Gr 11 Math June P1 (Easy)

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What is the rational number that can be written as a fraction with an integer in the numerator and the denominator?

A number that is always negative

A number that can be written as a fraction with an integer in the numerator and the denominator (correct)

A number that can only be written as a whole number

Any number that can be written as a decimal

What is the value of r in the equation r^n = a, where n ≥ 2?

√(a) (correct)

√(a^n)

a^(1/n)

√(a^(1/n))

What is the value of a^(1/n), where a > 0 and n ≥ 2?

√(a^n)

a^n

√(a) (correct)

a^(1/n^2)

What is the radical symbol that indicates the nth root of a?

√<a href="a">n</a> Signup and view all the answers

What is a surd?

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

What is the property of simplifying surds that states √(a) × √(b) = √(ab)?

Product of Radicals Signup and view all the answers

What is the purpose of rationalising the denominator?

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

What is the law of exponents that states a^m × a^n = a^(m+n)?

Product of Powers 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 purpose of rationalizing denominators?

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

What is the formula for a^(-m)?

1/a^m Signup and view all the answers

What is the purpose of the zero-product property in solving quadratic surd equations?

To solve for both factors Signup and view all the answers

What is the formula for a^(m/n)?

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

What is the first step in identifying the variables in an exponential growth or decay problem?

Determine the initial amount, growth rate, and time period Signup and view all the answers

What is the first step in solving surd equations?

Isolate the surd Signup and view all the answers

What is the set of natural numbers represented by?

ℕ Signup and view all the answers

What is the purpose of converting surds to exponential notation?

To make manipulation easier Signup and view all the answers

What is the formula for exponential growth or decay?

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

What is the formula for population growth?

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

What is the purpose of completing the square?

To solve quadratic equations Signup and view all the answers

What is the purpose of checking solutions in surd equations?

To verify the solution is correct 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 quadratic formula used for?

Solving quadratic equations 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 first step in solving quadratic equations by completing the square?

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

What is the definition of a^0?

a^0 = 1 Signup and view all the answers

What is the definition of a^(-n)?

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

What is the definition of √(a)?

√(a) = a^1/2 Signup and view all the answers

What is the formula to determine the roots of a quadratic equation?

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

What type of roots does a quadratic equation have when b^2 - 4ac > 0?

Real and distinct roots Signup and view all the answers

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

Identify restrictions Signup and view all the answers

What is the purpose of the discriminant in a quadratic equation?

To determine the type of roots Signup and view all the answers

What type of roots does a quadratic equation have when b^2 - 4ac < 0?

Complex conjugate roots Signup and view all the answers

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

Write the final answer Signup and view all the answers

When is the discriminant of a quadratic equation equal to zero?

When the equation has exactly one real root Signup and view all the answers

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

To simplify the equation by making a substitution Signup and view all the answers

What happens when the discriminant is a perfect square?

The roots are rational Signup and view all the answers

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

Write the equation as the product of two factors Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is less than 0?

Non-real Signup and view all the answers

What is the formula for 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 a table of signs in 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 a quadratic inequality?

A graph that shows the regions where the quadratic expression is positive or negative Signup and view all the answers

What is the purpose of solving simultaneous linear equations?

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

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

Substitution Signup and view all the answers

What is required to solve for the values of n unknown variables?

A system of n independent equations Signup and view all the answers

What is the main difference between solving quadratic equations and quadratic inequalities?

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

What is the purpose of sign analysis in solving quadratic inequalities?

To determine where each factor is positive or negative on the number line Signup and view all the answers

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

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

What is the purpose of equating the two equations in the elimination method?

To reduce the number of equations and variables by one. Signup and view all the answers

What is the final step in solving word problems?

Write the final answer. Signup and view all the answers

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

The graph is shifted vertically upwards. Signup and view all the answers

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

The graph becomes a 'frown'. Signup and view all the answers

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

The graph is shifted to the right. 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 role of problem-solving strategies in real-world applications?

To understand how the natural world works. Signup and view all the answers

What is the purpose of drawing the graph of each equation on the same system of axes in solving graphically?

To find the solution to the system of equations. Signup and view all the answers

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

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

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

It affects the vertical shift of the graph 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

How do you shift the graph of a quadratic function 2 units to the right?

Replace x with x - 2 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 general form of a hyperbolic function?

y = a/x + q Signup and view all the answers

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

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

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

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

What is the formula for finding the y-intercept of a quadratic function?

Set x = 0 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 domain of the graph of a quadratic function?

All real numbers Signup and view all the answers

What is the effect of a positive value of q on the graph of f(x) = 1/x + q?

