Gr 10 Math June P1 Medium
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Questions and Answers

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

  • $ ext{e}$ (correct)
  • $0.5$
  • $-3$
  • $ rac{4}{5}$

Which category do the numbers $0$ and $1$ belong to?

  • Whole Numbers (correct)
  • Irrational Numbers
  • Natural Numbers
  • Imaginary Numbers

What is the main feature of rational numbers?

  • They have infinite decimal expansions.
  • They include positive and negative values only.
  • They can be expressed as the fraction of two integers. (correct)
  • They are always integers.

Which of the following sets does not include the number $-5$?

<p>Natural Numbers (B)</p> Signup and view all the answers

Which of the following represents the set of integers?

<p>$ ext{Z}$ (B)</p> Signup and view all the answers

What differentiates real numbers from imaginary numbers?

<p>Real numbers have a defined place on the number line, while imaginary numbers do not. (D)</p> Signup and view all the answers

What is the highest exponent of the variable in a linear equation?

<p>1 (D)</p> Signup and view all the answers

How many solutions can a linear equation have at most?

<p>One solution (A)</p> Signup and view all the answers

What is the first step in solving a linear equation?

<p>Expand all brackets (D)</p> Signup and view all the answers

Which of the following methods is NOT used to solve quadratic equations?

<p>Substitution (C)</p> Signup and view all the answers

When solving quadratic equations, what form must the equation be in?

<p>ax^2 + bx + c = 0 (D)</p> Signup and view all the answers

What is the method of elimination primarily used for in simultaneous equations?

<p>To eliminate one variable (A)</p> Signup and view all the answers

If a quadratic equation has no solutions, what can be said about its graph?

<p>It does not intersect the x-axis. (C)</p> Signup and view all the answers

What should be done after solving for one variable in simultaneous equations by substitution?

<p>Substitute back into the first equation (D)</p> Signup and view all the answers

What operation must be performed on both sides of an equation to maintain balance?

<p>Any operation (A)</p> Signup and view all the answers

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

<p>Rewrite the equation (D)</p> Signup and view all the answers

Which statement accurately describes rational numbers?

<p>They can be expressed as fractions with a non-zero denominator. (D)</p> Signup and view all the answers

What characterizes an irrational number?

<p>It has a non-repeating, non-terminating decimal expansion. (B)</p> Signup and view all the answers

Which of the following is a correct way to estimate the value of the surd \( ext{√5}\)?

<p>By determining that \( ext{√5}\) is greater than 2 but less than 3. (A)</p> Signup and view all the answers

How can a terminating decimal be converted into a rational number?

<p>By writing it as a fraction where the denominator is a power of 10. (D)</p> Signup and view all the answers

Which of the following best illustrates the difference between rational and irrational decimal forms?

<p>0.333… is rational, while 0.101001001… is irrational. (A)</p> Signup and view all the answers

Which of the following statements about rounding off decimal numbers is correct?

<p>If the next digit is less than 5, you leave the rounding digit unchanged. (A)</p> Signup and view all the answers

In the expression 5x^2 + 3x - 2, which term is the coefficient?

<p>5 (C)</p> Signup and view all the answers

What defines a surd?

<p>It is the n-th root of a number that cannot be simplified to a rational number. (B)</p> Signup and view all the answers

Which of the following represents a method to convert recurring decimals to rational numbers?

<p>Identify and align the recurring part by multiplying with powers of 10. (C)</p> Signup and view all the answers

What does the gradient "m" represent in the equation of a straight-line graph?

<p>The steepness of the line (A)</p> Signup and view all the answers

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

<p>The value of y when x equals zero (D)</p> Signup and view all the answers

What effect does a negative value of "a" have on a parabolic graph?

<p>It opens downwards with a maximum point (C)</p> Signup and view all the answers

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

<p>All real numbers (A)</p> Signup and view all the answers

Which statement is true about the effect of "q" on the parabolic graph?

<p>It causes a vertical shift of the graph (B)</p> Signup and view all the answers

Which statement correctly describes the effect of increasing the absolute value of "a" on the parabolic graph?

<p>The graph becomes narrower (A)</p> Signup and view all the answers

In the expression $m = \frac{\text{change in } y}{\text{change in } x}$, what does "change in y" represent?

<p>The vertical rise between two points on the line (D)</p> Signup and view all the answers

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

<p>[q, \infty) (D)</p> Signup and view all the answers

Which characteristic must be calculated to draw a straight line using the gradient and y-intercept method?

<p>The y-intercept and one more point (B)</p> Signup and view all the answers

If a quadratic equation has a value of $q < 0$, where is the turning point located?

<p>Below the x-axis (D)</p> Signup and view all the answers

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

<p>Read the whole question. (A)</p> Signup and view all the answers

What can be concluded when two graphs of linear equations intersect?

<p>The coordinates of the intersection point represent the solution to the system. (B)</p> Signup and view all the answers

What effect does increasing the value of $m$ have on the graph of the function $y = mx + c$?

<p>The slope of the graph increases. (C)</p> Signup and view all the answers

When solving a linear inequality, what happens to the inequality sign if both sides are divided by a negative number?

<p>The inequality sign is reversed. (D)</p> Signup and view all the answers

In the equation of a circle $A = \pi r^2$, what variable is represented by $A$?

<p>The area of the circle. (A)</p> Signup and view all the answers

What does the value of $c$ affect in the linear equation $y = mx + c$?

<p>The y-intercept of the graph. (C)</p> Signup and view all the answers

What is meant by a literal equation?

<p>An equation with several letters or variables. (D)</p> Signup and view all the answers

Which of the following conditions would indicate that a system of equations has no solutions?

<p>The lines are parallel. (C)</p> Signup and view all the answers

Which action is inappropriate when solving literal equations?

<p>Distributing terms improperly. (D)</p> Signup and view all the answers

In the inequality $2x + 2 \leq 1$, how would you solve for $x$?

<p>Subtract 2 from both sides and divide by 2. (A)</p> Signup and view all the answers

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

<p>It influences the direction and width of the parabola. (D)</p> Signup and view all the answers

How can the vertical shift of a trigonometric graph be determined?

<p>By evaluating the value of 'q'. (B)</p> Signup and view all the answers

Where are the asymptotes for the tangent function located?

<p>At $θ = 90°$ and $θ = 270°$. (B)</p> Signup and view all the answers

What does the domain of a function represent?

<p>The set of all possible x values. (C)</p> Signup and view all the answers

In the equation of a hyperbola, what does the term 'q' signify?

