Gr 11 Math June P1 (Medium)

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What is the value of r when r^n = a?

r = √[n]a (correct)

r = √a

r = ∛a

r = ∜[n]a

Simplify the expression a^(3/4).

∜(a^3)

∛(a^3)

a^3 / a^4

√a^3 (correct)

What is the fifth root of 32?

8

4

16

2 (correct)

Simplify the expression (√a)^3.

a^(3/2) Signup and view all the answers

What is an example of a surd?

All of the above Signup and view all the answers

What is the purpose of rationalising denominators?

To eliminate the surd from the denominator Signup and view all the answers

What is the result of multiplying √a and √b?

√(ab) Signup and view all the answers

What is the result of dividing a^m by a^n?

a^(m-n) Signup and view all the answers

What is the value of a^0 for a ≠ 0?

1 Signup and view all the answers

What is the formula for exponential growth or decay?

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

What is the purpose of completing the square in quadratic equations?

To rewrite the equation in the form of a perfect square trinomial Signup and view all the answers

What is the formula for exponential growth or decay?

P(t) = P_0 × (1 + r)^t Signup and view all the answers

What is the quadratic formula?

x = (-b ± √(b^2 - 4ac)) / 2a Signup and view all the answers

What is the definition of a rational number?

A fraction or terminating or recurring decimal Signup and view all the answers

What is the purpose of raising both sides of the equation to the power corresponding to the root when solving surd equations?

To eliminate the surd on both sides of the equation Signup and view all the answers

What is the formula for a^(-m) in terms of fractional exponents?

a^(-m) = 1 / a^m Signup and view all the answers

What is the result of raising a number to a power of -1?

The reciprocal of the number Signup and view all the answers

What is the formula for a^m × a^n?

a^(m+n) Signup and view all the answers

What is the main goal when solving surd equations?

To eliminate the surd on one side of the equation Signup and view all the answers

What is the first step in solving a quadratic equation by completing the square?

Divide the entire equation by the coefficient of the x^2 term Signup and view all the answers

What is the formula for a^(m/n) in terms of roots?

a^(m/n) = √(a^m) Signup and view all the answers

What is the purpose of converting a percentage rate to a decimal before using it in the exponential growth or decay formula?

To allow the rate to be used in the formula Signup and view all the answers

What is the purpose of checking the solution when solving surd equations?

To verify if the solution is correct Signup and view all the answers

What is the definition of an irrational number?

A non-terminating, non-recurring decimal Signup and view all the answers

What type of equations typically involve the use of exponentials?

Exponential growth and decay models Signup and view all the answers

What is the formula for compound interest?

P(t) = P_0 × (1 + r)^t Signup and view all the answers

What is the value of a^0 when a is not equal to 0?

1 Signup and view all the answers

What is the purpose of writing surds in exponential notation when solving surd equations?

To make manipulation easier Signup and view all the answers

What is the quadratic formula?

x = -b ± √(b^2 - 4ac) / 2a Signup and view all the answers

What are the conditions for real and distinct roots?

b^2 - 4ac > 0 Signup and view all the answers

What is the purpose of making a substitution in solving quadratic equations?

To simplify the equation Signup and view all the answers

What is the first step in finding the quadratic equation given the roots?

Assign a variable and write roots as two equations Signup and view all the answers

What is the discriminant of a quadratic equation?

b^2 - 4ac Signup and view all the answers

What type of roots does a quadratic equation have if the discriminant is less than zero?

Imaginary roots Signup and view all the answers

What is the purpose of verifying restrictions in the substitution method?

To ensure the expression is not undefined Signup and view all the answers

What is the result of multiplying the binomials in finding the quadratic equation?

A quadratic equation in standard form Signup and view all the answers

What is the classification of roots if the discriminant is a perfect square?

Rational roots Signup and view all the answers

What is the purpose of the substitution method in solving quadratic equations?

To simplify complex quadratic equations Signup and view all the answers

What is the value of Delta (Δ) for a quadratic equation with real and equal roots?

Δ = 0 Signup and view all the answers

What is the formula to calculate the discriminant (Δ) of a quadratic equation in standard form?

Δ = b^2 - 4ac Signup and view all the answers

What is the first step in solving a quadratic inequality?

Write the quadratic in standard form Signup and view all the answers

What is the purpose of creating a table of signs when solving a quadratic inequality?

To identify where the quadratic expression is positive or negative Signup and view all the answers

What is the graphical representation of the solution to a quadratic inequality?

A graph of the quadratic function Signup and view all the answers

What is the method used to solve systems of simultaneous equations with linear and non-linear equations?

Substitution method Signup and view all the answers

What is the condition for a system of simultaneous equations to have a unique solution?