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

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

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

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

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

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

The graph lies in the first and third quadrants. Signup and view all the answers

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

The line y = q Signup and view all the answers

What is the effect of a positive value of b on the graph of f(x) = ab^x + q?

The graph is increasing and lies above the horizontal asymptote. Signup and view all the answers

What is the effect of a negative value of a on the graph of f(x) = ab^x + q?

The graph is reflected about the horizontal asymptote. Signup and view all the answers

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

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

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

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

What is the axes of symmetry intersect at in the graph of f(x) = a/(x + p) + q?

(-p, 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 property of surds that states $\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{ab}$?

Product of surds Signup and view all the answers

What is the purpose of rationalising the denominator?

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

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

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

What is the law of exponents that states $a^m \times a^n = a^{m+n}$?

Product of powers 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 value of $\sqrt[n]{a^m}$?

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

What is the property of surds that states $\frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}$?

Quotient of surds Signup and view all the answers

What is the purpose of identifying the variables in an exponential growth or decay problem?

To determine the initial amount, growth rate, and time period Signup and view all the answers

What is the result of multiplying a rational number by its reciprocal?

1 Signup and view all the answers

What is the formula for determining the roots of a quadratic equation?

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

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

Real numbers Signup and view all the answers

What type of roots does a quadratic equation have when b^2 - 4ac > 0?

Real and distinct roots Signup and view all the answers

What is the formula used to find the solutions of a quadratic equation?

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

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

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

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

To identify a repeated expression Signup and view all the answers

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

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

What is the result of raising a number to the power of 0?

1 Signup and view all the answers

What is the formula used to find the roots of a quadratic equation by completing the square?

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

What is the discriminant of a quadratic equation?

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

What is the definition of a surd?

A root of a number that cannot be expressed as a finite decimal Signup and view all the answers

What happens when the discriminant is a perfect square?

The roots are rational Signup and view all the answers

What is the purpose of the quadratic formula in solving quadratic equations?

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

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

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

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

Multiply by constants if required Signup and view all the answers

What is the result of raising a number to a negative power?

The reciprocal of the number Signup and view all the answers

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

Imaginary roots Signup and view all the answers

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

Write down as the product of two factors 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 one side of 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 purpose of converting surds to exponential notation?

To make manipulation easier Signup and view all the answers

What is the definition of a^0?

a^0 = 1, for a ≠ 0 Signup and view all the answers

What is the purpose of checking solutions in surd equations?

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

What is the formula for a^(m/n)?

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

What is the purpose of factorizing quadratic equations in surd form?

To solve for the variable Signup and view all the answers

What is the definition of a^(-m)?

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

What is the purpose of applying exponent laws when solving surd equations?

To make manipulation easier Signup and view all the answers

What is the first step in solving surd equations?

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

What is the nature of the roots of a quadratic equation if Δ = 0?

Real and equal roots Signup and view all the answers

What is the purpose of the discriminant Δ in a quadratic equation?

To determine the nature of the roots of the equation 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 a table of signs in solving a quadratic inequality?

To determine the sign of the quadratic expression on different intervals Signup and view all the answers

What is the graphical representation of a quadratic inequality?

The regions where the quadratic expression is positive or negative Signup and view all the answers

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

Substitution method Signup and view all the answers

What is required to solve for the values of n unknown variables?

A system of n independent equations Signup and view all the answers

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

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

What is the purpose of solving quadratic inequalities?

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

What is the main difference between solving quadratic equations and quadratic inequalities?

The purpose of solving them Signup and view all the answers

What is the purpose of solving simultaneous linear equations?

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

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

Vertical shift Signup and view all the answers

What is the first step in solving a word problem?

Read the problem carefully Signup and view all the answers

What is the purpose of translating words into algebraic expressions in a word problem?

To set up a system of equations Signup and view all the answers

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

Change in shape of the graph Signup and view all the answers

What is the purpose of solving systems of equations?

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

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

Horizontal shift Signup and view all the answers

What is the purpose of substitution in solving quadratic equations?

To eliminate one variable Signup and view all the answers

What is the purpose of elimination in solving quadratic equations?

To eliminate one variable Signup and view all the answers

What is the purpose of solving quadratic equations?

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

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

Causes a vertical shift Signup and view all the answers

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

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

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

Set x = 0 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 axis of symmetry for a quadratic function in the form f(x) = a(x + p)^2 + q?

x = -p Signup and view all the answers

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

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

What is the formula for the average gradient between two points on a curve?

Gradient = (y2 - y1) / (x2 - x1) Signup and view all the answers

What is the purpose of the average gradient formula?

