Gr 10 Math June P1 Easy
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Questions and Answers

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?

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

What is included in the set of real numbers?

<p>Both rational and irrational numbers (B)</p> Signup and view all the answers

Which of the following statements about imaginary numbers is true?

<p>They are not part of the real number system. (C)</p> Signup and view all the answers

What is a rational number?

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

Which of the following is a characteristic of irrational numbers?

<p>They cannot be expressed as fractions with integer numerator and denominator. (D)</p> Signup and view all the answers

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

<p>By identifying the integer part and calculating contributions from the decimal digits. (B)</p> Signup and view all the answers

What does the process of rounding depend on?

<p>The next digit after the required decimal place. (C)</p> Signup and view all the answers

Which of these is NOT a surd?

<p>( \sqrt{4} ) (D)</p> Signup and view all the answers

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

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

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

<p>Its surrounding perfect squares or cubes. (B)</p> Signup and view all the answers

What happens when rounding a digit that is 9?

<p>It turns into 0, and the preceding digit is rounded up by 1. (B)</p> Signup and view all the answers

Which statement regarding decimals is true?

<p>Terminating decimals are always rational numbers. (A)</p> Signup and view all the answers

What is a monomial?

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

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

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

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

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

What is factorisation?

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

What is the identity for the difference of two squares?

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

What technique is used when factorising by grouping?

<p>Grouping terms with common factors. (B)</p> Signup and view all the answers

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

<p>Factorise the numerator and the denominator. (A)</p> Signup and view all the answers

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

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

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

<p>$ rac{a + c}{b}$ (A)</p> Signup and view all the answers

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

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

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

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

Which expression correctly represents the zero exponent rule?

<p>$a^0 = 1$ (A)</p> Signup and view all the answers

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

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

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

<p>Applying the principle $a^x = a^y$ (B)</p> Signup and view all the answers

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

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

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

<p>$a^{5/4}$ (D)</p> Signup and view all the answers

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

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

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

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

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

<p>$a &gt; 0$ and $b &gt; 0$ (A)</p> Signup and view all the answers

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

<p>$a^{1}$ (B)</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 should you do after solving an equation algebraically?

<p>Check the solution. (D)</p> Signup and view all the answers

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

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

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

<p>Drawing both equations and locating their intersection. (A)</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 inverted. (D)</p> Signup and view all the answers

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

<p>The operations joining the variable to others. (D)</p> Signup and view all the answers

When solving by elimination, what is the primary goal?

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

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

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

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

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

What strategy can be employed to solve linear inequalities?

<p>Use similar methods as linear equations. (D)</p> 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?

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

Which of the following describes a linear equation?

<p>The highest exponent of the variable is 1 (D)</p> Signup and view all the answers

What is the first step in solving a linear equation?

<p>Expand all brackets (B)</p> 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?

<p>To find potential solutions by setting each factor to zero (C)</p> Signup and view all the answers

How many solutions does a quadratic equation typically have?

<p>At most two solutions (B)</p> Signup and view all the answers

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

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

What is crucial to check after solving any equation?

<p>Verify the solution in the original equation (D)</p> Signup and view all the answers

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

<p>Operations must be performed equally on both sides (A)</p> Signup and view all the answers

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

<p>Factoring out a greatest common factor (C)</p> Signup and view all the answers

What defines a quadratic equation compared to a linear equation?

<p>It has a higher exponent (A)</p> Signup and view all the answers

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

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

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

<p>Set y to 0. (A)</p> Signup and view all the answers

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

<p>If a &gt; 0. (C)</p> Signup and view all the answers

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

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

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

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

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

<p>Change in y divided by change in x. (C)</p> Signup and view all the answers

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

<p>The graph flattens or widens. (B)</p> Signup and view all the answers

What characteristic determines the steepness of a straight line graph?

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

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

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

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

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

What is the period of the tangent function?

<p>180° (D)</p> 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?