The number of equations is equal to the number of variables Signup and view all the answers

What is the purpose of solving quadratic inequalities?

To identify the regions where a quadratic expression satisfies an inequality Signup and view all the answers

What is the result of having a quadratic inequality with a restriction?

The inequality has multiple solutions, but we need to consider restrictions to avoid undefined expressions Signup and view all the answers

What is the benefit of using a graphical representation when solving a quadratic inequality?

It visually represents the regions where the quadratic expression satisfies the inequality Signup and view all the answers

What is the effect of a on the shape of the function y = a/x?

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

What is the horizontal asymptote of the function y = a/(x+p) + q?

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

What is the effect of p on the graph of the function y = a/x + q?

A horizontal shift of p units. Signup and view all the answers

What is the main goal when solving a system of linear equations using the substitution method?

To eliminate one of the variables Signup and view all the answers

What is the range of the function y = ab^x + q?

All real numbers greater than q. Signup and view all the answers

What is the vertical asymptote of the function y = a/(x+p) + q?

The line x = -p. Signup and view all the answers

Which of the following is an example of a real-world application of problem-solving strategies in mathematics?

Computer games Signup and view all the answers

What is the effect of q on the graph of the function y = a/(x+p) + q?

A vertical shift of q units. Signup and view all the answers

What is the effect of a positive value of q on the graph of a parabolic function y = ax^2 + q?

The graph is shifted vertically upwards by q units Signup and view all the answers

What is the axes of symmetry of the hyperbola y = a/(x+p) + q?

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

What is the purpose of assigning variables to unknown quantities in a word problem?

To translate the words into algebraic expressions Signup and view all the answers

What is the effect of a negative value of a on the shape of a parabolic function y = ax^2 + q?

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

What is the effect of q on the graph of a quadratic function?

Shifts the graph vertically Signup and view all the answers

What is the domain of the function y = a/(x+p) + q?

All real numbers except -p. Signup and view all the answers

What is the range of a quadratic function when a > 0?

{y : y ≥ q, y ∈ ℝ} Signup and view all the answers

What is the axis of symmetry of a parabolic function y = a(x + p)^2 + q?

The line x = -p Signup and view all the answers

What is the effect of a on the shape of the function y = ab^x + q?

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

What is the axis of symmetry for the graph of f(x) = a(x + p)^2 + q?

The vertical line x = -p Signup and view all the answers

What is the main goal of solving a system of linear equations?

To find the values of both variables Signup and view all the answers

What is the effect of b on the direction of the function y = ab^x + q?

If b > 1, the function is increasing. Signup and view all the answers

How do you find the y-intercept of a quadratic function?

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

What is the purpose of step 7 in the problem-solving strategy?

To check the solution to ensure it is correct Signup and view all the answers

What is the effect of a positive value of p on the graph of a parabolic function y = a(x + p)^2 + q?

The graph is shifted to the left by p units Signup and view all the answers

What is the formula for the turning point of a quadratic function in the form f(x) = a(x + p)^2 + q?

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

What is the first step in solving a word problem using the problem-solving strategy?

To read the problem carefully Signup and view all the answers

How do you shift a quadratic function horizontally by m units to the right?

Replace x with x - m Signup and view all the answers

What is the average gradient of a curve between two points A and C?

The gradient of the straight line passing through points A and C Signup and view all the answers

What is the formula for the average gradient of a curve between two points A and C?

(y_A - y_C) / (x_A - x_C) Signup and view all the answers

What is the effect of q on a hyperbolic function?

Shifts the graph vertically Signup and view all the answers

What is the horizontal asymptote of a hyperbolic function?

The line y = q Signup and view all the answers

What is the value of $a^{-rac{1}{n}}$?

$rac{1}{\sqrt[n]{a}}$ Signup and view all the answers

What is the result of multiplying $a^{rac{m}{n}}$ and $a^{rac{p}{q}}$?

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

What is the result of dividing $a^m$ by $a^n$?

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

What is the purpose of rationalizing the denominator?

To eliminate the surd from the denominator Signup and view all the answers

What is the result of raising $a^m$ to the power of $1/n$?

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

What is the value of $\sqrt[n]{a^m}$?

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

What is the result of multiplying $\sqrt[n]{a}$ and $\sqrt[n]{b}$?

$\sqrt[n]{ab}$ Signup and view all the answers

What is the condition for the radicand to have real roots when $n$ is even?

The radicand must be positive Signup and view all the answers

What is the formula for the roots of a quadratic equation in the standard form ax^2 + bx + c = 0?

x = -b ± √(b^2 - 4ac) / 2a Signup and view all the answers

What is the nature of the roots of a quadratic equation when the discriminant (Δ) is greater than zero?

