer part and calculating contributions from the decimal digits. Signup and view all the answers

What does the process of rounding depend on?

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

Which of these is NOT a surd?

( \sqrt{4} ) Signup and view all the answers

What is the correct order of the number hierarchy starting from natural numbers?

Natural Numbers ( (N) ) → Whole Numbers ( (N_0) ) → Integers ( (Z) ) → Rational Numbers ( (Q) ) → Irrational Numbers ( (Q') ) → Real Numbers ( (R) ) Signup and view all the answers

When estimating a surd, what should you compare to find its value?

Its surrounding perfect squares or cubes. Signup and view all the answers

What happens when rounding a digit that is 9?

It turns into 0, and the preceding digit is rounded up by 1. Signup and view all the answers

Which statement regarding decimals is true?

Terminating decimals are always rational numbers. Signup and view all the answers

What is a monomial?

An expression with one term. Signup and view all the answers

Which of the following represents the product of two linear binomials?

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

What is the result when a trinomial is multiplied by a binomial?

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

What is factorisation?

Breaking down an expression into simpler expressions. Signup and view all the answers

What is the identity for the difference of two squares?

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

What technique is used when factorising by grouping?

Grouping terms with common factors. Signup and view all the answers

In the simplification of fractions, what is the first step?

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

What is the product of $x^3 + y^3$ using cube identities?

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

Which expression correctly represents the addition of fractions with the same denominator?

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

Which of the following is NOT a term in a binomial?

Quadratic Signup and view all the answers

What is the result of simplifying the expression $\frac{a^5}{a^3}$ using exponent laws?

$a^2$ Signup and view all the answers

Which expression correctly represents the zero exponent rule?

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

How do you express the square root of $a$ in terms of rational exponents?

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

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

Applying the principle $a^x = a^y$ Signup and view all the answers

What is the correct simplification for the expression $\left(\frac{a}{b}\right)^{2}$?

$\frac{a^2}{b^2}$ Signup and view all the answers

Using the laws of exponents, what is the result of $a^{3/4} \times a^{1/2}$?

$a^{5/4}$ Signup and view all the answers

Which expression represents applying the laws of exponents for $(ab)^{3}$?

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

What is the result of $a^{-2}$ using the negative exponent law?

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

What is the main condition for the laws of exponents to apply?

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

How can the expression $\frac{a^{5/3}}{a^{2/3}}$ be simplified?

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

What is the first step in solving a word problem mathematically?

Read the whole question. Signup and view all the answers

What should you do after solving an equation algebraically?

Check the solution. Signup and view all the answers

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

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

Which method can be used to solve systems of equations graphically?

Drawing both equations and locating their intersection. Signup and view all the answers

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

The sign is inverted. Signup and view all the answers

To isolate an unknown variable in a literal equation, what should you first identify?

The operations joining the variable to others. Signup and view all the answers

When solving by elimination, what is the primary goal?

To eliminate one variable. Signup and view all the answers

If two equations have the same slope but different y-intercepts, what does that indicate about their graphs?

They are parallel lines. Signup and view all the answers

In the equation for the area of a circle, what does the variable 'r' represent?

The radius of the circle. Signup and view all the answers

What strategy can be employed to solve linear inequalities?

Use similar methods as linear equations. Signup and view all the answers

What method can be used to solve exponential equations when both sides can be expressed with the same base?

Equating the exponents Signup and view all the answers

Which of the following describes a linear equation?

The highest exponent of the variable is 1 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

When solving a quadratic equation in the form of $ax^2 + bx + c = 0$, what is the purpose of factorising?

To find potential solutions by setting each factor to zero Signup and view all the answers

How many solutions does a quadratic equation typically have?

At most two solutions Signup and view all the answers

In the process of solving simultaneous equations, what is often a key first step?

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

What is crucial to check after solving any equation?

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

Which statement is true about the relationship between operations performed on both sides of an equation?

Operations must be performed equally on both sides Signup and view all the answers

Which method might be used to facilitate solving a linear equation?

Factoring out a greatest common factor Signup and view all the answers

What defines a quadratic equation compared to a linear equation?

It has a higher exponent Signup and view all the answers

What effect does a positive value of c have on the graph of a straight line?

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

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

Set y to 0. Signup and view all the answers

Which condition indicates that a graph has a minimum turning point?

If a > 0. Signup and view all the answers

What happens to the graph of the function when a is negative?

The graph opens downwards. Signup and view all the answers

What is the effect of changing q in the parabola equation $y = ax^2 + q$?

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

How do you find the vertical change represented by the gradient m?

Change in y divided by change in x. Signup and view all the answers

If a < 1, what is the behavior of the graph for the function $y = ax^2 + q$?

The graph flattens or widens. Signup and view all the answers

What characteristic determines the steepness of a straight line graph?

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

When sketching the graph of $y = mx + c$, which characteristic is not necessary?

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

What does a zero value for m indicate in the equation $y = mx + c$?