<p>The vertical shift of the graph. (A)</p> Signup and view all the answers

When analyzing the graph of a function, how can x-intercepts be found?

<p>By setting y equal to zero. (D)</p> Signup and view all the answers

Which equation represents the general form of a sine function?

<p>y = a ext{sin} heta + q (B)</p> Signup and view all the answers

What is necessary to solve for 'a' in a hyperbola's equation?

<p>Substituting given points into the equation. (D)</p> Signup and view all the answers

What indicates a vertical shift in the graph of a tangent function?

<p>The value of 'q'. (A)</p> Signup and view all the answers

To determine the range of a parabolic function, which method is applicable?

<p>Analyzing the direction of opening of the parabola. (D)</p> Signup and view all the answers

What is the range of the function if the coefficient $a$ is less than zero?

<p>(-∞; q] (B)</p> Signup and view all the answers

What do the x-intercepts of the function $y = ax^2 + q$ represent?

<p>Values of $x$ for which $y$ equals zero. (B)</p> Signup and view all the answers

Which characteristic is true if the graph of $f(x) = ax^2 + q$ is a 'smile'?

<p>The axis of symmetry is $x = 0$. (A)</p> Signup and view all the answers

In the function $y = rac{a}{x} + q$, what is true about the vertical asymptote?

<p>It occurs at the y-axis, or $x = 0$. (A)</p> Signup and view all the answers

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

<p>It results in vertical shifts of the graph. (A)</p> Signup and view all the answers

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

<p>It does not exist since the function is undefined at $x = 0$. (D)</p> Signup and view all the answers

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

<p>{x: $x eq 0$, $x ext{ is a real number}$} (B)</p> Signup and view all the answers

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

<p>A line defined by $y = q$. (B)</p> Signup and view all the answers

How does the sign of $a$ affect the graph of the exponential function $y = ab^x + q$?

<p>It influences whether the graph increases or decreases. (A)</p> Signup and view all the answers

Which statement is true regarding the range of the exponential function $y = ab^x + q$ when $a > 0$?

<p>The range is $(q; ext{∞})$. (C)</p> Signup and view all the answers

What happens to the horizontal asymptote of the function when $q$ is decreased?

<p>It decreases vertically. (B)</p> Signup and view all the answers

Which statement about the effects of the coefficient $a$ in the function $y = a an heta + q$ is true?

<p>It causes a reflection over the y-axis if $a &lt; 0$. (B)</p> Signup and view all the answers

What is the effect of a coefficient $b$ where $0 < b < 1$ in an exponential function?

<p>The function represents exponential decay. (D)</p> Signup and view all the answers

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

<p>$[0°, 360°]$ (C)</p> Signup and view all the answers

Where do the x-intercepts of the cosine function occur?

<p>At $(180°, 0)$ and $(270°, 0)$ (B)</p> Signup and view all the answers

What distinguishes the range of the function $y = a an heta + q$ from the range of the sine function?

<p>It can take on all real values. (A)</p> Signup and view all the answers

For the sine function, which point signifies the maximum turning point?

<p>$(90°, 1)$ (B)</p> Signup and view all the answers

What is the vertical shift effect when $q$ is greater than zero in a cosine function?

<p>The graph shifts upward by $q$ units. (A)</p> Signup and view all the answers

What does the value of $|a|$ represent in the context of the sine function?

<p>The amplitude of the function. (D)</p> Signup and view all the answers

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

<p>A(C + D + E) + B(C + D + E) (C)</p> Signup and view all the answers

Which expression correctly represents the difference of two squares?

<p>(a + b)(a - b) (A)</p> Signup and view all the answers

What is the first step in factorizing a trinomial in the form of extbf{ax^2 + bx + c}?

<p>Identify the common factors. (D)</p> Signup and view all the answers

When simplifying the algebraic fraction extbf{(ax + b)/(cx + d)}, what must you do first?

<p>Factorize the numerator and denominator. (C)</p> Signup and view all the answers

What is the outcome of multiplying the monomial extbf{a} by the binomial extbf{(x + y)}?

<p>ax + ay (B)</p> Signup and view all the answers

Which operation represents the simplification of the algebraic fraction extbf{(3x^2)/(6x)}?

<p>x/2 (A)</p> Signup and view all the answers

In multiplying two binomials extbf{(ax + b)(cx + d)}, what term would be calculated to represent the coefficient of $x^2$?

<p>ac (D)</p> Signup and view all the answers

Which of the following correctly identifies a trinomial?

<p>x^2 + 2x + 1 (C)</p> Signup and view all the answers

What is the result of the operation extbf{(x + 2)(x + 3)} upon expansion?

<p>x^2 + 5x + 6 (B)</p> Signup and view all the answers

When performing multiplication of fractions, what expression shows the result of $ rac{2}{3} imes rac{4}{5}$?

<p>$ rac{8}{15}$ (D)</p> Signup and view all the answers

What is the result of applying the zero exponent law to the base 7?

<p>1 (B)</p> Signup and view all the answers

If you have the expression rac{a^5}{a^2}, what is the simplified form?

<p>a^3 (A)</p> Signup and view all the answers

Which of the following represents the application of raising a product to a power?

<p>(xy)^n = x^n y^n (A)</p> Signup and view all the answers

How would you simplify the expression a^{3/2} imes a^{1/2}?

<p>a^4 (B)</p> Signup and view all the answers

What is the first step in solving an exponential equation like 2^x = 16?

<p>Convert 16 to a power of 2 (C)</p> Signup and view all the answers

When applying the negative exponent rule to a^n, what is the result?

<p>1/a^n (A)</p> Signup and view all the answers

If 3^x = 81, what is the value of x?

<p>4 (A)</p> Signup and view all the answers

Which method can be used when the bases of an exponential equation are difficult to match?

<p>Use logarithms (B)</p> Signup and view all the answers

How can rational exponents be expressed in terms of roots?

<p>a^{m/n} = rac{ oot{n}{a}^m} (C)</p> Signup and view all the answers

What is the simplified form of rac{(2^3)(2^2)}{2^5}?

<p>2^0 (B)</p> Signup and view all the answers

Which statement about integer representation is accurate?

<p>All integers are rational numbers but not all rational numbers are integers. (B), Integers can be expressed as fractions with a denominator of 1. (C)</p> Signup and view all the answers

What is the outcome when rounding the number 2.675 to two decimal places?

<p>2.68 (B)</p> Signup and view all the answers

Which decimal representation indicates a rational number?

<p>0.333... (A), 0.123123123... (C)</p> Signup and view all the answers

Which method can be used to convert the recurring decimal 0.666... into a rational number?