The roots are real and distinct. Signup and view all the answers

What is the purpose of making a substitution in solving quadratic equations?

To identify a common factor or repeated expression. Signup and view all the answers

What is the first step in finding the quadratic equation given the roots?

Assign a variable and write the roots as two equations. Signup and view all the answers

What is the condition for a quadratic equation to have real and equal roots?

Δ = 0 Signup and view all the answers

What is the result of multiplying the binomials in finding the quadratic equation given the roots?

A quadratic equation in the standard form. Signup and view all the answers

What is the purpose of verifying restrictions in the substitution method?

To ensure the solution is valid. Signup and view all the answers

What is the classification of roots if the discriminant is a perfect square?

Rational roots. Signup and view all the answers

What is the purpose of determining the restrictions in the substitution method?

To ensure the solution is valid. Signup and view all the answers

What is the formula to calculate the discriminant (Δ) of a quadratic equation in the standard form?

Δ = b^2 - 4ac Signup and view all the answers

What is the result of raising both sides of the equation to the power corresponding to the root when solving surd equations?

Eliminate the surd and simplify the equation Signup and view all the answers

What is the formula for exponential growth or decay when the initial amount is P₀, the growth rate is r, and the time period is t?

P(t) = P₀ × (1 + r)^t Signup and view all the answers

What is the purpose of converting a percentage rate to a decimal before using it in the exponential growth or decay formula?

To make the calculation easier Signup and view all the answers

What is the result of simplifying the expression (√a)³?

a^(3/2) Signup and view all the answers

What is the purpose of factorizing the quadratic equation when solving surd equations?

To solve for the variable using the zero-product property Signup and view all the answers

What is the formula for a^(-m) in terms of fractional exponents?

1/a^m Signup and view all the answers

What is the main goal when solving surd equations?

To eliminate the surd from the equation Signup and view all the answers

What is the purpose of writing surds in exponential notation when solving surd equations?

To apply the exponent laws to simplify the equation Signup and view all the answers

What is the result of multiplying a^(m) by a^(n)?

a^(m+n) Signup and view all the answers

What is the purpose of checking the solution when solving surd equations?

To verify the solution is correct and extraneous solutions are eliminated Signup and view all the answers

In the formula for exponential growth or decay, what is the purpose of converting a percentage rate to a decimal?

To make the calculation easier Signup and view all the answers

What is the result of raising a number to a power of -1?

The reciprocal of the number Signup and view all the answers

What is the purpose of completing the square in quadratic equations?

To rewrite the equation in a more convenient form Signup and view all the answers

What is the formula for $a^{m/n}$ in terms of roots?

$\sqrt[n]{a^m}$ Signup and view all the answers

What is the purpose of the quadratic formula?

To find the roots of a quadratic equation Signup and view all the answers

What is the result of multiplying $a^m$ and $a^n$?

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

What is the definition of a rational number?

A number that can be expressed as a fraction or a terminating decimal Signup and view all the answers

What is the purpose of rewriting a quadratic equation in the form of a perfect square trinomial?

To find the roots of the equation Signup and view all the answers

What is the result of dividing $a^m$ by $a^n$?

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

What is the definition of an irrational number?

A number that can be expressed as an irrational number or a non-terminating decimal Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is equal to 0?

Real and equal Signup and view all the answers

What is the purpose of creating a table of signs when solving a quadratic inequality?

To determine where the quadratic expression is positive or negative Signup and view all the answers

What is the method used to solve systems of simultaneous equations with linear and non-linear equations?

Substitution method Signup and view all the answers

What is the classification of roots if the discriminant Δ is a perfect square?

Rational Signup and view all the answers

What is the first step in solving a quadratic inequality?

Write the quadratic inequality in standard form Signup and view all the answers

What is the graphical representation of the solution to a quadratic inequality?

A region on a number line Signup and view all the answers

What is the purpose of solving quadratic inequalities?

To determine which part of the graph of a quadratic function lies above or below the x-axis Signup and view all the answers

What is the condition for a system of simultaneous equations to have a unique solution?

The system has at least two independent equations Signup and view all the answers

What is the formula to calculate the discriminant Δ of a quadratic equation in standard form?

Δ = b^2 - 4ac Signup and view all the answers

What type of roots does a quadratic equation have if the discriminant Δ is less than 0?

Non-real Signup and view all the answers

What is the main goal of solving word problems in mathematics?

To write a set of equations that describe the problem mathematically Signup and view all the answers

What is the effect of q on the graph of a parabolic function of the form y = ax^2 + q?

It shifts the graph vertically Signup and view all the answers

What is the purpose of assigning variables to unknown quantities in word problems?

To translate the words into algebraic expressions Signup and view all the answers

What is the effect of a on the shape of the graph of a parabolic function of the form y = ax^2 + q?