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

What is the general form of a hyperbolic function?

y = a/x + q Signup and view all the answers

What is the purpose of finding the average gradient between two points on a curve?

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

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

A horizontal shift 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 effect of a change in q on the graph of y = a/(x + p) + q?

A vertical shift Signup and view all the answers

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

All real numbers except y = q Signup and view all the answers

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

The line y = q Signup and view all the answers

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

A change in shape Signup and view all the answers

What is the equation of the vertical asymptote of the graph of y = ab^x + q?

There is no vertical asymptote Signup and view all the answers

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

A vertical shift Signup and view all the answers

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

All real numbers Signup and view all the answers

What is the effect of a change in b on the graph of y = ab^x + q?

A change in direction 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 value of $a^{rac{m}{n}}$?

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

What is the purpose of rationalising the denominator?

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

What is the property of simplifying surds that states $\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{ab}$?

Simplifying surds Signup and view all the answers

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

$\sqrt[n]{a}$ 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 the laws of exponents?

To extend the rules of exponents to include rational numbers Signup and view all the answers

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

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

What is the purpose of exponent laws in algebra?

To govern the manipulation of expressions involving exponents Signup and view all the answers

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

Eliminating the surd 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 purpose of factorizing a quadratic equation in solving surd equations?

To solve for both factors Signup and view all the answers

What is the definition of a^0?

a^0 = 1, for a ≠ 0 Signup and view all the answers

What is the purpose of converting surds to exponential notation in solving surd equations?

To make manipulation easier Signup and view all the answers

What is the result of substituting a solution back into the original equation in solving surd equations?

Verifying the solution is correct Signup and view all the answers

What is the purpose of isolating the surd in solving surd equations?

To get the surd term by itself on one side of the equation Signup and view all the answers

What is the definition of a^(-m)?

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

What is the formula for population growth?

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

What is the first step in identifying the variables in an exponential growth or decay problem?

Determine the initial amount (P0) Signup and view all the answers

What is the purpose of converting percentage rates into decimal form in exponential growth or decay problems?

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

What is the set of real numbers represented by?

ℝ Signup and view all the answers

What is the formula to determine the roots of a quadratic equation?

x = -b/2a ± √(b² - 4ac)/2a Signup and view all the answers

What is the formula for completing the square in a quadratic equation?

x^2 + bx + c = (x + b/2a)^2 - (b/2a)^2 + c/a Signup and view all the answers

What happens when the discriminant is less than 0?

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

What is the purpose of the discriminant in a quadratic equation?

To determine the type of roots of the equation Signup and view all the answers

What is the purpose of the quadratic formula?

To solve quadratic equations Signup and view all the answers

What is the definition of a^(1/n) in exponential notation?

the nth root of a Signup and view all the answers

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

Determine the restrictions Signup and view all the answers

What is the formula for a^(-m) in exponential notation?

1/a^m Signup and view all the answers

What type of roots does a quadratic equation have when b² - 4ac = 0?

One real root Signup and view all the answers

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

Write the final answer Signup and view all the answers

What is the purpose of rationalizing the denominator in a surd expression?

To simplify the expression Signup and view all the answers

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

Δ = b² - 4ac Signup and view all the answers

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

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

What type of roots does a quadratic equation have when b² - 4ac > 0?

Two distinct real roots Signup and view all the answers

What is the purpose of solving quadratic equations by completing the square?

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

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

To make the equation easier to solve Signup and view all the answers

When is the discriminant of a quadratic equation equal to zero?

When the equation has one real root 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 solving a quadratic inequality?

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

What is the formula for 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 required to solve for the values of n unknown variables?

A system of n independent equations Signup and view all the answers

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

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

What is the graphical representation of a quadratic inequality?

A region on a coordinate plane Signup and view all the answers

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

Substitution method Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is greater than 0?

Real and unequal Signup and view all the answers

What is the purpose of solving simultaneous linear equations?

To determine the point of intersection Signup and view all the answers

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

A vertical shift upwards 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 effect of a negative p on the graph of y = a/(x + p) + q?

A horizontal shift to the left Signup and view all the answers

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

All real numbers except y = q Signup and view all the answers

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

It determines if the graph lies in the first and third quadrants or the second and fourth quadrants Signup and view all the answers

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

x = -p Signup and view all the answers

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

y = q Signup and view all the answers

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

A vertical shift Signup and view all the answers

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

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

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

A horizontal shift Signup and view all the answers

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

Solve one of the equations for one variable Signup and view all the answers

What is the purpose of writing a set of equations when solving a word problem?

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

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

Vertical shift Signup and view all the answers

What is the purpose of solving simultaneous linear equations in real-world applications?