<p>Write as 2/3 by defining it as x. (A)</p> Signup and view all the answers

Which of the following correctly describes surds?

<p>Surds are always irrational numbers. (D)</p> Signup and view all the answers

In estimating a surd like $ ext{√12}$, which perfect squares are nearest?

<p>3 and 4 (D)</p> Signup and view all the answers

Which of the following is a characteristic of rational numbers?

<p>They can always be expressed in the form ${ rac{a}{b}}$. (D)</p> Signup and view all the answers

If the number $x = 4.7825$ is rounded to three decimal places, what will be the result?

<p>4.79 (D)</p> Signup and view all the answers

Which property distinguishes irrational numbers from rational numbers?

<p>Irrational numbers have non-repeating, non-terminating decimals. (C)</p> Signup and view all the answers

Which of the following correctly explains how to find the coefficient in an expression?

<p>The coefficient is the numerical factor that multiplies the variable. (C)</p> Signup and view all the answers

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

<p>Two solutions (A)</p> Signup and view all the answers

Which step is NOT included in the method for solving linear equations?

<p>Group unlike terms together (B)</p> Signup and view all the answers

What must be true for an equation to be valid after performing operations?

<p>Both sides must remain equal (A)</p> Signup and view all the answers

When solving quadratic equations, what must the equation be in the form of?

<p>$ax^2 + bx + c = 0$ (C)</p> Signup and view all the answers

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

<p>Identify the simpler equation (C)</p> Signup and view all the answers

What happens after isolating a variable when using the substitution method?

<p>The other variable is plugged back into the original equation (D)</p> Signup and view all the answers

In which of the following methods do you eliminate a variable by making coefficients the same?

<p>Elimination (C)</p> Signup and view all the answers

What indicates a quadratic equation can have no solutions?

<p>The discriminant is negative (C)</p> Signup and view all the answers

Which algebraic method is specifically included in solving quadratic equations?

<p>Factorisation (B)</p> Signup and view all the answers

What is true about the solutions of a simultaneous equation system with two equations and two variables?

<p>They represent the intersection point on a graph (D)</p> Signup and view all the answers

What is a monomial?

<p>An expression with one term (B)</p> Signup and view all the answers

Which of the following correctly represents the product of a binomial and a trinomial?

<p>(A + B)(C + D + E) = A(C + D + E) + B(C + D + E) (A)</p> Signup and view all the answers

What is the purpose of factorization?

<p>To break down an expression into simpler expressions (C)</p> Signup and view all the answers

Which identity is used for factoring a difference of two squares?

<p>a^2 - b^2 = (a + b)(a - b) (C)</p> Signup and view all the answers

What does the term 'coefficient' refer to in an expression?

<p>The numerical factor in a term (A)</p> Signup and view all the answers

Which method can be used to simplify a complex fraction?

<p>Factorise all terms in the numerator and denominator (B)</p> Signup and view all the answers

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

<p>Identify any common factors (D)</p> Signup and view all the answers

What is the product of two binomials described by the formula (ax + b)(cx + d)?

<p>acx^2 + bcx + adx + bd (C)</p> Signup and view all the answers

What is the result when simplifying the fraction ( \frac{a}{b} \div \frac{c}{d} )?

<p>( \frac{a}{b} \times \frac{d}{c} ) (D)</p> Signup and view all the answers

What does the sum of cubes identity express?

<p>x^3 + y^3 = (x + y)(x^2 - xy + y^2) (B)</p> Signup and view all the answers

What happens to the value of an exponent when a number is raised to the power of zero?

<p>It equals one (C)</p> Signup and view all the answers

Which of the following correctly simplifies the expression $\frac{a^{3}}{a^{5}}$?

<p>$a^{-2}$ (A)</p> Signup and view all the answers

When combining the expressions $a^{2} \times a^{3}$, what is the resulting exponent?

<p>$a^{5}$ (A)</p> Signup and view all the answers

How do you express the square root of a number using exponents?

<p>$a^{1/2}$ (A)</p> Signup and view all the answers

Which property of exponents allows you to write $(ab)^{n}$ as $a^{n}b^{n}$?

<p>Power of a Product Property (C)</p> Signup and view all the answers

What does a negative exponent indicate?

<p>It indicates reciprocal in the denominator (D)</p> Signup and view all the answers

What is the result of simplifying the expression $\left( \frac{a}{b} \right)^{3}$?

<p>$\frac{a^{3}}{b^{3}}$ (B)</p> Signup and view all the answers

Which of the following is required to solve exponential equations when the bases are not the same?

<p>Use logarithms (D)</p> Signup and view all the answers

What is the first step in simplifying an expression with rational exponents?

<p>Convert roots to fractional exponents (B)</p> Signup and view all the answers

Which strategy can be used to solve exponential equations of the form $a^x = a^y$?

<p>Equate the exponents (B)</p> Signup and view all the answers

What is the first step in solving a set of word problems mathematically?

<p>Read the whole question. (C)</p> Signup and view all the answers

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

<p>The inequality sign is flipped. (B)</p> Signup and view all the answers

What does the value of 'c' in the linear equation $y = mx + c$ determine?

<p>The y-intercept of the graph. (A)</p> Signup and view all the answers

What is a literal equation primarily used for?

<p>To represent a relationship among various variables. (B)</p> Signup and view all the answers

What graphical representation is used to solve simultaneous equations?

<p>The intersection of the graphs. (D)</p> Signup and view all the answers

In the equation $v = \frac{D}{t}$, what does 'v' represent?

<p>Speed. (C)</p> Signup and view all the answers

How should an unknown variable in a literal equation be isolated?

<p>By performing the opposite operation of what it is joined by. (B)</p> Signup and view all the answers

If a linear function has a positive gradient, what can be inferred about its graph's direction?

<p>It slopes upwards from left to right. (A)</p> Signup and view all the answers

When rearranging the formula for the area of a circle, what is a necessary consideration?

<p>Understanding how the variables are related. (D)</p> Signup and view all the answers

In the inequality $\frac{3x + 1}{2} \geq 4$, what must be done first to isolate 'x'?

<p>Multiply both sides by 2. (D)</p> Signup and view all the answers

How does the sign of the coefficient 'a' in the equation of a parabola affect its graph?

<p>It indicates whether the graph opens upwards or downwards. (D)</p> Signup and view all the answers

What is the value of the y-intercept in the equation of a straight line represented by the function $y = mx + c$?