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

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

Make one of the variables the subject of both equations Signup and view all the answers

What is the purpose of solving systems of simultaneous equations?

To model real-world problems Signup and view all the answers

What is the effect of p on the graph of a parabolic function of the form y = a(x + p)^2 + q?

It causes a horizontal shift Signup and view all the answers

What is the purpose of checking the solution when solving a system of simultaneous equations?

To ensure the solution is correct Signup and view all the answers

What is the benefit of using a graphical representation when solving a system of simultaneous equations?

It provides a visual representation of the solution Signup and view all the answers

What is the purpose of solving quadratic inequalities?

To find the range of possible values of a variable Signup and view all the answers

What is the effect of q on the graph of y = a/x + q?

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

What is the turning point of the graph of f(x) = a(x + p)^2 + q?

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

What is the axis of symmetry for f(x) = a(x + p)^2 + q?

The vertical line x = -p Signup and view all the answers

What is the range of the graph of f(x) = a(x + p)^2 + q if a > 0?

{y : y ≥ q, y ∈ ℝ} Signup and view all the answers

What is the average gradient of the curve between points A and C?

Gradient of the line passing through points A and C Signup and view all the answers

What is the formula for the average gradient of a curve f(x) with points P(a, f(a)) and Q(a + h, f(a + h))?

[f(a + h) - f(a)]/h Signup and view all the answers

What is the effect of a on the shape of the graph of f(x) = a(x + p)^2 + q?

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

What is the domain of the graph of f(x) = a(x + p)^2 + q?

{x : x ∈ ℝ} Signup and view all the answers

What is the y-intercept of the graph of f(x) = a(x + p)^2 + q?

f(-p) Signup and view all the answers

What is the x-intercept of the graph of f(x) = a(x + p)^2 + q?

The roots of the equation f(x) = 0 Signup and view all the answers

What is the effect of a on the shape of the function y = a/(x+p) + q?

It affects the vertical asymptote Signup and view all the answers

What is the domain of the function y = a/(x+p) + q?

All real numbers except x = -p Signup and view all the answers

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

All real numbers greater than q Signup and view all the answers

What is the effect of p on the graph of the function y = a/(x+p) + q?

It shifts the graph horizontally Signup and view all the answers

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

y = q Signup and view all the answers

What is the effect of q on the graph of the function y = ab^x + q?

It shifts the graph vertically Signup and view all the answers

What is the axes of symmetry of the hyperbola y = a/(x+p) + q?

The lines x = -p and y = q Signup and view all the answers

What is the effect of a on the shape of the function y = ab^x + q?

It affects the direction of the graph Signup and view all the answers

What is the vertical asymptote of the function y = a/(x+p) + q?

x = -p Signup and view all the answers

What is the effect of b on the shape of the function y = ab^x + q?

It affects the direction of the graph Signup and view all the answers

What is the value of a^(1/n) where a > 0 and n is a positive integer?

$\sqrt[n]{a}$ Signup and view all the answers

Simplify the expression (a)^2.

$a$ Signup and view all the answers

What is the purpose of rationalizing the denominator in surd expressions?

To eliminate the surd from the denominator Signup and view all the answers

What is the value of a^(m/n) where a > 0 and m, n are integers?

$\left(a^m ight)^{rac{1}{n}}$ Signup and view all the answers

What is the result of multiplying a and b?

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

What is the purpose of using surds in mathematical expressions?

To represent irrational numbers Signup and view all the answers

What is the result of raising a number to a power of -1?

The reciprocal of the number Signup and view all the answers

What is the definition of a surd?

A radical resulting in an irrational number Signup and view all the answers

What is the purpose of using the exponential growth or decay formula?

To find the final amount after a certain period of time Signup and view all the answers

What is the result of raising a number to a power of -1?

The reciprocal of the number Signup and view all the answers

What is the first step in solving a quadratic equation by completing the square?

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

What is the correct formula to simplify the expression $a^{rac{m}{n}}$?

$\sqrt[n]{a^m}$ Signup and view all the answers

What is the formula for exponential growth or decay when the initial amount is A, the rate of growth or decay is r, and the time is t?

A(1 + r)^t Signup and view all the answers

When solving surd equations, what is the main goal?

To eliminate the surd from the equation. Signup and view all the answers

What is the purpose of converting a percentage rate to a decimal before using it in the exponential growth or decay formula?

To ensure the formula works correctly Signup and view all the answers

What is the purpose of exponential growth or decay formula?

To model population growth and decay. Signup and view all the answers

What is the result of multiplying a^m by a^n?

a^(m+n) Signup and view all the answers

What is the formula for the nth root of a number?

a^(1/n) Signup and view all the answers

When solving quadratic surd equations, what is the next step after isolating and simplifying the equation?