The line is horizontal. Signup and view all the answers

What is the period of the tangent function?

180° Signup and view all the answers

What happens to the graph of the function when the value of 'a' in the form y = a tan θ + q increases?

The steepness of the graph branches increases. Signup and view all the answers

Which of the following shifts the cosine graph to overlap with the sine graph?

Shift right by 90° Signup and view all the answers

In the equation of a hyperbola, how does the sign of 'a' affect the graph's orientation?

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

What is the domain of the function y = tan θ?

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

How can you determine the vertical shift in the equation y = ax^2 + q of a parabola?

By determining the y-intercept point Signup and view all the answers

What are the x-intercepts of the function y = tan θ within the specified domain?

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

Which method is used to solve for 'a' and 'q' when interpreting a trigonometric graph?

Substituting given points into the equation Signup and view all the answers

Which points are considered asymptotes for the tangent function?

θ = 90° and θ = 270° Signup and view all the answers

What is the domain of the function defined by the equation $y = ax^2 + q$?

All real numbers Signup and view all the answers

For a parabola with $a < 0$, what is the range of the function?

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

What can be determined from the sign of $a$ in the equation $y = ax^2 + q$?

The direction and shape of the graph Signup and view all the answers

What is the axis of symmetry for the function $y = ax^2 + q$?

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

What is the effect of increasing $q$ on the function $y = rac{a}{x} + q$?

Shifts the graph upward Signup and view all the answers

What is the x-intercept of the hyperbolic function defined by $y = rac{a}{x} + q$?

Calculated by setting $y = 0$ Signup and view all the answers

What type of asymptote is represented by the line $y = q$ in hyperbolic functions?

Horizontal asymptote Signup and view all the answers

Which of the following statements about the y-intercept of the function $y = rac{a}{x} + q$ is true?

It is always undefined Signup and view all the answers

For a hyperbola defined by $y = rac{a}{x} + q$ where $a < 0$, in which quadrants does the graph lie?

Second and fourth quadrants Signup and view all the answers

What characteristic is associated with the coordinates of the turning point of the parabola $y = ax^2 + q$?

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

What does the sign of the constant 'a' in an exponential function determine?

Whether the graph curves upwards or downwards Signup and view all the answers

Which of the following statements about the y-intercept of a function is correct?

It is the value of y when x is zero. Signup and view all the answers

What does a positive value of 'q' in an exponential function's equation do to the graph?

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

Which characteristic defines the horizontal asymptote of an exponential function?

It is determined by the value of constant 'q'. Signup and view all the answers

In the sine function, the maximum turning point occurs at which angle?

90° Signup and view all the answers

What effect does a negative value of 'a' have on the graph of the sine function?

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

What is the period of both sine and cosine functions?

360° Signup and view all the answers

Given the function form $y = a an heta + q$, what effect does the value of 'q' have?

It provides vertical shift effects. Signup and view all the answers

Which of the following correctly describes the range of the sine function?

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

Which of the following values of 'b' signifies exponential decay?

0 Signup and view all the answers

Which set includes all negative and positive whole numbers along with zero?

Integers Signup and view all the answers

What defines a rational number?

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

Which symbol represents irrational numbers?

Q' Signup and view all the answers

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

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

What type of numbers are included in the real number system?

Both rational and irrational numbers Signup and view all the answers

Which statement about imaginary numbers is correct?

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

Which type of decimal can be classified as a rational number?

Terminating decimals Signup and view all the answers

What characterizes an irrational number?

It has a non-repeating, non-terminating decimal form. 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

When converting a recurring decimal into a rational number, what is the initial step?

Subtract the original equation from the multiplied equation. Signup and view all the answers

Which of the following represents a surd?

$ ext{sqrt}(5)$ Signup and view all the answers

What is not a characteristic of rational numbers?

They can have non-repeating decimals. Signup and view all the answers

Which of the following is true regarding the decimal forms of irrational numbers?

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

What must be true for a number to be considered a surd?

It cannot simplify to a rational number. Signup and view all the answers

When estimating the value of a surd, what should you first identify?

The nearest perfect powers. Signup and view all the answers

What is the purpose of rounding a number?

To provide a simpler or more manageable form. Signup and view all the answers

What is the first step in simplifying a complex fraction?

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

Which exponent law applies when multiplying two exponents with the same base?

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

How should one simplify the expression $a^{-2}$ using the negative exponent law?

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

When dealing with rational exponents, how would you represent the square root of $a$?

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

Which of the following is true about exponential equations where the variable is in the exponent?

If $a^x = a^y$, then $x = y$. Signup and view all the answers

What does the zero exponent rule state for any non-zero number 'a'?

a^0 = 1 Signup and view all the answers

In simplifying expressions with rational exponents, what is the first step?

Convert to rational exponents if necessary. Signup and view all the answers

What is the outcome of applying the power of a power rule to $(a^{m/n})^{p/q}$?