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

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

<p>Shift right by 90° (D)</p> Signup and view all the answers

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

<p>It decides the direction and shape of the hyperbola. (B)</p> Signup and view all the answers

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

<p>{ θ : 0° ≤ θ ≤ 360°, θ ≠ 90°, 270° } (B)</p> Signup and view all the answers

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

<p>By determining the y-intercept point (B)</p> Signup and view all the answers

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

<p>(0°, 0) and (180°, 0) (C)</p> Signup and view all the answers

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

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

Which points are considered asymptotes for the tangent function?

<p>θ = 90° and θ = 270° (D)</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 (D)</p> Signup and view all the answers

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

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

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

<p>The direction and shape of the graph (D)</p> Signup and view all the answers

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

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

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

<p>Shifts the graph upward (D)</p> Signup and view all the answers

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

<p>Calculated by setting $y = 0$ (B)</p> Signup and view all the answers

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

<p>Horizontal asymptote (D)</p> 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?

<p>It is always undefined (A)</p> 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?

<p>Second and fourth quadrants (A)</p> Signup and view all the answers

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

<p>It is located at (0, q) (A)</p> Signup and view all the answers

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

<p>Whether the graph curves upwards or downwards (A)</p> Signup and view all the answers

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

<p>It is the value of y when x is zero. (B)</p> Signup and view all the answers

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

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

Which characteristic defines the horizontal asymptote of an exponential function?

<p>It is determined by the value of constant 'q'. (B)</p> Signup and view all the answers

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

<p>90° (D)</p> Signup and view all the answers

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

<p>It reflects the graph about the x-axis. (D)</p> Signup and view all the answers

What is the period of both sine and cosine functions?

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

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

<p>It provides vertical shift effects. (A)</p> Signup and view all the answers

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

<p>[-1; 1] (C)</p> Signup and view all the answers

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

<p>0 &lt; b &lt; 1 (A)</p> Signup and view all the answers

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

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

What defines a rational number?

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

Which symbol represents irrational numbers?

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

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

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

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

<p>Both rational and irrational numbers (A)</p> Signup and view all the answers

Which statement about imaginary numbers is correct?

<p>They have a negative square root. (A)</p> Signup and view all the answers

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

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

What characterizes an irrational number?

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

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

<p>Identify the required decimal place. (C)</p> Signup and view all the answers

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

<p>Subtract the original equation from the multiplied equation. (D)</p> Signup and view all the answers

Which of the following represents a surd?

<p>$ ext{sqrt}(5)$ (C)</p> Signup and view all the answers

What is not a characteristic of rational numbers?

<p>They can have non-repeating decimals. (A)</p> Signup and view all the answers

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

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

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

<p>It cannot simplify to a rational number. (C)</p> Signup and view all the answers

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

<p>The nearest perfect powers. (D)</p> Signup and view all the answers

What is the purpose of rounding a number?

<p>To provide a simpler or more manageable form. (B)</p> Signup and view all the answers

What is the first step in simplifying a complex fraction?

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

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

<p>a^m imes a^n = a^{m + n} (D)</p> Signup and view all the answers

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

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

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

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

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

<p>If $a^x = a^y$, then $x = y$. (C)</p> Signup and view all the answers

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

<p>a^0 = 1 (B)</p> Signup and view all the answers

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

<p>Convert to rational exponents if necessary. (C)</p> Signup and view all the answers

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

<p>a^{mp/nq} (C)</p> Signup and view all the answers

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

<p>Division of Exponents (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

What is the first step for simplifying algebraic fractions?

<p>Factorise both the numerator and denominator (C)</p> Signup and view all the answers

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

<p>$ rac{a}{b} imes rac{d}{c}$ (B)</p> Signup and view all the answers

Which formula correctly represents the sum of two cubes $x^3 + y^3$?

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

What does factorising by grouping generally involve?

<p>Grouping terms with common factors and factorising each group (C)</p> Signup and view all the answers

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

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

What is the general form of a quadratic function?

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

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

<p>The line falls from left to right. (C)</p> Signup and view all the answers

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

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

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

<p>The parabola opens downwards. (B)</p> Signup and view all the answers

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

<p>It has a minimum turning point. (A)</p> Signup and view all the answers

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

<p>It determines vertical shifts of the graph. (B)</p> Signup and view all the answers

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

<p>The rate of change of y with respect to x. (A)</p> Signup and view all the answers

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

<p>By letting y = 0. (A)</p> Signup and view all the answers

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

<p>The graph becomes narrower. (C)</p> 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?