Square both sides of the equation. Signup and view all the answers

What is the purpose of completing the square in quadratic equations?

To transform a quadratic equation into a perfect square trinomial Signup and view all the answers

What is the formula for compound interest?

$P(t) = P_0 imes (1 + r)^t$ Signup and view all the answers

What is the formula for the quadratic formula?

x = (-b ± √(b^2 - 4ac)) / 2a Signup and view all the answers

What is the result of raising both sides of a surd equation to the power corresponding to the root?

The surd is eliminated. Signup and view all the answers

What is the purpose of writing surds in exponential notation when solving surd equations?

To make manipulation easier. Signup and view all the answers

What is the purpose of checking the solution when solving surd equations?

To verify the solution is correct. Signup and view all the answers

What type of equations typically involve the use of exponentials?

Exponential growth or decay equations. Signup and view all the answers

What is the formula for $a^{-m}$ in terms of fractional exponents?

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

What is the condition for a quadratic equation to have real and equal roots?

b^2 - 4ac = 0 Signup and view all the answers

What is the purpose of making a substitution in solving quadratic equations?

To simplify the process of finding the roots Signup and view all the answers

What is the formula to calculate the discriminant (Δ) of a quadratic equation in standard form?

b^2 - 4ac Signup and view all the answers

What is the result of having a quadratic equation with a discriminant less than zero?

The equation has no real roots, only imaginary ones Signup and view all the answers

What is the final step in finding the quadratic equation given the roots?

Multiply the binomials Signup and view all the answers

What is the purpose of verifying restrictions in the substitution method?

To ensure the solutions are valid Signup and view all the answers

What is the classification of roots if the discriminant is a perfect square?

Rational Signup and view all the answers

What is the purpose of finding the quadratic equation given the roots?

To work backwards from the roots to the original equation Signup and view all the answers

What is the first step in solving quadratic equations by substitution?

Identify restrictions Signup and view all the answers

What is the nature of the roots of a quadratic equation with a discriminant greater than zero?

Real and distinct Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is equal to 0?

Real and equal Signup and view all the answers

What is the formula to calculate the discriminant Δ of a quadratic equation in standard form?

Δ = b^2 - 4ac Signup and view all the answers

What is the first step in solving a quadratic inequality?

Write the quadratic inequality in standard form Signup and view all the answers

What is the purpose of creating a table of signs when solving a quadratic inequality?

To determine the sign of each factor on intervals defined by the critical values Signup and view all the answers

What is the graphical representation of the solution to a quadratic inequality?

The regions of the graph where the quadratic function is positive or negative Signup and view all the answers

What is the main goal of solving a system of equations?

To find the values of all variables Signup and view all the answers

What is the method used to solve systems of simultaneous equations with linear and non-linear equations?

Substitution method Signup and view all the answers

What is the effect of q on the graph of y = ax^2 + q?

It shifts the graph vertically Signup and view all the answers

What is the condition for a system of simultaneous equations to have a unique solution?

The number of equations is equal to the number of variables Signup and view all the answers

What is the purpose of translating words into algebraic expressions when solving word problems?

To describe the problem mathematically Signup and view all the answers

What is the purpose of solving quadratic inequalities?

To determine the intervals where the quadratic function is positive or negative Signup and view all the answers

What is the effect of p on the graph of y = a(x + p)^2 + q?

It shifts the graph horizontally Signup and view all the answers

What is the purpose of checking the solution when solving a system of equations?

To verify the solution Signup and view all the answers

What is the result of having a quadratic inequality with a restriction?

The solution is restricted to a certain domain Signup and view all the answers

What is the result of solving a system of equations using the substitution method?

One equation with one unknown variable Signup and view all the answers

What is the benefit of using a graphical representation when solving a quadratic inequality?

It helps to visualize the solution intervals Signup and view all the answers

What is the purpose of solving word problems?

To describe real-life situations mathematically Signup and view all the answers

What is the effect of a on the shape of the parabola y = ax^2 + q?

It changes the shape of the parabola Signup and view all the answers

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

Add or subtract the equations to eliminate one variable Signup and view all the answers

What is the purpose of using mathematical language to describe real-life situations?

To solve the problem mathematically Signup and view all the answers

What is the effect of a on the shape of the function y = a/x?

The function is reflected about the x-axis if a < 0. Signup and view all the answers

What is the vertical asymptote of the function y = a/(x+p) + q?

The line x = -p. Signup and view all the answers

What is the effect of p on the graph of the function y = a/(x+p) + q?

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

What is the range of the function y = ab^x + q?

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

What is the effect of q on the graph of the function y = ab^x + q?

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

What is the domain of the function y = a/(x+p) + q?