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

To simplify the expression $rac{a^{5/3}}{a^{2/3}}$, which exponent law do you apply?

Division of Exponents Signup and view all the answers

What is the result of multiplying a monomial $a$ by a binomial $(x + y)$?

$ax + ay$ Signup and view all the answers

Which expression represents the product of two binomials $(ax + b)(cx + d)$?

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

How is the product of a binomial $(A + B)$ and a trinomial $(C + D + E)$ calculated?

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

In factorisation, what process involves breaking down an expression into simpler expressions?

Factorisation Signup and view all the answers

Which identity is used to factorise a difference of two squares?

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

What is the first step for simplifying algebraic fractions?

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

When dividing two fractions, which of the following processes is correct?

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

Which formula 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 does factorising by grouping generally involve?

Grouping terms with common factors and factorising each group Signup and view all the answers

What effect does a positive value of c have on the graph of y = mx + c?

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

What is the general form of a quadratic function?

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

If the gradient m of a line is negative, what can be inferred about the line's slope?

The line falls from left to right. Signup and view all the answers

Where does the y-intercept occur in the equation y = mx + c?

When x = 0. Signup and view all the answers

What happens to the shape of a parabola when the value of a is negative?

The parabola opens downwards. Signup and view all the answers

Which characteristic describes the graph of f(x) = ax^2 + q when a > 0?

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

What is the significance of the turning point in a parabola determined by q?

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

What information can be obtained from the gradient m in a linear function?

The rate of change of y with respect to x. Signup and view all the answers

How can the x-intercept of a linear equation be calculated?

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

What impact does a larger absolute value of a (where a > 1) have on a parabola?

The graph becomes narrower. Signup and view all the answers

What is the first step to solving an exponential equation when both sides can be expressed with the same base?

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

In solving a linear equation, what does it mean to group like terms together?

Combine terms that have the same variable Signup and view all the answers

When factorising a quadratic equation, what is the final form after the factoring process?

Two binomials set equal to zero Signup and view all the answers

What is necessary to solve a system of simultaneous equations with two unknowns?

Two independent equations Signup and view all the answers

What occurs if you divide both sides of an equation by a negative number?

The sign of the inequality switches Signup and view all the answers

What should you do after solving a linear equation?

Check the solution in the original equation Signup and view all the answers

How many solutions does a typical quadratic equation have?

At most two solutions Signup and view all the answers

What is the first step in solving a quadratic equation?

Set it equal to zero Signup and view all the answers

What does isolating the variable mean in linear equations?

Getting the variable alone on one side of the equation Signup and view all the answers

What is the role of logarithms in solving exponential equations?

To isolate the exponent when bases are not easily made the same Signup and view all the answers

What can be concluded about the cosine graph in relation to the sine graph?

The cosine graph can be shifted to the right by 90°. Signup and view all the answers

Which is a characteristic of the tangent function within its domain?

It is undefined at 90° and 270°. Signup and view all the answers

What is the effect of the parameter 'q' in the function $y = a \tan \theta + q$?

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

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

It affects the steepness of the graph branches. Signup and view all the answers

To find the equation of a parabola in the form $y = ax^2 + q$, which of the following is NOT necessary?

The x-intercept to find a. Signup and view all the answers

What determines whether a parabola shown in a sketch is a 'smile' or 'frown' shape?

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

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

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

For the function $y = a \tan \theta + q$, what does the value of the y-intercept represent?

It represents the vertical shift q. Signup and view all the answers

When determining the elements of a hyperbola in the form $y = \frac{a}{x} + q$, what does 'a' control?

The direction and shape of the hyperbola. Signup and view all the answers

What aspect of the sine and cosine graphs can be altered by shifting their graphs?

Their alignment along the y-axis. Signup and view all the answers

What is the vertical shift of the graph for the equation in the form of $y = ax^2 + q$?

Defined by the value of $q$ only Signup and view all the answers

Which describes the range of the function $y = ax^2 + q$ when $a < 0$?

From negative infinity to $q$ Signup and view all the answers

Where is the y-intercept located for functions of the form $y = rac{a}{x} + q$?

Undefined for these functions Signup and view all the answers

What is the horizontal asymptote for the hyperbolic function $y = rac{a}{x} + q$?

The line $y = q$ Signup and view all the answers

For the function $y = ax^2 + q$, how does the sign of $a$ affect the graph?

Indicates the direction of the graph (smile or frown) Signup and view all the answers

What happens to the graph of a hyperbolic function when $q < 0$?

The graph shifts downwards Signup and view all the answers

In the equation $y = ax^2 + q$, what is the turning point of the graph?

At (0, q) Signup and view all the answers

Which of the following represents the domain of the function $y = rac{a}{x} + q$?

Real numbers except zero Signup and view all the answers

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

Lines of the form $y = x + q$ and $y = -x + q$ Signup and view all the answers

Which statement is true regarding the x-intercept of a hyperbolic function $y = rac{a}{x} + q$?