<p>The value of 'c' when $x = 0$. (C)</p> Signup and view all the answers

If the value of 'c' in the equation $y = mx + c$ is less than zero, what can be stated about the y-intercept?

<p>It lies below the x-axis. (B)</p> Signup and view all the answers

What impact does increasing the value of 'q' have on the parabola defined by $y = ax^2 + q$?

<p>It shifts the graph upward. (C)</p> Signup and view all the answers

What is the range of the function represented by $y = ax^2 + q$ when $a < 0$ and $q < 0$?

<p>[−∞; q) (D)</p> Signup and view all the answers

If a linear graph has a positive gradient 'm' while having a y-intercept 'c' that is equal to zero, what does this imply about the graph?

<p>The line passes through the origin and rises as it moves from left to right. (D)</p> Signup and view all the answers

What happens to the shape of a parabola when the absolute value of 'a' becomes larger than 1?

<p>It becomes narrower. (D)</p> Signup and view all the answers

In the gradient formula $m = \frac{\text{change in } y}{\text{change in } x}$, what does 'change in x' refer to?

<p>The horizontal distance between two points on the graph. (A)</p> Signup and view all the answers

If a parabola described by $y = ax^2 + q$ has a minimum turning point, what can be inferred about the values of 'a' and 'q'?

<p>a must be greater than 0 and q can be any real number. (B)</p> Signup and view all the answers

Which set includes all whole numbers?

<p>Whole Numbers (B)</p> Signup and view all the answers

What defines a rational number?

<p>Any number that can be expressed as a fraction with a non-zero denominator (D)</p> Signup and view all the answers

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

<p>$ rac{5}{ ext{√2}}$ (B)</p> Signup and view all the answers

Which statement correctly identifies the set of integers?

<p>Includes all whole numbers and their negative counterparts (C)</p> Signup and view all the answers

What distinguishes real numbers from imaginary numbers?

<p>Real numbers cannot have negative square roots, whereas imaginary numbers do (B)</p> Signup and view all the answers

Which set does not include the number zero?

<p>Natural Numbers (A)</p> Signup and view all the answers

What is the effect of the coefficient 'a' in the equation of a trigonometric function?

<p>It affects the amplitude and reflection of the graph. (C)</p> Signup and view all the answers

How can the parameter 'q' in the equation of a parabola be determined?

<p>Using the y-intercept point to solve for it. (B)</p> Signup and view all the answers

Where are the asymptotes of the tangent function located?

<p>At $ heta = 90°$ and $ heta = 270°$. (A)</p> Signup and view all the answers

What is the behavior of the graph when the coefficient 'a' is negative for an exponential function with base 'b' greater than 1?

<p>The graph will curve downwards. (A)</p> Signup and view all the answers

For the function defined as $y = a an \theta + q$, what effect does a positive 'q' have on the graph?

<p>It shifts the graph vertically upwards by 'q' units. (D)</p> Signup and view all the answers

What determines the width and direction of a parabola?

<p>The absolute value of 'a' only. (B)</p> Signup and view all the answers

To determine the equation of a hyperbola, what initial step should be taken?

<p>Examine the quadrants where the curves lie. (A)</p> Signup and view all the answers

What forms the horizontal asymptote for exponential functions such as $y = ab^x + q$?

<p>The line $y = q$. (B)</p> Signup and view all the answers

What is the domain of the function defined by the equation $y = a an heta + q$?

<p>$ heta$ cannot equal 90° or 270°. (B)</p> Signup and view all the answers

How does the value of 'b' affect the behavior of the function $y = ab^x$?

<p>It defines whether the function represents growth or decay. (D)</p> Signup and view all the answers

What is the range of the sine function $y = a ext{ sin } \theta + q$ when $a > 0$?

<p>[q - a, q + a] (A)</p> Signup and view all the answers

What method is used to determine the value of 'a' in the equation of a parabola?

<p>Substituting another given point into the equation. (A)</p> Signup and view all the answers

In the functions of the form $y = a ext{ cos } \theta + q$, what is the effect of applying $a < 0$?

<p>It causes a reflection about the x-axis. (C)</p> Signup and view all the answers

What do the y-intercepts of graph functions allow you to find?

<p>The vertical shift and value of 'q'. (D)</p> Signup and view all the answers

In the context of interpreting graphs, what is calculated to find distances between points?

<p>The distance formula or simple subtraction of coordinates. (A)</p> Signup and view all the answers

What distinguishes exponential decay from growth in the function $y = ab^x$?

<p>The base 'b' must be less than 1. (B)</p> Signup and view all the answers

For the sine function, what is the maximum obtainable value of $y = a ext{ sin } \theta + q$ when $a > 0$?

<p>q + a (D)</p> Signup and view all the answers

What is the significance of identifying the vertical shifts in trigonometric graphs?

<p>It affects the vertical position of the graph described by 'q'. (A)</p> Signup and view all the answers

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

<p>180° (C)</p> Signup and view all the answers

What is the vertical shift of the cosine function $y = a ext{ cos } \theta + q$ when $q < 0$?

<p>It shifts down by 'q' units. (C)</p> Signup and view all the answers

What can be concluded about the range of the function when $a < 0$ in the equation $y = ax^2 + q$?

<p>The range is $(- ext{infinity}; q]$ (A)</p> Signup and view all the answers

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

<p>There is no y-intercept (B)</p> Signup and view all the answers

What is the effect of a positive value for $a$ in the equation $y = rac{a}{x} + q$?

<p>The graph lies in the first and third quadrants (C)</p> Signup and view all the answers

What type of turning point occurs when $a > 0$ in the quadratic function $f(x) = ax^2 + q$?

<p>Minimum turning point (D)</p> Signup and view all the answers

Where is the axis of symmetry for any quadratic function of the form $f(x) = ax^2 + q$?

<p>The y-axis, or the line $x = 0$ (D)</p> Signup and view all the answers

Which statement is true regarding the range of an exponential function $y = ab^x + q$ when $a < 0$?

<p>The range is $( ext{infinity}; q)$ (B)</p> Signup and view all the answers

What is the primary characteristic of the vertical asymptote in the hyperbolic function $y = \frac{a}{x} + q$?

<p>Defined at $x = 0$ (A)</p> Signup and view all the answers

What happens to the graph of $f(x) = ax^2 + q$ if $q < 0$?

<p>The turning point will be below the x-axis (D)</p> Signup and view all the answers

In the graph of a function of the form $y = ab^x + q$, what does the value of $q$ control?

<p>Vertical shift (A)</p> Signup and view all the answers

What is true about the x-intercept for functions of the form $y = \frac{a}{x} + q$?