All real numbers except -p. Signup and view all the answers

What is the axis of symmetry of the hyperbola y = a/(x+p) + q?

The point (-p, q). Signup and view all the answers

What is the effect of a on the shape of the function y = ab^x + q?

It determines whether the function is increasing or decreasing. Signup and view all the answers

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

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

What is the effect of b on the shape of the function y = ab^x + q?

It determines the direction of the function. Signup and view all the answers

What is the effect of the value of q on the graph of the function y = ax^2 + q?

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

What is the turning point of the function f(x) = a(x+p)^2 + q?

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

What is the axis of symmetry of the function f(x) = a(x+p)^2 + q?

The vertical line x = -p. Signup and view all the answers

What is the effect of a on the shape of the graph of the function y = ax^2?

It changes the shape of the graph. Signup and view all the answers

What is the formula for calculating the average gradient of a curve between two points A and C?

Gradient = (y_A - y_C) / (x_A - x_C) Signup and view all the answers

What is the effect of q on the graph of the function y = a/x + q?

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

What is the purpose of finding the average gradient of a curve?

To find the gradient of the tangent at a point. Signup and view all the answers

What is the form of the equation of a quadratic function with a turning point at (-p, q)?

y = a(x + p)^2 + q Signup and view all the answers

What is the effect of a horizontal shift on the graph of the function y = ax^2?

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

What is the formula for the equation of a quadratic function with a turning point at (p, q)?

y = a(x - p)^2 + q Signup and view all the answers

What is the cube root of 27?

3 Signup and view all the answers

What is the value of a^(3/2) when a = 9?

27 Signup and view all the answers

Simplify the expression (√a)^2.

a Signup and view all the answers

What is the result of multiplying √a and √b?

√(ab) Signup and view all the answers

What is the purpose of rationalising denominators?

To eliminate the surd from the denominator. Signup and view all the answers

What is the value of a^(-3/4) when a = 16?

1/8 Signup and view all the answers

Simplify the expression √(a^3).

a^(3/2) Signup and view all the answers

What is the result of dividing a^m by a^n?

a^(m-n) Signup and view all the answers

What is the goal when solving surd equations?

To eliminate the surd term from the equation Signup and view all the answers

What is the formula for exponential growth or decay?

P(t) = P_0 × (1 + r)^t Signup and view all the answers

What is the result of raising both sides of an equation to the power corresponding to the root when solving surd equations?

Elimination of the surd term Signup and view all the answers

What is the purpose of rationalising denominators?

To eliminate radicals from the denominator Signup and view all the answers

What is the result of multiplying a^m by a^n?

a^(m+n) Signup and view all the answers

What is the purpose of converting a percentage rate to a decimal before using it in the exponential growth or decay formula?

To ensure accuracy in the calculation Signup and view all the answers

What is the formula for compound interest?

A = P_0 × (1 + r)^t Signup and view all the answers

What type of equations typically involve the use of exponentials?

Exponential growth or decay models Signup and view all the answers

What is the purpose of writing surds in exponential notation when solving surd equations?

To make manipulation of the surd easier Signup and view all the answers

What is the benefit of verifying the solution when solving surd equations?

To check for extraneous solutions Signup and view all the answers

What is the condition for a quadratic equation to have real and distinct roots?

b^2 - 4ac > 0 Signup and view all the answers

What is the purpose of making a substitution in solving quadratic equations?

To simplify the process significantly Signup and view all the answers

If the discriminant is less than zero, what type of roots does the quadratic equation have?

Imaginary roots Signup and view all the answers

What is the formula for finding the quadratic equation given the roots?

(x - r1)(x - r2) = 0 Signup and view all the answers

What is the first step in finding the quadratic equation given the roots?

Write down the roots as two equations Signup and view all the answers

What is the purpose of verifying restrictions in the substitution method?

To ensure the values obtained do not result in undefined expressions Signup and view all the answers

What is the value of x in the equation x^2 + 4x + 4 = 0, solved by completing the square?

-2 Signup and view all the answers

If the discriminant is a perfect square, what type of roots does the quadratic equation have?

Rational roots Signup and view all the answers

Which of the following is a step in solving a quadratic equation by completing the square?

Add and subtract the square of half the coefficient of the x term Signup and view all the answers

What is the formula to calculate the discriminant (Δ) of a quadratic equation in standard form?

Δ = b^2 - 4ac Signup and view all the answers

What is the formula for solving quadratic equations, derived from completing the square?

x = -b ± √(b^2 - 4ac) / 2a Signup and view all the answers

What is the value of Delta (Δ) for a quadratic equation with real and equal roots?

Δ = 0 Signup and view all the answers

What is the purpose of taking half the coefficient of the x term and squaring it when completing the square?