To find the solution to a system of linear equations Signup and view all the answers

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

Change in shape Signup and view all the answers

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

Write the final answer Signup and view all the answers

What is the purpose of solving quadratic equations in real-world applications?

To find the solution to a quadratic equation Signup and view all the answers

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

Horizontal shift Signup and view all the answers

What is the first step in solving a word problem?

Read the problem carefully Signup and view all the answers

What is the purpose of solving systems of linear equations in real-world applications?

To find the solution to a system of linear equations Signup and view all the answers

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

It affects whether the turning point is above or below the x-axis Signup and view all the answers

What is the domain of a quadratic function?

All real numbers Signup and view all the answers

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

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

How do you shift a quadratic function 2 units to the right?

Replace x with x - 2 Signup and view all the answers

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

The gradient of the line passing through the two points Signup and view all the answers

What is the formula for the average gradient of a curve?

(y2 - y1) / (x2 - x1) Signup and view all the answers

What is a hyperbolic function?

A function of the form y = a / x + q Signup and view all the answers

What is the purpose of finding the equation of a parabola from the graph?

To write the equation of the parabola in the form y = ax^2 + bx + c Signup and view all the answers

What is the effect of a negative value of a on the shape of a quadratic function?

It makes the graph open downwards Signup and view all the answers

What is the value of a^(1/n) when a > 0 and n ≥ 2?

√(a) Signup and view all the answers

What is the property of surds that states √(a) × √(b) = √(ab)?

Simplification of Surds Signup and view all the answers

What is the purpose of rationalising the denominator in a surd expression?

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

What is the value of a^(-1/n) when a > 0 and n ≥ 2?

1/√(a) Signup and view all the answers

What is the value of a^(m/n) when a > 0, m ∈ ℤ, and n ∈ ℤ, n ≠ 0?

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

What is the property of rational exponents that states a^(m/n) = √(a^m)^(1/n)?

Rational Exponents Signup and view all the answers

What is the purpose of expressing surds in exponential notation?

To simplify the surd expression Signup and view all the answers

What is the value of a^(m/n) when a < 0, m ∈ ℤ, and n ∈ ℤ, n ≠ 0?

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

What is the purpose of isolating the surd in surd equations?

To eliminate the surd 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 purpose of checking solutions in surd equations?

To eliminate extraneous solutions Signup and view all the answers

What is the formula for a^(-m)?

1/a^m Signup and view all the answers

What is the purpose of rationalizing the denominator?

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

What is the formula for a^(m/n)?

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

What is the first step in solving quadratic surd equations?

Write in exponential notation Signup and view all the answers

What is the purpose of applying the exponent laws in surd equations?

To simplify the equation Signup and view all the answers

What is the formula for population growth?

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

What is the purpose of converting surds to exponential notation?

To make manipulation easier Signup and view all the answers

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

Write the equation in the standard form ax^2 + bx + c = 0 Signup and view all the answers

What is the purpose of the quadratic formula?

To solve any quadratic equation of the form ax^2 + bx + c = 0 Signup and view all the answers

What is the set of whole numbers represented by?

ℕ Signup and view all the answers

What is the formula to find the final amount in an exponential growth or decay problem?

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

What is the definition of a^m × a^n?

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

What is the purpose of converting percentages into decimal form in exponential growth or decay problems?

To ensure the correct answer Signup and view all the answers

What is the formula to determine the roots of a quadratic equation?

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

What is the formula to find the square root of a?

a^(1/2) Signup and view all the answers

What type of roots does a quadratic equation have when b^2 - 4ac = 0?

One real root (a repeated root) Signup and view all the answers

What is the purpose of the discriminant in a quadratic equation?

To determine the number of solutions Signup and view all the answers

What is the formula to find the value of x in a quadratic equation using the quadratic formula?

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

What is the purpose of the discriminant in a quadratic equation?

To determine the type of roots of the equation Signup and view all the answers

What is the definition of a rational number?

A number that can be written as a fraction with an integer numerator and denominator Signup and view all the answers

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

Identify the restrictions on the variables Signup and view all the answers

What happens when the discriminant is a perfect square?

The roots are rational Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is less than 0?

The roots are complex conjugate Signup and view all the answers

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

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

When is the discriminant of a quadratic equation equal to zero?

When the equation has one real root (a repeated root) Signup and view all the answers

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

Multiplying by constants (optional) Signup and view all the answers

What type of roots does a quadratic equation have when b^2 - 4ac > 0?

Two distinct real roots 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 solving a quadratic inequality?

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

How do you determine the critical values in a quadratic inequality?