<p>Set the exponents equal to each other (C)</p> Signup and view all the answers

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

<p>Combine terms that have the same variable (D)</p> Signup and view all the answers

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

<p>Two binomials set equal to zero (D)</p> Signup and view all the answers

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

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

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

<p>The sign of the inequality switches (D)</p> Signup and view all the answers

What should you do after solving a linear equation?

<p>Check the solution in the original equation (C)</p> Signup and view all the answers

How many solutions does a typical quadratic equation have?

<p>At most two solutions (A)</p> Signup and view all the answers

What is the first step in solving a quadratic equation?

<p>Set it equal to zero (A)</p> Signup and view all the answers

What does isolating the variable mean in linear equations?

<p>Getting the variable alone on one side of the equation (A)</p> Signup and view all the answers

What is the role of logarithms in solving exponential equations?

<p>To isolate the exponent when bases are not easily made the same (A)</p> Signup and view all the answers

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

<p>The cosine graph can be shifted to the right by 90°. (A)</p> Signup and view all the answers

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

<p>It is undefined at 90° and 270°. (B)</p> Signup and view all the answers

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

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

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

<p>It affects the steepness of the graph branches. (B)</p> 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?

<p>The x-intercept to find a. (C)</p> Signup and view all the answers

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

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

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

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

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

<p>It represents the vertical shift q. (C)</p> 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?

<p>The direction and shape of the hyperbola. (D)</p> Signup and view all the answers

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

<p>Their alignment along the y-axis. (B)</p> Signup and view all the answers

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

<p>Defined by the value of $q$ only (A)</p> Signup and view all the answers

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

<p>From negative infinity to $q$ (C)</p> Signup and view all the answers

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

<p>Undefined for these functions (B)</p> Signup and view all the answers

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

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

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

<p>Indicates the direction of the graph (smile or frown) (C)</p> Signup and view all the answers

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

<p>The graph shifts downwards (D)</p> Signup and view all the answers

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

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

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

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

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

<p>Lines of the form $y = x + q$ and $y = -x + q$ (D)</p> Signup and view all the answers

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

<p>Calculated by setting $y = 0$ (C)</p> Signup and view all the answers

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

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

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

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

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

<p>Reflection about the x-axis (A)</p> Signup and view all the answers

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

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

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

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

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

<p>It is the y-intercept (D)</p> Signup and view all the answers

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

<p>It shifts the graph upwards (A)</p> Signup and view all the answers

What is the period of the sine and cosine functions?

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

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

<p>(0°, a + q) (A)</p> Signup and view all the answers

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

<p>It is the line y = q (B)</p> Signup and view all the answers

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

<p>Substitute one equation into the other (A)</p> Signup and view all the answers

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

<p>Substitute the value into the other equation (C)</p> Signup and view all the answers

What represents the solution of simultaneous equations when solved graphically?

<p>The coordinates where the two lines intersect (D)</p> Signup and view all the answers

Which step should follow after reading a word problem?

<p>Determine what needs to be solved (B)</p> 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?

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

What is the purpose of rearranging a literal equation?

<p>To change the subject of the formula (D)</p> Signup and view all the answers

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

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

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

<p>Isolate the variable on one side (C)</p> Signup and view all the answers

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

<p>The radius of the circle (C)</p> Signup and view all the answers

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

<p>Create equations based on the problem (C)</p> Signup and view all the answers

Which of the following is a characteristic of a surd?

<p>It is a root of a number that cannot be simplified. (A)</p> Signup and view all the answers

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

<p>Terminating decimals (C), Decimals that have both terminating and repeating patterns (D)</p> Signup and view all the answers

Which of the following examples represents a rational number?

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

Which statement correctly describes an irrational number?