<p>It is determined by setting $y = 0$ (A)</p> Signup and view all the answers

Which of the following best defines natural numbers?

<p>The set of positive integers starting from 1. (B)</p> Signup and view all the answers

What is included in the set of whole numbers?

<p>All natural numbers and zero. (C)</p> Signup and view all the answers

Which statement is true regarding irrational numbers?

<p>Irrational numbers cannot be expressed as a fraction of two integers. (C)</p> Signup and view all the answers

What do real numbers encompass?

<p>All rational numbers and irrational numbers. (D)</p> Signup and view all the answers

Which of the following best describes rational numbers?

<p>Numbers that can be expressed as a fraction of two integers. (B)</p> Signup and view all the answers

Which of the following statements about imaginary numbers is accurate?

<p>Imaginary numbers are those having a negative square root. (A)</p> Signup and view all the answers

Which of the following correctly describes a rational number?

<p>A number that can be written as a repeating decimal. (C)</p> Signup and view all the answers

What is an example of an irrational number?

<p>$ ext{√7}$ (B)</p> Signup and view all the answers

What happens to the digit being rounded if it is 9 and is in the decimal place to be rounded?

<p>It becomes 0, and the preceding digit increases by 1. (A)</p> Signup and view all the answers

If a decimal is non-terminating and non-repeating, what type of number is it classified as?

<p>Irrational Number (B)</p> Signup and view all the answers

How can a recurring decimal be represented as a rational number?

<p>By aligning the decimal and subtracting from a multiple of ten. (D)</p> Signup and view all the answers

Which statement accurately describes surds?

<p>Surds are square roots of numbers that cannot be simplified to rational. (A)</p> Signup and view all the answers

What is the first step in estimating a surd like $ ext{√5}$?

<p>Finding nearby perfect squares. (B)</p> Signup and view all the answers

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

<p>Leave the last digit unchanged. (C)</p> Signup and view all the answers

What is a characteristic feature of rational numbers?

<p>They can be expressed in the form $ rac{a}{b}$ where $b eq 0$. (D)</p> Signup and view all the answers

What is the process of breaking down an expression into simpler expressions known as?

<p>Factorization (A)</p> Signup and view all the answers

When multiplying the binomial $(A + B)$ by the trinomial $(C + D + E)$, which of the following correctly represents the product?

<p>$A(C + D + E) + B(C + D + E)$ (C)</p> Signup and view all the answers

Which identity is used for factorizing the difference of two squares?

<p>$a^2 - b^2 = (a + b)(a - b)$ (D)</p> Signup and view all the answers

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

<p>Identify any common factors. (C)</p> Signup and view all the answers

Which formula represents the general product of two linear binomials?

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

What must be true for the denominator of a fraction when performing operations like multiplication or division?

<p>It must not be zero. (D)</p> Signup and view all the answers

In the expression $a(x + y)$, what does the entire expression represent following multiplication?

<p>$ax + ay$ (D)</p> Signup and view all the answers

Which of the following correctly describes the sum of two cubes?

<p>$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$ (C)</p> Signup and view all the answers

What is the outcome when cancelling common factors in a fraction during simplification?

<p>The fraction is simplified to its lowest terms. (C)</p> Signup and view all the answers

When performing the operation $ rac{a}{b} imes rac{c}{d}$, what is the resulting expression?

<p>$ rac{ac}{bd}$ (A)</p> Signup and view all the answers

What is the primary method to determine the solution of a system of simultaneous equations graphically?

<p>Finding the intersection point of the graphs (D)</p> Signup and view all the answers

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

<p>Ignore the final solution (B)</p> Signup and view all the answers

What does isolating the unknown variable often involve when solving literal equations?

<p>Multiplying through by the lowest common denominator (C)</p> Signup and view all the answers

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

<p>The sign is reversed (D)</p> Signup and view all the answers

What effect does increasing the value of the constant 'm' in the equation of a straight line have on the graph?

<p>It increases the slope of the line (A)</p> Signup and view all the answers

When given the area formula of a circle, what does the variable 'r' represent?

<p>The radius (A)</p> Signup and view all the answers

What characterizes a linear inequality compared to a linear equation?

<p>It involves an inequality sign (B)</p> Signup and view all the answers

Which of the following describes the y-intercept in the equation of a straight line accurately?

<p>The point where the line intersects the y-axis (A)</p> Signup and view all the answers

What is the initial step in solving a set of simultaneous equations using substitution?

<p>Express one variable in terms of the other (A)</p> Signup and view all the answers

What is the effect on the graph of the function as the value of 'c' becomes negative in the linear equation?

<p>It shifts the graph vertically downwards (C)</p> Signup and view all the answers

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

<p>It shifts the graph vertically upwards by q units. (A)</p> Signup and view all the answers

Which of the following describes the range of the function $f(x) = ax^2 + q$ when $a < 0$?

<p>The range is $(- ext{infinity}; q)$. (B)</p> Signup and view all the answers

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

<p>By setting $x = 0$ in the equation. (C)</p> Signup and view all the answers

What characterizes the graph of the function $y = mx + c$ if 'm' is negative?

<p>The graph decreases as x increases. (A)</p> Signup and view all the answers

Which of the following statements is true regarding the gradient 'm' in the equation of a straight-line graph?

<p>It represents the steepness of the line. (D)</p> Signup and view all the answers

What happens to the graph of the function $y = ax^2 + q$ as 'a' approaches zero but remains positive?

<p>The graph becomes wider. (D)</p> Signup and view all the answers

Which of the following best describes the domain of a function defined by the equation $y = mx + c$?

<p>All real numbers. (C)</p> Signup and view all the answers

What characteristic must be determined to plot a straight line using the gradient and y-intercept method?

<p>The gradient and at least one intercept are needed. (B)</p> Signup and view all the answers

If the gradient 'm' is zero in the equation $y = mx + c$, what is true about the graph?

<p>The graph is a horizontal line. (A)</p> Signup and view all the answers

What determines the direction in which the graph of the quadratic function $y = ax^2 + q$ opens?

<p>The sign of 'a'. (B)</p> Signup and view all the answers

What is the effect of a negative value of 'a' on the graph of the function defined by $y = ax^2 + q$?

<p>The graph has a maximum turning point. (D)</p> Signup and view all the answers

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

<p>All real numbers except zero. (C)</p> Signup and view all the answers

Which of the following statements is true regarding the x-intercept of the function $y = ax^2 + q$?

<p>It is calculated by setting $y = 0$. (C)</p> Signup and view all the answers

What does the range of the function $y = ax^2 + q$ depend on?