Calculated by setting $y = 0$ Signup and view all the answers

What determines the direction in which the graph of an exponential function curves?

The sign of a Signup and view all the answers

How is the y-intercept of an exponential function found?

By letting x = 0 Signup and view all the answers

What is the effect of a negative value of a in the function y = a sin θ + q?

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

Which statement correctly describes the range of the function y = a cos θ + q when a > 0?

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

What determines the rate of growth or decay in an exponential function?

The value of b Signup and view all the answers

What is the characteristic of the sine function at x = 0°?

It is the y-intercept Signup and view all the answers

How does a positive value of q affect the graph of an exponential function?

It shifts the graph upwards Signup and view all the answers

What is the period of the sine and cosine functions?

360° Signup and view all the answers

Which of the following intercepts corresponds to y = a cos θ + q when a > 0?

(0°, a + q) Signup and view all the answers

What is true regarding the horizontal asymptote of the function y = ab^x + q?

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

What is the first step in solving a system of equations by substitution?

Substitute one equation into the other Signup and view all the answers

What should be done after solving for one variable in elimination?

Substitute the value into the other equation Signup and view all the answers

What represents the solution of simultaneous equations when solved graphically?

The coordinates where the two lines intersect Signup and view all the answers

Which step should follow after reading a word problem?

Determine what needs to be solved Signup and view all the answers

In a linear equation, what happens to the inequality sign when both sides are multiplied by a negative number?

The sign is flipped Signup and view all the answers

What is the purpose of rearranging a literal equation?

To change the subject of the formula Signup and view all the answers

What characteristic defines the slope 'm' in the linear function equation?

It describes the steepness of the line Signup and view all the answers

What is a common first step when solving a linear inequality?

Isolate the variable on one side Signup and view all the answers

When dealing with the area of a circle, what does 'r' represent?

The radius of the circle Signup and view all the answers

What is a key strategy to employ when solving word problems mathematically?

Create equations based on the problem Signup and view all the answers

Which of the following is a characteristic of a surd?

It is a root of a number that cannot be simplified. Signup and view all the answers

What type of decimal can be converted into a rational number?

Terminating decimals Signup and view all the answers

Which of the following examples represents a rational number?

3/4 Signup and view all the answers

Which statement correctly describes an irrational number?

It has a non-terminating, non-repeating decimal expansion. Signup and view all the answers

In rounding off a number, when should you round up?

When the digit after the rounding place is greater than or equal to 5. Signup and view all the answers

Which of the following processes can be used to convert a recurring decimal into a rational number?

Multiply by 10, align decimals, and solve. Signup and view all the answers

Which set of numbers cannot be expressed as fractions with integer numerator and denominator?

Irrational Numbers Signup and view all the answers

When estimating the value of a surd, what should you identify first?

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

What is the main factor that differentiates rational numbers from irrational numbers?

Rational numbers can be written as a fraction of integers. Signup and view all the answers

What is the first step to solve an exponential equation using the method of equating exponents?

Rewrite the equation with the same base Signup and view all the answers

Which method can be used to solve a linear equation effectively?

Expand all brackets Signup and view all the answers

What distinguishes a quadratic equation from a linear equation?

Quadratic equations have a variable raised to the power of 2 Signup and view all the answers

What is a crucial step to verify the correctness of a solution in an equation?

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

How many solutions can a quadratic equation have at most?

Two solutions Signup and view all the answers

When solving simultaneous equations, what is required?

Two independent equations and two variables Signup and view all the answers

What is the primary goal when solving linear equations by elimination?

To isolate one variable completely Signup and view all the answers

When is it appropriate to use logarithms to solve equations?

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

What must be true about the operations performed on an equation?

Both sides must remain balanced Signup and view all the answers

Which of the following is NOT a method for solving quadratic equations?

Setting exponents equal Signup and view all the answers

What is the first step in simplifying complex fractions?

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

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

Multiplication of Exponents Law Signup and view all the answers

What is the outcome when you simplify $rac{a^5}{a^3}$ using exponent laws?

a^2 Signup and view all the answers

What does the expression $(a^m)^n$ simplify to?

a^{mn} Signup and view all the answers

When faced with the expression $rac{a^{5/3}}{a^{2/3}}$, what is the result after simplification?

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

What is the simplified form of $rac{1}{a^{-n}}$ according to the negative exponent law?

a^n Signup and view all the answers

What describes the equation $a^x = a^y$ in relation to exponential equations?

It shows that $x$ must equal $y$ under certain conditions. Signup and view all the answers

How do you apply the laws of exponents to the expression $(ab)^n$?

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

What is true about how to convert roots to fractional exponents?

The square root $, ext{is } a^{1/2}$. Signup and view all the answers

What method is employed to solve exponential equations when both sides can be expressed with the same base?

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

What is the first step in solving a system of linear equations by substitution?