By solving the quadratic equation Signup and view all the answers

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

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

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

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

What type of roots does a quadratic equation have when b^2 - 4ac is greater than 0?

Real and unequal Signup and view all the answers

What is the graphical representation of a quadratic inequality?

A graph showing the regions where the quadratic function is positive or negative Signup and view all the answers

What is the purpose of sign analysis in solving quadratic inequalities?

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

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

Substitution Signup and view all the answers

What is required to solve for the values of n unknown variables?

A system of n independent equations Signup and view all the answers

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

Substitute the expression of one variable into the other equation Signup and view all the answers

What is the purpose of solving word problems in mathematics?

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

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

The graph is shifted vertically upwards by q units 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 negative value of a on the graph of the 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 purpose of checking the solution in word problems?

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

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

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

What is the purpose of solving systems of linear equations?

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

What is the first step in solving a word problem?

Read the problem carefully and identify the question Signup and view all the answers

What is the purpose of solving quadratic equations?

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

What is the effect of q on a quadratic function?

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

What is the domain of a quadratic function?

All real numbers. Signup and view all the answers

What is the formula for finding the y-intercept of a quadratic function?

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

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

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

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

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

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

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

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

(y2 - y1) / (x2 - x1) Signup and view all the answers

What is the formula for the average gradient of a curve f(x) between 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 name of the function of the form y = a/x + q?

Hyperbolic function. Signup and view all the answers

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

To find the gradient of the tangent to the curve. Signup and view all the answers

What is the effect of q on the graph of y = 1/x + q?

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

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

The graph is stretched vertically. Signup and view all the answers

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

y = q Signup and view all the answers

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

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

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

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

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

All real numbers except y = q Signup and view all the answers

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

x = -p Signup and view all the answers

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

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

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

The graph is stretched vertically. Signup and view all the answers

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

y = q Signup and view all the answers

Gr 11 Math June P1 (Easy)

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Questions and Answers

What is the rational number that can be written as a fraction with an integer in the numerator and the denominator?

What is the value of r in the equation r^n = a, where n ≥ 2?

What is the value of a^(1/n), where a > 0 and n ≥ 2?

What is the radical symbol that indicates the nth root of a?

What is a surd?

What is the property of simplifying surds that states √(a) × √(b) = √(ab)?

What is the purpose of rationalising the denominator?

What is the law of exponents that states a^m × a^n = a^(m+n)?

What is the formula for exponential growth or decay?

What is the purpose of rationalizing denominators?

What is the formula for a^(-m)?

What is the purpose of the zero-product property in solving quadratic surd equations?

What is the formula for a^(m/n)?

What is the first step in identifying the variables in an exponential growth or decay problem?

What is the first step in solving surd equations?

What is the set of natural numbers represented by?

What is the purpose of converting surds to exponential notation?

What is the formula for exponential growth or decay?

What is the formula for population growth?

What is the purpose of completing the square?

What is the purpose of checking solutions in surd equations?

What is the formula for compound interest?

What is the quadratic formula used for?

What is the formula for the quadratic formula?

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

What is the definition of a^0?

What is the definition of a^(-n)?

What is the definition of √(a)?

What is the formula to determine the roots of a quadratic equation?

What type of roots does a quadratic equation have when b^2 - 4ac > 0?

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

What is the purpose of the discriminant in a quadratic equation?

What type of roots does a quadratic equation have when b^2 - 4ac < 0?

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

When is the discriminant of a quadratic equation equal to zero?

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

What happens when the discriminant is a perfect square?

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

What is the nature of the roots of a quadratic equation if the discriminant Δ is less than 0?

What is the formula for 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 a table of signs in solving a quadratic inequality?

What is the graphical representation of a quadratic inequality?

What is the purpose of solving simultaneous linear equations?

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

What is required to solve for the values of n unknown variables?

What is the main difference between solving quadratic equations and quadratic inequalities?

What is the purpose of sign analysis in solving quadratic inequalities?

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

What is the purpose of equating the two equations in the elimination method?

What is the final step in solving word problems?

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

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

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

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

What is the role of problem-solving strategies in real-world applications?

What is the purpose of drawing the graph of each equation on the same system of axes in solving graphically?

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

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

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

How do you shift the graph of a quadratic function 2 units to the right?

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

What is the general form of a hyperbolic function?

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

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

What is the formula for finding the y-intercept of a quadratic function?

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

What is the domain of the graph of a quadratic function?

What is the effect of a positive value of q on the graph of f(x) = 1/x + q?

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

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

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

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

What is the effect of a positive value of b on the graph of f(x) = ab^x + q?

What is the effect of a negative value of a on the graph of f(x) = ab^x + q?

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