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

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

<p>When the digit after the rounding place is greater than or equal to 5. (D)</p> Signup and view all the answers

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

<p>Multiply by 10, align decimals, and solve. (A)</p> Signup and view all the answers

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

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

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

<p>The nearest perfect squares or cubes. (A)</p> Signup and view all the answers

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

<p>Rational numbers can be written as a fraction of integers. (C)</p> Signup and view all the answers

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

<p>Rewrite the equation with the same base (A)</p> Signup and view all the answers

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

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

What distinguishes a quadratic equation from a linear equation?

<p>Quadratic equations have a variable raised to the power of 2 (D)</p> Signup and view all the answers

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

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

How many solutions can a quadratic equation have at most?

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

When solving simultaneous equations, what is required?

<p>Two independent equations and two variables (D)</p> Signup and view all the answers

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

<p>To isolate one variable completely (D)</p> Signup and view all the answers

When is it appropriate to use logarithms to solve equations?

<p>When the bases are not easily made the same (D)</p> Signup and view all the answers

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

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

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

<p>Setting exponents equal (D)</p> Signup and view all the answers

What is the first step in simplifying complex fractions?

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

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

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

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

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

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

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

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

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

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

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

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

<p>It shows that $x$ must equal $y$ under certain conditions. (B)</p> Signup and view all the answers

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

<p>a^n b^n (D)</p> Signup and view all the answers

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

<p>The square root $, ext{is } a^{1/2}$. (A)</p> Signup and view all the answers

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

<p>Setting the exponents equal to each other. (D)</p> Signup and view all the answers

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

<p>Substituting one variable into the other equation (B)</p> Signup and view all the answers

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

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

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

<p>To write equations that represent the problem (C)</p> Signup and view all the answers

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

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

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

<p>Rearranging variables to isolate the unknown (C)</p> Signup and view all the answers

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

<p>The point where the two graphs intersect (C)</p> Signup and view all the answers

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

<p>Consider the operations connecting the unknown variable (A)</p> Signup and view all the answers

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

<p>What is being asked to solve for (C)</p> Signup and view all the answers

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

<p>The gradient of the graph increases (A)</p> Signup and view all the answers

When solving by elimination, what is the goal?

<p>To make the coefficients of one variable the same (B)</p> Signup and view all the answers

Which set includes all positive integers and zero?

<p>Whole Numbers (N0) (D)</p> Signup and view all the answers

Which of the following best describes irrational numbers?

<p>They cannot be expressed as simple fractions. (D)</p> Signup and view all the answers

What characterizes integers?

<p>They consist of whole numbers and their negatives. (B)</p> Signup and view all the answers

Which of the following is true about rational numbers?

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

What is the main definition of real numbers?

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

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

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

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

<p>The y-intercept (D)</p> Signup and view all the answers

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

<p>The graph shifts vertically upwards (B)</p> Signup and view all the answers

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

<p>The rate of change of y with respect to x (D)</p> 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 $y = ax^2 + q$?

<p>Parabolic graph with a maximum point (D)</p> Signup and view all the answers

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

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

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

<p>The line falls from left to right (D)</p> Signup and view all the answers

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

<p>All real numbers (B)</p> 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 $y = ax^2 + q$?

<p>It narrows the parabola (B)</p> Signup and view all the answers

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

<p>x-intercept and y-intercept (C)</p> Signup and view all the answers

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

<p>It has a minimum turning point (C)</p> Signup and view all the answers

What is a trinomial?

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

Which formula represents the multiplication of two linear binomials?

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

What occurs in the process of factorisation?

<p>Breaking down an expression into simpler expressions (A)</p> Signup and view all the answers

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

<p>Multiplying a binomial and a trinomial (B)</p> Signup and view all the answers

What is the purpose of identifying common factors during factorisation?

<p>To simplify the expression (D)</p> Signup and view all the answers

What is the identity for the difference of two squares?

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

Which step is NOT part of simplifying algebraic fractions?

<p>Expanding expressions before simplification (D)</p> Signup and view all the answers

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

<p>It increases the number of terms by one (C)</p> Signup and view all the answers

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

<p>Generate possible pairs of factors and check (A)</p> Signup and view all the answers

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

<p>$ rac{ac}{bd}$ where $b = 0$ or $d = 0$ (D)</p> Signup and view all the answers

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

<p>The graph shifts vertically upwards. (D)</p> 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?