Substituting one variable into the other equation Signup and view all the answers

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

The inequality sign is reversed Signup and view all the answers

In the context of solving word problems mathematically, what is the purpose of translating words into algebraic expressions?

To write equations that represent the problem Signup and view all the answers

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

The slope of the graph Signup and view all the answers

What is the primary procedure when solving an equation to change it into a literal equation?

Rearranging variables to isolate the unknown Signup and view all the answers

What represents the solution of a system of simultaneous equations when solved graphically?

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

What is one important rule to remember when isolating an unknown variable in a literal equation?

Consider the operations connecting the unknown variable Signup and view all the answers

When setting up equations to solve a word problem, what is crucial to identify first?

What is being asked to solve for Signup and view all the answers

What effect does an increasing 'm' have on the graph of the linear function?

The gradient of the graph increases Signup and view all the answers

When solving by elimination, what is the goal?

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

Which set includes all positive integers and zero?

Whole Numbers (N0) Signup and view all the answers

Which of the following best describes irrational numbers?

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

What characterizes integers?

They consist of whole numbers and their negatives. 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

What is the main definition of real numbers?

All rational and irrational numbers. Signup and view all the answers

Which subset of numbers includes solely positive integers starting from 1?

Natural Numbers (N) Signup and view all the answers

What does the variable 'c' represent in the linear equation $y = mx + c$?

The y-intercept Signup and view all the answers

How does increasing the value of 'c' (where c > 0) affect the graph of a linear equation?

The graph shifts vertically upwards Signup and view all the answers

What is the correct representation of the gradient (m) in a linear graph?

The rate of change of y with respect to x Signup and view all the answers

What type of graph is created when the value of 'a' is less than 0 in the quadratic function $y = ax^2 + q$?

Parabolic graph with a maximum point Signup and view all the answers

Which of the following statements is true regarding the effect of 'q' in the parabolic function?

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

What characteristic of a straight line does a negative gradient (m < 0) indicate?

The line falls from left to right Signup and view all the answers

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

All real numbers Signup and view all the answers

What effect does an increase in the value of 'a' (with a > 0) have on the parabola defined by $y = ax^2 + q$?

It narrows the parabola Signup and view all the answers

What two points are primarily used to plot a straight-line graph?

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

In the context of the quadratic functions, what does a positive value of 'a' indicate about the graph?

It has a minimum turning point Signup and view all the answers

What is a trinomial?

An expression with three terms Signup and view all the answers

Which formula represents the multiplication of two linear binomials?

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

What occurs in the process of factorisation?

Breaking down an expression into simpler expressions Signup and view all the answers

Which operation includes finding the product of a binomial and a trinomial?

Multiplying a binomial and a trinomial Signup and view all the answers

What is the purpose of identifying common factors during factorisation?

To simplify the expression Signup and view all the answers

What is the identity for the difference of two squares?

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

Which step is NOT part of simplifying algebraic fractions?

Expanding expressions before simplification Signup and view all the answers

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

It increases the number of terms by one Signup and view all the answers

What is contained in the general procedure for factorising a trinomial?

Generate possible pairs of factors and check Signup and view all the answers

When simplifying the expression $rac{a}{b} imes rac{c}{d}$, what is the result?

$rac{ac}{bd}$ where $b = 0$ or $d = 0$ Signup and view all the answers

What happens to the graph of an exponential function when the value of 'q' is increased?

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

What is the range of the function when 'a' is negative and 'q' is 0 in an exponential function?

Less than 0 Signup and view all the answers

Which of the following describes the effect of a negative 'a' in an exponential function?

The graph shows exponential decay. Signup and view all the answers

What is the y-intercept of the function $y = a imes rac{1}{2}^x + q$ when $x = 0$?

$a + q$ Signup and view all the answers

For the sine function, what is the maximum y-value within one full cycle?

1 Signup and view all the answers

What does the value of 'b' indicate in an exponential function of the form $y = ab^x + q$?

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

In the sine function, what effect does a negative 'a' have on the graph?

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

What is the period of the sine and cosine functions?

360° Signup and view all the answers

Which x-intercept does the sine function have within the domain of 0° to 360°?

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

What is the range of the parabola given by the equation $y = ax^2 + q$ when $a < 0$?

$(- ext{infinity}; q]$ Signup and view all the answers

In the equation $y = ax^2 + q$, what does the variable $a$ determine?

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

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

The function has no y-intercept Signup and view all the answers

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

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

When graphing the function $y = rac{a}{x} + q$, what is the characteristic of its asymptotes?

There is a horizontal asymptote at $y = q$ and a vertical asymptote at $x = 0$ 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 minimum turning point Signup and view all the answers

What happens to the graph when $q < 0$ in the hyperbola $y = rac{a}{x} + q$?

It shifts downwards Signup and view all the answers

For the hyperbolic function $y = rac{a}{x} + q$, what describes the domain?