To create a perfect square trinomial Signup and view all the answers

What is the nature of the roots of a quadratic equation determined by?

The discriminant Signup and view all the answers

What is the value of x in the equation x^2 - 6x + 8 = 0, solved using the quadratic formula?

2 or 4 Signup and view all the answers

What is the definition of a rational number?

A number that can be expressed as a fraction or terminating or recurring decimal Signup and view all the answers

What is the purpose of converting a percentage rate to a decimal before using it in the exponential growth or decay formula?

To ensure the formula is accurate Signup and view all the answers

What is the formula for exponential growth or decay?

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

What is the result of raising a number to a power of -1?

The reciprocal of the number Signup and view all the answers

What is the definition of an irrational number?

A number that is not a rational number Signup and view all the answers

What is the nature of roots of a quadratic equation if the discriminant Δ is equal to zero?

Real and equal Signup and view all the answers

What is the formula to calculate the discriminant Δ of a quadratic equation in standard form?

Δ = b^2 - 4ac Signup and view all the answers

What is the purpose of creating a table of signs when solving a quadratic inequality?

To determine where the quadratic expression is positive or negative Signup and view all the answers

What is the method used to solve systems of simultaneous equations with linear and non-linear equations?

All of the above Signup and view all the answers

What type of roots does a quadratic equation have if the discriminant Δ is less than zero?

Imaginary Signup and view all the answers

What is the first step in solving a quadratic inequality?

Write the quadratic inequality in standard form Signup and view all the answers

What is the graphical representation of the solution to a quadratic inequality?

A region above or below the x-axis Signup and view all the answers

What is the condition for a system of simultaneous equations to have a unique solution?

The number of equations is equal to the number of variables Signup and view all the answers

What is the purpose of solving quadratic inequalities?

To determine which part of the graph lies above or below the x-axis Signup and view all the answers

What is the result of having a quadratic inequality with a restriction?

The solution must be checked to ensure it is valid Signup and view all the answers

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

Make one of the variables the subject of both equations Signup and view all the answers

What is the purpose of solving word problems in mathematics?

To model real-world situations Signup and view all the answers

What is the effect of a negative value of q on the graph of y = ax^2 + q?

The graph is shifted vertically downwards Signup and view all the answers

What is the purpose of assigning variables to unknown quantities in word problems?

To translate the words into algebraic expressions Signup and view all the answers

What is the result of solving a system of simultaneous equations using the elimination method?

One equation with one unknown variable Signup and view all the answers

What is the effect of a on the shape of the graph of y = ax^2 + q?

It makes the graph wider or narrower Signup and view all the answers

What is the purpose of solving quadratic equations in mathematics?

To find the roots of the equation Signup and view all the answers

What is the effect of p on the graph of y = a(x + p)^2 + q?

It shifts the graph horizontally Signup and view all the answers

What is the final step in solving a system of simultaneous equations using the substitution method?

Write the final answer Signup and view all the answers

What is the purpose of solving systems of simultaneous equations in mathematics?

To find the intersection of two graphs Signup and view all the answers

What is the effect of a on the shape of the function y = a/x?

It changes the shape of the graph, making it a 'smile' or a 'frown'. Signup and view all the answers

What is the turning point of the function f(x) = a(x + p)^2 + q?

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

What is the axis of symmetry for the function f(x) = a(x + p)^2 + q?

The vertical line x = -p Signup and view all the answers

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

{y : y ≥ q, y ∈ ℝ} Signup and view all the answers

What is the effect of q on the graph of the function f(x) = a/(x + p) + q?

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

What is the average gradient of the curve between two points A and C?

The gradient of the line passing through points A and C. Signup and view all the answers

What is the formula for the average gradient of a curve f(x) between two points P(a, f(a)) and Q(a + h, f(a + h))?

(f(a + h) - f(a)) / h Signup and view all the answers

What is the y-intercept of the function f(x) = a(x + p)^2 + q?

The point (0, q + ap^2) Signup and view all the answers

What is the effect of a on the graph of the function f(x) = a(x + p)^2 + q?

It affects the shape of the graph, making it a 'smile' or a 'frown'. Signup and view all the answers

What is the domain of the function f(x) = a(x + p)^2 + q?

{x : x ∈ ℝ} Signup and view all the answers

What is the effect of a on the shape of the function y = a/x?

It determines the quadrants in which the function lies. Signup and view all the answers

What happens to the graph of y = a/(x+p) + q when p is increased?

The graph is shifted horizontally to the right. Signup and view all the answers

What is the vertical asymptote of the function y = a/(x+p) + q?

The line x = -p. Signup and view all the answers

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

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

What is the effect of q on the graph of y = ab^x + q?