<p>Less than 0 (A)</p> Signup and view all the answers

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

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

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

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

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

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

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

<p>The rate of growth or decay. (C)</p> Signup and view all the answers

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

<p>It reflects the graph about the x-axis. (B)</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

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

<p>(90°, 0) (B), (180°, 0) (C)</p> Signup and view all the answers

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

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

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

<p>The direction and shape of the parabola (B)</p> Signup and view all the answers

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

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

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

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

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

<p>There is a horizontal asymptote at $y = q$ and a vertical asymptote at $x = 0$ (C)</p> 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?

<p>A minimum turning point (C)</p> Signup and view all the answers

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

<p>It shifts downwards (D)</p> Signup and view all the answers

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

<p>$ ext{R} ackslash olimits ext{0}$ (C)</p> Signup and view all the answers

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

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

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

<p>It affects the quadrants where the graph lies (C)</p> Signup and view all the answers

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

<p>It affects the steepness of the graph branches. (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

<p>Examine the sketch and identify the quadrants. (A)</p> Signup and view all the answers

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

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

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

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

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

<p>$(0°, 0)$, $(180°, 0)$, and $(360°, 0)$ (C)</p> Signup and view all the answers

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

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

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

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

Which statement about irrational numbers is correct?

<p>Irrational numbers cannot be expressed as simple fractions. (B)</p> Signup and view all the answers

What do rational numbers include?

<p>Numbers that can be expressed as fractions (A)</p> Signup and view all the answers

Which of the following is NOT considered a real number?

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

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

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

Which characteristic defines real numbers?

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

What is a trinomial?

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

What is the main purpose of factorisation?

<p>To break down an expression into simpler expressions that can multiply to give the original (D)</p> Signup and view all the answers

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

<p>The sum of coefficients only (D)</p> Signup and view all the answers

Which of the following represents the sum of two cubes?

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

What is the correct procedure for multiplying a binomial and a trinomial?

<p>Multiply each term of the binomial by each term of the trinomial once (A)</p> Signup and view all the answers

When simplifying algebraic fractions, what should be done first?

<p>Factorise the numerator and denominator to identify common factors (A)</p> Signup and view all the answers

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

<p>$a(x + y) = ax + ay$ (B)</p> Signup and view all the answers

What does a coefficient represent in a term?

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

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

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

What is a characteristic of rational numbers?

<p>Can be expressed in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$ (C)</p> Signup and view all the answers

Which of the following best describes an irrational number?

<p>Has a decimal form that is non-repeating and non-terminating (A)</p> 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?

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

What is the primary purpose of estimating surds?

<p>To approximate their values using perfect squares or cubes (B)</p> Signup and view all the answers

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

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

Which of the following statements about surds is true?

<p>Surds are always of the form $\sqrt[n]{a}$ where $a$ cannot be simplified (D)</p> Signup and view all the answers

Which of the following describes a terminating decimal?

<p>Can be expressed as a fraction of integers (D)</p> Signup and view all the answers

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

<p>Multiply by a power of 10 aligning the recurring digits (C)</p> Signup and view all the answers

What are the key components of a mathematical expression?

<p>Terms, expressions, coefficients, and exponents (A)</p> Signup and view all the answers

What type of decimal numbers include repeating patterns?

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

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

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

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

<p>The graph shifts vertically upwards (D)</p> Signup and view all the answers

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

<p>By letting x equal 0 (A)</p> Signup and view all the answers

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

<p>Its shape changes based on the value of 'a' (D)</p> Signup and view all the answers

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

<p>The graph is a parabola that opens downwards (A)</p> Signup and view all the answers

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

<p>The turning point shifts upwards by 'q' units (D)</p> Signup and view all the answers

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

<p>A negative 'm' means a downward line (B)</p> Signup and view all the answers

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

<p>It defines where the graph cuts the y-axis (A)</p> Signup and view all the answers

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

<p>The range is all real numbers (D)</p> Signup and view all the answers

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

<p>There is no change in the y-values (D)</p> Signup and view all the answers

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

<p>Setting the Exponents Equal (C)</p> Signup and view all the answers

How many solutions can a linear equation typically have?