$ ext{R} ackslash olimits ext{0}$ Signup and view all the answers

How can the x-intercept of the hyperbolic function $y = rac{a}{x} + q$ be determined?

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

Which effect does the sign of $a$ have on the graph of the hyperbolic function $y = rac{a}{x} + q$?

It affects the quadrants where the graph lies Signup and view all the answers

What effect does the parameter 'a' have on the graph of the function $y = a \tan \theta + q$?

It affects the steepness of the graph branches. Signup and view all the answers

Which of the following correctly describes the domain of the function $y = \tan \theta$?

${ \theta : 0° \leq \theta \leq 360°, \theta \neq 90°, 270° }$ Signup and view all the answers

What determines the vertical shift in the equation of the parabola $y = ax^2 + q$?

The parameter 'q'. Signup and view all the answers

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

180° Signup and view all the answers

What does the y-intercept of the function $y = a \tan \theta + q$ equal?

q Signup and view all the answers

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

Examine the sketch and identify the quadrants. Signup and view all the answers

Which of the following equations represents a function with asymptotes at $\theta = 90°$ and $\theta = 270°$?

$y = a \tan \theta + q$ Signup and view all the answers

In the context of graphing, how is the value of 'a' interpreted for the equation of a parabola $y = ax^2 + q$?

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

What are the x-intercepts of the function $y = \tan \theta$ within the interval $0° \leq \theta \leq 360°$?

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

When interpreting trigonometric graphs, which of the following is crucial in determining the effects of 'q'?

The vertical shifts of the graph. 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

Which statement about irrational numbers is correct?

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

What do rational numbers include?

Numbers that can be expressed as fractions Signup and view all the answers

Which of the following is NOT considered a real number?

i Signup and view all the answers

Which of the following sets includes both negative and positive whole numbers?

Integers (Z) Signup and view all the answers

Which characteristic defines real numbers?

Includes both rational and irrational numbers Signup and view all the answers

What is a trinomial?

An expression with three terms Signup and view all the answers

What is the main purpose of factorisation?

To break down an expression into simpler expressions that can multiply to give the original Signup and view all the answers

When multiplying two binomials, which term is not included in the result?

The sum of coefficients only Signup and view all the answers

Which of the following 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 the correct procedure for multiplying a binomial and a trinomial?

Multiply each term of the binomial by each term of the trinomial once Signup and view all the answers

When simplifying algebraic fractions, what should be done first?

Factorise the numerator and denominator to identify common factors Signup and view all the answers

Which of the following is a valid expression for multiplying a monomial by a binomial?

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

What does a coefficient represent in a term?

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

Which identity should be used for the difference of two squares?

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

What is a characteristic of rational numbers?

Can be expressed in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$ Signup and view all the answers

Which of the following best describes an irrational number?

Has a decimal form that is non-repeating and non-terminating Signup and view all the answers

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

Leave the last digit unchanged Signup and view all the answers

What is the primary purpose of estimating surds?

To approximate their values using perfect squares or cubes Signup and view all the answers

What happens to a digit when rounding off if it is followed by another digit that is 9?

It becomes 0 and the preceding digit increases by 1 Signup and view all the answers

Which of the following statements about surds is true?

Surds are always of the form $\sqrt[n]{a}$ where $a$ cannot be simplified Signup and view all the answers

Which of the following describes a terminating decimal?

Can be expressed as a fraction of integers Signup and view all the answers

What action is required when converting a recurring decimal into a rational number?

Multiply by a power of 10 aligning the recurring digits Signup and view all the answers

What are the key components of a mathematical expression?

Terms, expressions, coefficients, and exponents Signup and view all the answers

What type of decimal numbers include repeating patterns?

Rational numbers Signup and view all the answers

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

The steepness of the line Signup and view all the answers

What effect does a positive value of 'c' have on the graph of a straight line?

The graph shifts vertically upwards Signup and view all the answers

How is the y-intercept determined in a straight line equation?

By letting x equal 0 Signup and view all the answers

What characterizes a parabolic function in the form of $y = ax^2 + q$?

Its shape changes based on the value of 'a' Signup and view all the answers

What does a negative value of 'a' indicate about the graph of a quadratic function?

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

What is the impact of having 'q' greater than zero on the graph of a quadratic function?

The turning point shifts upwards by 'q' units Signup and view all the answers

What is the relationship between the gradient 'm' and the steepness of a line?

A negative 'm' means a downward line Signup and view all the answers

How does the value of 'c' affect the position of the graph concerning the y-axis?

It defines where the graph cuts the y-axis Signup and view all the answers

Which of these statements is true regarding the range of a linear function?

The range is all real numbers Signup and view all the answers

What is indicated by a gradient 'm' that is equal to zero in a straight line graph?

There is no change in the y-values Signup and view all the answers

What is the primary method used when the bases of an exponential equation can be made the same?

Setting the Exponents Equal Signup and view all the answers

How many solutions can a linear equation typically have?