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

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

All real numbers greater than q. Signup and view all the answers

What is the domain of the function y = a/(x+p) + q?

All real numbers except x = -p. Signup and view all the answers

What is the axis of symmetry of the function y = a/(x+p) + q?

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

What is the effect of a on the shape of the function y = ab^x + q?

It determines whether the graph lies above or below the horizontal asymptote. Signup and view all the answers

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

The graph becomes more steep. Signup and view all the answers

Gr 11 Math June P1 (Medium)

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Questions and Answers

What is the value of r when r^n = a?

Simplify the expression a^(3/4).

What is the fifth root of 32?

Simplify the expression (√a)^3.

What is an example of a surd?

What is the purpose of rationalising denominators?

What is the result of multiplying √a and √b?

What is the result of dividing a^m by a^n?

What is the value of a^0 for a ≠ 0?

What is the formula for exponential growth or decay?

What is the purpose of completing the square in quadratic equations?

What is the formula for exponential growth or decay?

What is the quadratic formula?

What is the definition of a rational number?

What is the purpose of raising both sides of the equation to the power corresponding to the root when solving surd equations?

What is the formula for a^(-m) in terms of fractional exponents?

What is the result of raising a number to a power of -1?

What is the formula for a^m × a^n?

What is the main goal when solving surd equations?

What is the first step in solving a quadratic equation by completing the square?

What is the formula for a^(m/n) in terms of roots?

What is the purpose of converting a percentage rate to a decimal before using it in the exponential growth or decay formula?

What is the purpose of checking the solution when solving surd equations?

What is the definition of an irrational number?

What type of equations typically involve the use of exponentials?

What is the formula for compound interest?

What is the value of a^0 when a is not equal to 0?

What is the purpose of writing surds in exponential notation when solving surd equations?

What is the quadratic formula?

What are the conditions for real and distinct roots?

What is the purpose of making a substitution in solving quadratic equations?

What is the first step in finding the quadratic equation given the roots?

What is the discriminant of a quadratic equation?

What type of roots does a quadratic equation have if the discriminant is less than zero?

What is the purpose of verifying restrictions in the substitution method?

What is the result of multiplying the binomials in finding the quadratic equation?

What is the classification of roots if the discriminant is a perfect square?

What is the purpose of the substitution method in solving quadratic equations?

What is the value of Delta (Δ) for a quadratic equation with real and equal roots?

What is the formula to calculate the discriminant (Δ) of a quadratic equation in standard form?

What is the first step in solving a quadratic inequality?

What is the purpose of creating a table of signs when solving a quadratic inequality?

What is the graphical representation of the solution to a quadratic inequality?

What is the method used to solve systems of simultaneous equations with linear and non-linear equations?

What is the condition for a system of simultaneous equations to have a unique solution?

What is the purpose of solving quadratic inequalities?

What is the result of having a quadratic inequality with a restriction?

What is the benefit of using a graphical representation when solving a quadratic inequality?

What is the effect of a on the shape of the function y = a/x?

What is the horizontal asymptote of the function y = a/(x+p) + q?

What is the effect of p on the graph of the function y = a/x + q?

What is the main goal when solving a system of linear equations using the substitution method?

What is the range of the function y = ab^x + q?

What is the vertical asymptote of the function y = a/(x+p) + q?

Which of the following is an example of a real-world application of problem-solving strategies in mathematics?

What is the effect of q on the graph of the function y = a/(x+p) + q?

What is the effect of a positive value of q on the graph of a parabolic function y = ax^2 + q?

What is the axes of symmetry of the hyperbola y = a/(x+p) + q?

What is the purpose of assigning variables to unknown quantities in a word problem?

What is the effect of a negative value of a on the shape of a parabolic function y = ax^2 + q?

What is the effect of q on the graph of a quadratic function?

What is the domain of the function y = a/(x+p) + q?

What is the range of a quadratic function when a > 0?

What is the axis of symmetry of a parabolic function y = a(x + p)^2 + q?

What is the effect of a on the shape of the function y = ab^x + q?

What is the axis of symmetry for the graph of f(x) = a(x + p)^2 + q?

What is the main goal of solving a system of linear equations?

What is the effect of b on the direction of the function y = ab^x + q?

How do you find the y-intercept of a quadratic function?

What is the purpose of step 7 in the problem-solving strategy?

What is the effect of a positive value of p on the graph of a parabolic function y = a(x + p)^2 + q?

What is the formula for the turning point of a quadratic function in the form f(x) = a(x + p)^2 + q?

What is the first step in solving a word problem using the problem-solving strategy?

How do you shift a quadratic function horizontally by m units to the right?

What is the average gradient of a curve between two points A and C?

What is the formula for the average gradient of a curve between two points A and C?