<p>The sign of 'a' and the value of 'q'. (D)</p> Signup and view all the answers

Where is the vertical asymptote located for the hyperbolic function $y = \frac{a}{x} + q$?

<p>At $x = 0$. (A)</p> Signup and view all the answers

How does the variable 'q' affect the graph of the function $y = \frac{a}{x} + q$?

<p>It introduces a vertical shift. (C)</p> Signup and view all the answers

What best describes a characteristic of exponential functions of the form $y = ab^x + q$ when $a > 0$?

<p>The range consists of values greater than 'q'. (B)</p> Signup and view all the answers

Which statement correctly describes the axis of symmetry for parabolic functions of the form $f(x) = ax^2 + q$?

<p>The axis of symmetry is along $x = 0$. (A)</p> Signup and view all the answers

What does the turning point of the parabolic function $y = ax^2 + q$ indicate when $a > 0$?

<p>It is a minimum point of the graph. (C)</p> Signup and view all the answers

What happens to the graph of an exponential function if 'a' is set to a negative value?

<p>The graph flips downwards. (A)</p> Signup and view all the answers

What describes the range of an exponential function when $a < 0$?

<p>$f(x) &lt; q$ (B)</p> Signup and view all the answers

Which statement is true concerning the effect of the parameter $q$ on the graph of an exponential function?

<p>It causes a vertical shift. (D)</p> Signup and view all the answers

What is the y-intercept of the function $y = a an heta + q$ when evaluated at $ heta = 0°$?

<p>$q$ (D)</p> Signup and view all the answers

For the function $y = a heta + q$ ($ heta$ in degrees), how does the value of $a$ affect the graph?

<p>It adjusts the amplitude of the wave. (A), It results in a vertical reflection. (B)</p> Signup and view all the answers

Which characteristic distinguishes the cosine function from the sine function within their respective shares?

<p>The cosine function starts at its maximum value. (C)</p> Signup and view all the answers

What is the period of the sine and cosine functions?

<p>360° (D)</p> Signup and view all the answers

What defines the behavior of the function $y = a an heta + q$ concerning its vertical shift?

<p>$q$ affects the asymptotes of the tangent function. (A), $q &lt; 0$ indicates a downward shift. (C)</p> Signup and view all the answers

In the function $y = a an heta + q$, what defines the intercepts?

<p>Both the x and y intercepts are at $(0, 0)$. (B)</p> Signup and view all the answers

What effect does a coefficient $a < 0$ have on the graph of the sine function?

<p>The graph reflects across the x-axis. (C)</p> Signup and view all the answers

Which of the following characteristics is solely based on the parameter $q$ in the sine and cosine functions?

<p>Establishing the vertical shift. (D)</p> Signup and view all the answers

What is the result of applying the rule for division of exponents when simplifying the expression ( \frac{a^5}{a^2} )?

<p>a^{3} (B)</p> Signup and view all the answers

Which expression can be simplified using the power of a power rule?

<p>(x^2)^3 (C)</p> Signup and view all the answers

Which of the following statements about rational exponents is true?

<p>Rational exponents can represent both roots and powers. (B)</p> Signup and view all the answers

What happens when simplifying the expression ( (3x^2y^3)^2 )?

<p>3^2x^{2<em>2}y^{3</em>2} (B), 3^2x^4y^6 (C)</p> Signup and view all the answers

To solve the equation ( 4^x = 16 ), what is the first step?

<p>Convert 4 and 16 to the same base. (B)</p> Signup and view all the answers

What is the result of ( a^{-3} ) when expressed in terms of positive exponents?

<p>\frac{1}{a^3} (C)</p> Signup and view all the answers

How would you simplify the expression ( \left(\frac{2}{3}\right)^{-2} )?

<p>\frac{9}{4} (C)</p> Signup and view all the answers

Which of the following is the correct process for solving ( a^x = a^5 )?

<p>Set x = 5. (B)</p> Signup and view all the answers

Which expression represents a correct simplification using the laws of exponents?

<p>a^{2/3} / a^{1/3} = a^{1/3} (A), a^{1/2}(b^{1/2}) = (ab)^{1/2} (D)</p> Signup and view all the answers

What effect does an increase in the value of 'a' have on the graph of a parabola?

<p>Increases the curvature steepness (A)</p> Signup and view all the answers

What are the y-intercepts of the function defined by the equation $y = a an heta + q$?

<p>At $y = q$ (D)</p> Signup and view all the answers

What do the vertical shifts in trigonometric graphs determine?

<p>The value of 'q' (D)</p> Signup and view all the answers

Where are the asymptotes of the hyperbola defined by the equation $y = \frac{a}{x} + q$ located?

<p>At $x = 0$ and $y = 0$ (C)</p> Signup and view all the answers

How can the domain of the function $y = a an heta + q$ be defined?

<p>${ \theta : 0° \leq \theta \leq 360°, \theta \neq 90°, 270° }$ (A)</p> Signup and view all the answers

What is the correct way to determine the vertical shift of a hyperbola?

<p>By determining the value of 'q' (D)</p> Signup and view all the answers

What information can be gathered from the x-intercepts of a graph?

<p>They show where the function outputs a value of zero (C)</p> Signup and view all the answers

What is the shape of a parabola characterized by when 'a' is negative?

<p>A 'frown' shape (D)</p> Signup and view all the answers

What is a characteristic of the tangent function graph?

<p>It intersects the x-axis periodically (D)</p> Signup and view all the answers

Which of the following describes the process of finding the equation of a parabola?

<p>Using the y-intercept to determine 'q' and another point for 'a' (C)</p> Signup and view all the answers

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

<p>Two (C)</p> Signup and view all the answers

Which of the following steps is NOT part of solving a linear equation?

<p>Add constants to both sides (D)</p> Signup and view all the answers

When solving simultaneous equations by substitution, what is the primary goal?

<p>To reduce the equations to a single variable (C)</p> Signup and view all the answers

What form must a quadratic equation take before it can be solved?

<p>ax^2 + bx + c = 0 (A)</p> Signup and view all the answers

Which operation maintains balance when manipulating an equation?

<p>Performing the same operation on both sides (D)</p> Signup and view all the answers

How can one check if the solution of an equation is valid?

<p>By substituting the solution back into the original equation (A)</p> Signup and view all the answers

What is the purpose of factorising a quadratic equation during the solving process?

<p>To create two linear equations (A)</p> Signup and view all the answers

What is unique about the solutions to a linear equation compared to a quadratic equation?