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

What is the first step in simplifying a complex fraction?

<p>Rewrite the division as multiplication by the reciprocal (D)</p> Signup and view all the answers

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

<p>Check for Extraneous Solutions (D)</p> Signup and view all the answers

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

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

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

<p>Both sides must undergo the same operation (C)</p> Signup and view all the answers

Which expression correctly represents raising a quotient to a power?

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

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

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

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

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

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

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

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

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

What is the first step in solving linear equations?

<p>Expand All Brackets (A)</p> Signup and view all the answers

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

<p>(a^{m})^{n} = a^{mn} (D)</p> Signup and view all the answers

What does solving a quadratic equation often require?

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

What is an outcome when a quadratic equation is factorised?

<p>Setting each factor equal to zero (D)</p> Signup and view all the answers

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

<p>To ensure all terms are written with the same base (C)</p> Signup and view all the answers

Which of the following statements about rational exponents is true?

<p>Rational exponents follow the same laws as integer exponents (D)</p> Signup and view all the answers

What is the role of substitution in solving simultaneous equations?

<p>To express one variable in terms of another (A)</p> Signup and view all the answers

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

<p>Change the base on the right side (A)</p> Signup and view all the answers

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

<p>(-\infty; q] (D)</p> Signup and view all the answers

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

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

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

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

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

<p>Substitute one variable into the second equation. (D)</p> Signup and view all the answers

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

<p>It affects the slope of the graph. (B)</p> Signup and view all the answers

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

<p>They are undefined for $x = 0$. (A)</p> Signup and view all the answers

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

<p>To make the coefficients of one variable the same in both equations. (D)</p> Signup and view all the answers

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

<p>y = q (A)</p> Signup and view all the answers

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

<p>The domain is all real numbers. (A)</p> Signup and view all the answers

What determines the solution when solving simultaneous equations graphically?

<p>The coordinates of the point at which the two graphs intersect. (A)</p> Signup and view all the answers

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

<p>To isolate a specific variable on one side of the equation. (A)</p> Signup and view all the answers

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

<p>Changing the value of $q$ (A)</p> Signup and view all the answers

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

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

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

<p>Switch the inequality sign. (A)</p> Signup and view all the answers

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

<p>Assign a variable to the unknown quantity. (D)</p> Signup and view all the answers

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

<p>They are found by setting $y = 0$. (B)</p> Signup and view all the answers

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

<p>Combinations of substitution and elimination methods. (B)</p> Signup and view all the answers

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

<p>The maximum or minimum point of the graph (D)</p> Signup and view all the answers

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

<p>By isolating the variable from constants and coefficients. (A)</p> Signup and view all the answers

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

<p>They may have no solutions or infinitely many solutions. (A)</p> Signup and view all the answers

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

<p>It is shifted to the right by 90°. (D)</p> Signup and view all the answers

What is the period of the tangent function?

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

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

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

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

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

Which of these points is an x-intercept of the tangent function within its domain?

<p>(180°, 0) (C)</p> Signup and view all the answers

Which equation represents a parabola?

<p>$y = ax^2 + q$ (A)</p> Signup and view all the answers

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

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

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

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

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

<p>Angles equal to 90° or 270°. (D)</p> Signup and view all the answers

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

<p>To use the y-intercept to solve for 'q'. (A)</p> Signup and view all the answers

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

<p>It causes the graph to curve upwards. (C)</p> Signup and view all the answers

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

<p>The graph moves down by q units. (A)</p> Signup and view all the answers

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

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

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

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

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

<p>The period is 360°. (C)</p> Signup and view all the answers

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

<p>It determines the rate of growth or decay. (D)</p> Signup and view all the answers

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

<p>Single horizontal asymptote at y = q. (A)</p> Signup and view all the answers

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

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

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

<p>They are exclusively at (90°, 0) and (270°, 0). (B)</p> Signup and view all the answers

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

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

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