One Signup and view all the answers

What is the first step in simplifying a complex fraction?

Rewrite the division as multiplication by the reciprocal Signup and view all the answers

What is a crucial step to take after solving an equation?

Check for Extraneous Solutions Signup and view all the answers

What does the law of exponents state for multiplying two expressions with the same base?

You add the exponents Signup and view all the answers

Which of the following is a necessary condition for balancing an equation?

Both sides must undergo the same operation Signup and view all the answers

Which expression correctly represents raising a quotient to a power?

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

In which form should a quadratic equation be rewritten for solving?

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

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

Three Signup and view all the answers

In simplifying $a^{-n}$, what is the result using the negative exponent law?

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

How can the expression $a^{5/3} / a^{2/3}$ be simplified?

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

What is the first step in solving linear equations?

Expand All Brackets Signup and view all the answers

Which of the following is a correct application of the power of a power exponent law?

(a^{m})^{n} = a^{mn} Signup and view all the answers

What does solving a quadratic equation often require?

Factorisation Signup and view all the answers

What is an outcome when a quadratic equation is factorised?

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

What is the purpose of using prime factorization in the simplification of exponential expressions?

To ensure all terms are written with the same base Signup and view all the answers

Which of the following statements about rational exponents is true?

Rational exponents follow the same laws as integer exponents Signup and view all the answers

What is the role of substitution in solving simultaneous equations?

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

What is the first step in solving an exponential equation such as $2^x = 8$?

Change the base on the right side Signup and view all the answers

What is the range of a parabolic graph when the coefficient $a$ is less than zero?

(-\infty; q] Signup and view all the answers

What determines the direction of a parabolic graph of the form $y = ax^2 + q$?

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

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

(0; q) Signup and view all the answers

What is the first step in solving a system of equations using substitution?

Substitute one variable into the second equation. Signup and view all the answers

What is the effect of changing the value of 'm' in the linear function equation $y = mx + c$?

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

Which of the following statements is true about hyperbolic functions of the form $y = \frac{a}{x} + q$?

They are undefined for $x = 0$. Signup and view all the answers

When applying the elimination method to solve equations, what is primarily aimed for?

To make the coefficients of one variable the same in both equations. Signup and view all the answers

What is the horizontal asymptote of the hyperbolic function $y = \frac{a}{x} + q$?

y = q Signup and view all the answers

Which characteristic of a parabola is always true regardless of the values of $a$ and $q$?

The domain is all real numbers. Signup and view all the answers

What determines the solution when solving simultaneous equations graphically?

The coordinates of the point at which the two graphs intersect. Signup and view all the answers

What does it mean to solve a literal equation when changing the subject of the formula?

To isolate a specific variable on one side of the equation. Signup and view all the answers

When sketching the graph of a hyperbolic function $y = \frac{a}{x} + q$, what represents a vertical shift?

Changing the value of $q$ Signup and view all the answers

What is the axis of symmetry for the function $y = ax^2 + q$?

x = 0 Signup and view all the answers

When solving linear inequalities, what should be done when dividing by a negative number?

Switch the inequality sign. Signup and view all the answers

In the problem-solving strategy, what should be done after determining what to solve for?

Assign a variable to the unknown quantity. Signup and view all the answers

Which statement correctly describes the x-intercepts of the function $y = \frac{a}{x} + q$?

They are found by setting $y = 0$. Signup and view all the answers

Which method can be used to solve a system of equations with multiple variables?

Combinations of substitution and elimination methods. Signup and view all the answers

What does the term 'turning point' refer to in the context of parabolic functions?

The maximum or minimum point of the graph Signup and view all the answers

How do you rearrange a literal equation to solve for a particular variable?

By isolating the variable from constants and coefficients. Signup and view all the answers

What is a characteristic of linear inequalities compared to linear equations?

They may have no solutions or infinitely many solutions. Signup and view all the answers

What transformation occurs to the cosine graph to overlap with the sine graph?

It is shifted to the right by 90°. Signup and view all the answers

What is the period of the tangent function?

180° Signup and view all the answers

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

It shifts the graph up. 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 of these points is an x-intercept of the tangent function within its domain?

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

Which equation represents a parabola?

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

What determines the direction of a hyperbola in the equation $y = \frac{a}{x} + q$?

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

To interpret the graph of a trigonometric function, which point is most critical for determining the vertical shift?

The y-intercept. Signup and view all the answers

Which of the following conditions would lead to a vertical asymptote in the tangent function?

Angles equal to 90° or 270°. Signup and view all the answers

What is the primary goal when determining the equation of a parabola?

To use the y-intercept to solve for 'q'. Signup and view all the answers

What is the effect of a positive constant 'a' in an exponential function on the graph's curvature?

It causes the graph to curve upwards. Signup and view all the answers

What is the vertical shift when the constant 'q' is less than zero in an exponential function?