<p>Linear equations can have at most one solution (D)</p> Signup and view all the answers

What step comes after 'group like terms together' in solving a linear equation?

<p>Factorise if necessary (D)</p> Signup and view all the answers

In the elimination method for solving simultaneous equations, what is the purpose of making coefficients the same?

<p>To easily add or subtract the equations (C)</p> Signup and view all the answers

Which set of numbers is defined as including all positive integers starting from 1?

<p>Natural Numbers (A)</p> Signup and view all the answers

What is the primary distinction of irrational numbers compared to rational numbers?

<p>Their decimal expansions are non-repeating and non-terminating. (C)</p> Signup and view all the answers

Which of the following correctly represents the set of integers?

<p>{..., -2, -1, 0, 1, 2, ...} (D)</p> Signup and view all the answers

Which set includes both negative and positive numbers, as well as zero?

<p>Integers (B)</p> Signup and view all the answers

What symbol represents rational numbers in the real number system?

<p>Q (A)</p> Signup and view all the answers

Which of the following best defines real numbers?

<p>All rational and irrational numbers (D)</p> Signup and view all the answers

Which statement accurately characterizes irrational numbers?

<p>Irrational numbers have non-repeating, non-terminating decimal expansions. (D)</p> Signup and view all the answers

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

<p>Identify the integer part and convert each decimal place to a fraction. (C)</p> Signup and view all the answers

Which of the following methods is used to estimate the value of a surd?

<p>By identifying the nearest perfect squares or cubes surrounding the surd. (A)</p> Signup and view all the answers

Which process is essential when rounding off a decimal number?

<p>Identify the next digit and apply rules based on its value. (B)</p> Signup and view all the answers

What distinguishes a rational number from an irrational number in terms of decimal representation?

<p>Rational numbers can be expressed as decimals with periodic digits. (B)</p> Signup and view all the answers

What happens if an irrational number is rounded off?

<p>It can become a rational approximation. (C)</p> Signup and view all the answers

When converting recurring decimals to rational numbers, what is the first step?

<p>Multiply by a power of 10 to align the recurring parts. (B)</p> Signup and view all the answers

Which term refers to the root of a number that cannot be simplified to produce a rational result?

<p>Surd (C)</p> Signup and view all the answers

What defines a rational number in relation to its representation?

<p>It can be expressed in the form of a fraction where the denominator is non-zero. (A)</p> Signup and view all the answers

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

<p>Two solutions (D)</p> Signup and view all the answers

What step should be taken immediately after expanding all brackets when solving a linear equation?

<p>Rearrange the terms (B)</p> Signup and view all the answers

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

<p>It distributes the monomial to each term of the binomial. (D)</p> Signup and view all the answers

In solving simultaneous equations by elimination, what is the first step that must be taken?

<p>Make coefficients of one variable the same (D)</p> Signup and view all the answers

Which of the following represents the correct expansion of the expression $(ax + b)(cx + d)$?

<p>$acx^2 + adx + bcx + bd$ (B)</p> Signup and view all the answers

How can a quadratic equation be identified as having no solutions?

<p>When the discriminant is negative (A)</p> Signup and view all the answers

How is a trinomial defined in terms of its terms?

<p>An expression with three terms. (A)</p> Signup and view all the answers

What is the main purpose of factorization in algebra?

<p>To simplify complex expressions into simpler products. (B)</p> Signup and view all the answers

What is the last step in solving both linear and quadratic equations?

<p>Check the answer (C)</p> Signup and view all the answers

Which method involves expressing one variable in terms of another to solve simultaneous equations?

<p>Substitution (D)</p> Signup and view all the answers

Which identity is used for factoring a difference of two squares?

<p>$a^2 - b^2 = (a + b)(a - b)$ (D)</p> Signup and view all the answers

What is a common approach to simplifying algebraic fractions?

<p>Factorize both the numerator and denominator, then cancel common factors. (D)</p> Signup and view all the answers

When solving a quadratic equation, what is the form that it should be rewritten into?

<p>ax^2 + bx + c = 0 (D)</p> Signup and view all the answers

Which configuration correctly represents the multiplication of fractions?

<p>$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$ (C)</p> Signup and view all the answers

What is a crucial point to remember when manipulating equations?

<p>Operations on one side must be performed on the other side (C)</p> Signup and view all the answers

Which formula is used to factor the sum of two cubes?

<p>$x^3 + y^3 = (x + y)(x^2 + xy + y^2)$ (B)</p> Signup and view all the answers

What is the primary focus when checking for extraneous solutions?

<p>To confirm whether the solution satisfies the original equation (D)</p> Signup and view all the answers

What does the process of factorizing a quadratic trinomial typically involve?

<p>Finding two binomials that multiply to give the original trinomial. (B)</p> Signup and view all the answers

Which method reduces the number of variables by substituting one variable into another equation?

<p>Substitution (D)</p> Signup and view all the answers

Which law of exponents states that when multiplying two expressions with the same base, you add the exponents?

<p>Multiplication of Exponents (C)</p> Signup and view all the answers

What happens when you raise a quotient to a power?

<p>Both the numerator and denominator are raised to the power. (D)</p> Signup and view all the answers

Which of the following correctly represents the expression with a negative exponent rewritten as a fraction?

<p>$a^{-n} = \frac{1}{a^n}$ (B)</p> Signup and view all the answers

Which method is recommended when the bases of an exponential equation are not the same?

<p>Using Logarithms (C)</p> Signup and view all the answers

What is the simplified form of the expression $\frac{a^{3/4}}{a^{1/4}}$?

<p>$a^{2/4}$ (C)</p> Signup and view all the answers

How would you express the square root of 'a' as a rational exponent?

<p>$a^{1/2}$ (C)</p> Signup and view all the answers

In the equation $a^x = a^5$, what conclusion can be drawn if $a > 0$ and $a \neq 1$?

<p>x must equal 5. (A)</p> Signup and view all the answers

What is the first step in solving an exponential equation involving different bases?

<p>Change the bases to be the same. (A)</p> Signup and view all the answers

What is the primary method for finding the solution of simultaneous equations graphically?

<p>Identifying the intersection point of the lines (B)</p> Signup and view all the answers

Which statement is true regarding the expression $(3x^2y)^3$?

<p>It simplifies to $3^3x^{2*3}y^3$. (C)</p> Signup and view all the answers

When given the expression $a^{m/n}$, what does it represent?

<p>It is the n-th root of $a^m$. (A)</p> Signup and view all the answers

In solving a word problem, which of the following is the initial step according to the problem-solving strategy?