The graph moves down by q units. Signup and view all the answers

Which statement accurately describes the intercepts of the function defined as y = a sin θ + q?

The y-intercept equals q. Signup and view all the answers

For the sine function, where does the maximum turning point occur when no vertical shifts are present?

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

What is the characteristic of the period for both sine and cosine functions?

The period is 360°. Signup and view all the answers

How does the constant 'b' in an exponential function determine the type of function it is?

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

What type of asymptote does an exponential function of the form y = ab^x + q have?

Single horizontal asymptote at y = q. Signup and view all the answers

What happens to the sine function when 'a' is less than zero?

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

Which of the following statements is true about the x-intercepts of the cosine function?

They are exclusively at (90°, 0) and (270°, 0). Signup and view all the answers

In the function y = a cos θ + q, what does |a| > 1 signify?

Vertical stretch. Signup and view all the answers

Gr 10 Math June P1 Easy

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Questions and Answers

Which set includes only positive integers starting from 1?

Which of the following sets includes zero?

What distinguishes rational numbers from irrational numbers?

Which of the following represents irrational numbers?

What is included in the set of real numbers?

Which of the following statements about imaginary numbers is true?

What is a rational number?

Which of the following is a characteristic of irrational numbers?

How can you convert a terminating decimal into a rational number?

What does the process of rounding depend on?

Which of these is NOT a surd?

What is the correct order of the number hierarchy starting from natural numbers?

When estimating a surd, what should you compare to find its value?

What happens when rounding a digit that is 9?

Which statement regarding decimals is true?

What is a monomial?

Which of the following represents the product of two linear binomials?

What is the result when a trinomial is multiplied by a binomial?

What is factorisation?

What is the identity for the difference of two squares?

What technique is used when factorising by grouping?

In the simplification of fractions, what is the first step?

What is the product of $x^3 + y^3$ using cube identities?

Which expression correctly represents the addition of fractions with the same denominator?

Which of the following is NOT a term in a binomial?

What is the result of simplifying the expression $\frac{a^5}{a^3}$ using exponent laws?

Which expression correctly represents the zero exponent rule?

How do you express the square root of $a$ in terms of rational exponents?

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

What is the correct simplification for the expression $\left(\frac{a}{b}\right)^{2}$?

Using the laws of exponents, what is the result of $a^{3/4} \times a^{1/2}$?

Which expression represents applying the laws of exponents for $(ab)^{3}$?

What is the result of $a^{-2}$ using the negative exponent law?

What is the main condition for the laws of exponents to apply?

How can the expression $\frac{a^{5/3}}{a^{2/3}}$ be simplified?

What is the first step in solving a word problem mathematically?

What should you do after solving an equation algebraically?

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

Which method can be used to solve systems of equations graphically?

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

To isolate an unknown variable in a literal equation, what should you first identify?

When solving by elimination, what is the primary goal?

If two equations have the same slope but different y-intercepts, what does that indicate about their graphs?

In the equation for the area of a circle, what does the variable 'r' represent?

What strategy can be employed to solve linear inequalities?

What method can be used to solve exponential equations when both sides can be expressed with the same base?

Which of the following describes a linear equation?

What is the first step in solving a linear equation?

When solving a quadratic equation in the form of $ax^2 + bx + c = 0$, what is the purpose of factorising?

How many solutions does a quadratic equation typically have?

In the process of solving simultaneous equations, what is often a key first step?

What is crucial to check after solving any equation?

Which statement is true about the relationship between operations performed on both sides of an equation?

Which method might be used to facilitate solving a linear equation?

What defines a quadratic equation compared to a linear equation?

What effect does a positive value of c have on the graph of a straight line?

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

Which condition indicates that a graph has a minimum turning point?

What happens to the graph of the function when a is negative?

What is the effect of changing q in the parabola equation $y = ax^2 + q$?

How do you find the vertical change represented by the gradient m?

If a < 1, what is the behavior of the graph for the function $y = ax^2 + q$?

What characteristic determines the steepness of a straight line graph?

When sketching the graph of $y = mx + c$, which characteristic is not necessary?

What does a zero value for m indicate in the equation $y = mx + c$?

What is the period of the tangent function?

What happens to the graph of the function when the value of 'a' in the form y = a tan θ + q increases?

Which of the following shifts the cosine graph to overlap with the sine graph?

In the equation of a hyperbola, how does the sign of 'a' affect the graph's orientation?

What is the domain of the function y = tan θ?

How can you determine the vertical shift in the equation y = ax^2 + q of a parabola?

What are the x-intercepts of the function y = tan θ within the specified domain?

Which method is used to solve for 'a' and 'q' when interpreting a trigonometric graph?

Which points are considered asymptotes for the tangent function?

What is the domain of the function defined by the equation $y = ax^2 + q$?

For a parabola with $a < 0$, what is the range of the function?

To simplify the expression $rac{a^{5/3}}{a^{2/3}}$, which exponent law do you apply?