<p>Read the whole question (C)</p> Signup and view all the answers

How should the unknown variable be treated if it appears in two or more terms in a literal equation?

<p>Take it out as a common factor (B)</p> Signup and view all the answers

Which statement correctly describes what happens to an inequality sign during division by a negative number?

<p>The inequality is reversed (A)</p> Signup and view all the answers

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

<p>It indicates the vertical position of the line (D)</p> Signup and view all the answers

When solving inequalities, what happens after multiplying by -1?

<p>The inequality sign is inverted (B)</p> Signup and view all the answers

In the expression for speed given by $v = \frac{D}{t}$, what does 'D' represent?

<p>Distance traveled (C)</p> Signup and view all the answers

To solve a literal equation in terms of one variable, what is the first thing to do?

<p>Rearrange it to isolate the variable (C)</p> Signup and view all the answers

What characteristic must be evaluated to accurately plot a straight line using the gradient and y-intercept method?

<p>Both the gradient and the y-intercept (A)</p> Signup and view all the answers

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

<p>It shifts the graph vertically upwards by 'q' units. (D)</p> Signup and view all the answers

For an exponential function where 'a' is negative and 'b' is greater than 1, what can be said about the shape of the graph?

<p>The graph will curve downwards exhibiting exponential decay. (C)</p> Signup and view all the answers

How does the amplitude of a sine function change if the value of 'a' is negative?

<p>The graph will reflect about the x-axis. (A)</p> Signup and view all the answers

What is the period of a sine or cosine function of the form $y = a ext{sin} heta + q$?

<p>360° (A)</p> Signup and view all the answers

What does the range of the function $y = a ext{sin} heta + q$ become when 'a' is equal to 1 and 'q' is equal to 2?

<p>[1, 3] (D)</p> Signup and view all the answers

In the context of trigonometric functions, what defines the vertical shift produced by the parameter 'q'?

<p>It moves the graph vertically by 'q' units. (B)</p> Signup and view all the answers

How are the x-intercepts of the sine function positioned within the domain [0°, 360°]?

<p>At 0°, 180°, and 360°. (A)</p> Signup and view all the answers

What is true about the asymptotes of the tangent function?

<p>They occur at 90° and 270°. (B)</p> Signup and view all the answers

For an exponential function with parameters a < 0 and b < 1, which statement is true?

<p>The function will experience rapid decay and curve upwards. (D)</p> Signup and view all the answers

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

<p>The graph is a 'smile' and has a minimum turning point. (C)</p> Signup and view all the answers

How does increasing 'm' in the equation $y = mx + c$ affect the slope of the line?

<p>The line becomes steeper. (A)</p> Signup and view all the answers

What characterizes the y-intercept in the equation $y = mx + c$?

<p>It is determined by setting $x = 0$. (B)</p> Signup and view all the answers

What does the sign of 'q' influence in the parabolic function $y = ax^2 + q$?

<p>The y-intercept of the graph. (A)</p> Signup and view all the answers

Which of the following conditions provides the range of the function $f(x) = mx + c$?

<p>The range is $ ext{R}$ because 'y' can take any real value. (C)</p> Signup and view all the answers

How is the x-intercept calculated for the function $y = mx + c$?

<p>By setting $y = 0$ and solving for $x$. (D)</p> Signup and view all the answers

What effect does a negative value of 'a' have on the graph of the parabola $y = ax^2 + q$?

<p>The graph is flipped upside down. (D)</p> Signup and view all the answers

In the standard form $y = ax^2 + q$, what happens to the graph when 'q' is positive?

<p>The graph shifts vertically upwards by $q$ units. (C)</p> Signup and view all the answers

When using the gradient and y-intercept method, what is the first step to plot the graph of $y = mx + c$?

<p>Calculate the y-intercept by setting $x = 0$. (D)</p> Signup and view all the answers

Which of the following accurately defines the term 'gradient' in the context of linear functions?

<p>The ratio of the vertical change to horizontal change. (A)</p> Signup and view all the answers

What determines the steepness of the branches in the graph of a tangent function?

<p>The value of a (C)</p> Signup and view all the answers

Where are the asymptotes located for the function defined as $y = a \tan \theta + q$?

<p>$\theta = 90°$ and $\theta = 270°$ (B)</p> Signup and view all the answers

In the equation of a parabolic graph $y = ax^2 + q$, what does the term q affect?

<p>The vertical shift (C)</p> Signup and view all the answers

What is the range of the function defined by $y = ax^2 + q$ where $a > 0$?

<p>${ f(x) : f(x) \geq q }$ (C)</p> Signup and view all the answers

Which of the following is essential to determine the equation of a hyperbola?

<p>Substituting given points into the equation (C)</p> Signup and view all the answers

What does the amplitude of a trigonometric graph depend on?

<p>The value of a (B)</p> Signup and view all the answers

When an asymptote is present in the function $y = \frac{a}{x} + q$, what does this indicate?

<p>The graph will have no limits in that direction (D)</p> Signup and view all the answers

To find the output values of a function with respect to different inputs, which characteristics must be examined?

<p>Intercepts and shifts (A)</p> Signup and view all the answers

What is the correct form of the equation of a trigonometric function that includes both sine and a vertical shift?

<p>$y = a \sin \theta + q$ (B)</p> Signup and view all the answers

What must be true about the angle ( \theta ) in the domain of the tangent function?

<p>It cannot equal 90° or 270° (A)</p> Signup and view all the answers

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

<p>(0, q) (C)</p> Signup and view all the answers

For the function $y = \frac{a}{x} + q$, which of the following statements is true regarding its intercepts?

<p>It has no y-intercept. (B)</p> Signup and view all the answers

What happens to the range of the function $f(x) = ax^2 + q$ when $a < 0$?

<p>The range is (-\infty, q]. (B)</p> Signup and view all the answers

Which line represents the vertical asymptote for the hyperbolic function $y = \frac{a}{x} + q$?

<p>x = 0 (C)</p> Signup and view all the answers

How does the value of $q$ affect the graph of the hyperbolic function $y = \frac{a}{x} + q$?

<p>It determines the horizontal asymptote. (A)</p> Signup and view all the answers

For the function $f(x) = ab^x + q$, what is the correct domain?

<p>All real numbers (A)</p> Signup and view all the answers

Which characteristic is used to determine the direction of the parabola represented by $y = ax^2 + q$?

<p>The sign of $a$ (C)</p> Signup and view all the answers

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

<p>It is a maximum point at (0, q). (C)</p> Signup and view all the answers

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