Gr 11 Math Nov P1 (Easy)

Play an AI-generated podcast conversation about this lesson

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

r = √(n/a)

r = ∛(a^n)

r = √(a/n)

r = √(a) (correct)

What is the value of a^(1/n)?

√(n/a)

n√(a)

√(a) (correct)

1/√(n/a)

What is the value of a^(-1/n)?

n/√(a)

1/√(a) (correct)

1/√(n/a)

What is the purpose of rationalising the denominator?

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) by √(b)?

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

What is the result of raising √(a) to the power of m?

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

What is the power of a power rule in exponentiation?

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

What is the definition of a negative exponent?

a^(-m) = 1/a^m 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 first step in solving a surd equation?

Isolate the surd 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 exponential growth and decay?

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

What is the purpose of compound interest in finance?

To calculate the amount of money accumulated over time Signup and view all the answers

What is the definition of a fractional exponent?

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

What is the purpose of writing surds in exponential notation?

To make manipulation easier Signup and view all the answers

What is the formula for solving quadratic surd equations?

Isolate and simplify, then square both sides 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 nature of the roots of a quadratic equation if the discriminant Δ is less than 0?

Imaginary Signup and view all the answers

What is the set of whole numbers represented by?

ℕ₀ 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 formula for a⁻ⁿ?

1/aⁿ 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 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 formula for solving quadratic equations of the form ax² + bx + c = 0?

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

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

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

What is the graphical representation of a quadratic function used for in solving quadratic inequalities?

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

What is the result of a⁰, where a ≠ 0?

1 Signup and view all the answers

What is the restriction to consider when solving inequalities with fractions?

Ensure the denominator is not zero Signup and view all the answers

What is the notation for the set of rational numbers?

ℚ Signup and view all the answers

What is the number of independent equations required to solve for n unknown variables?

n Signup and view all the answers

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

To use the exponential growth or decay formula Signup and view all the answers

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

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

What method is mostly used for solving systems of simultaneous equations with linear and non-linear equations?

Substitution Signup and view all the answers

What is the result of √(aⁿ), where n is a positive integer?

a^(n⁄²) Signup and view all the answers

What is the purpose of the critical values in solving quadratic inequalities?

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

What is the general method for solving quadratic inequalities?

Factorize, find critical values, create a table of signs, and graph the solution 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 type of roots does a quadratic equation have when b^2 - 4ac = 0?

Real and equal roots 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 solving a quadratic equation by substitution?

Identify restrictions Signup and view all the answers

How can you determine the original quadratic equation given its roots?

By working backwards from the roots 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 when Δ < 0?

Imaginary roots Signup and view all the answers

What type of roots does a quadratic equation have when Δ = 0?

Real and equal roots Signup and view all the answers

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

Δ > 0 Signup and view all the answers

What happens when Δ is a perfect square in a quadratic equation?

The roots are rational Signup and view all the answers

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

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

What is the purpose of solving word problems?

To describe real-life contexts using mathematical language Signup and view all the answers

What is the definition of a quadratic sequence?

A sequence of numbers with a constant second difference Signup and view all the answers

What is the general form of the nth term of a quadratic sequence?

Tn = an^2 + bn + c Signup and view all the answers

What is the effect of q > 0 on a parabolic function?

The turning point of f(x) is above the x-axis Signup and view all the answers

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

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

What is the role of problem-solving strategies in natural sciences and engineering disciplines?

To solve real-life problems Signup and view all the answers

What is the final step in solving a word problem?

Write the final answer Signup and view all the answers

What is the purpose of finding the general term of a quadratic sequence?

To determine the values of a, b, and c Signup and view all the answers

What is the effect of a > 0 on the graph of f(x)?

The graph is a 'smile' and has a minimum turning point. Signup and view all the answers

What is the effect of p on the graph of f(x)?

A horizontal shift. Signup and view all the answers

What is the domain of the function f(x)?

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

What is the axis of symmetry of the graph of f(x)?

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

What is the formula to find the y-intercept of the graph of f(x)?

Set x = 0. Signup and view all the answers

What is the turning point of the graph of f(x)?

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

What is the range of the function f(x) when a > 0?

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

What is the formula to shift the graph of f(x) to the right by m units?

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

What is the formula to calculate the average gradient of a curve?

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

What is the method to find the equation of a parabola from the graph?

Use the equation y = a(x - x_1)(x - x_2). Signup and view all the answers

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

(y_2 - y_1) / (x_2 - x_1) Signup and view all the answers

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

Vertical shift Signup and view all the answers

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

x = -p 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 on the shape of the graph of y = a/x + q?

Changes the shape of the graph in quadrants Signup and view all the answers

What is the formula for the hyperbolic function of the form y = a/(x + p) + q?

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

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

Horizontal shift Signup and view all the answers

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

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

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

Changes the shape of the graph to increasing or decreasing Signup and view all the answers

What happens to the graph of y = ab^(x+p) + q when p > 0?

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

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

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

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

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

What is the formula for simple depreciation?

A = P(1 - in) Signup and view all the answers

What is the characteristic of the depreciation amount in simple depreciation?

It remains the same every year. Signup and view all the answers

What is the formula for compound depreciation?

A = P(1 - i)^n Signup and view all the answers

What is the effect of compounding more than once a year on an investment?

The interest rate is divided by p and the number of years is multiplied by p. Signup and view all the answers

What is the purpose of using timelines in finance?

To visualize the periods and changes in compounding and interest rates. Signup and view all the answers

What happens to the depreciation amount in compound depreciation?

It decreases each year. Signup and view all the answers

What is the key point about the book value in compound depreciation?

The book value never reaches zero. Signup and view all the answers

What is the first step in calculating the accumulated value of an investment?

Break down the timeline into segments and calculate each period separately Signup and view all the answers

What is the formula for calculating compound interest?

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

What is the formula for the probability of three events A, B, and C occurring?

P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C) Signup and view all the answers

What is the purpose of calculating the accumulated value at the end of each segment?

To adjust the principal for the next period Signup and view all the answers

What is the condition for two events to be independent?

P(A ∩ B) = P(A) × P(B) Signup and view all the answers

What is the purpose of a tree diagram?

To visualize the outcomes of a sequence of events Signup and view all the answers

What is the formula for calculating the effective interest rate?

1 + i_effective = (1 + i_nominal/m)^m Signup and view all the answers

What is the definition of independent events?

Two events that do not affect the probability of each other Signup and view all the answers

What is the formula for the probability of a path in a tree diagram?

P(Event 1) × P(Event 2) × ... Signup and view all the answers

What is the formula for calculating the probability of two independent events?

P(A and B) = P(A) * P(B) Signup and view all the answers

What is the purpose of a two-way contingency table?

To compute the probability of two events and their complements Signup and view all the answers

What is the purpose of using Venn diagrams?

To visualize the relationships between events Signup and view all the answers

What is the formula for the conditional probability of an event A given event B?

P(A and B) / P(B) Signup and view all the answers

What is the condition for two events to be mutually exclusive?

P(A ∩ B) = 0 Signup and view all the answers

What is the formula for calculating the probability of two mutually exclusive events?

P(A or B) = P(A) + P(B) Signup and view all the answers

What is the definition of conditional probability?

The probability of event A occurring given that event B has occurred Signup and view all the answers

What is the formula for the probability of an event A in a contingency table?

n(A) / n(Total) Signup and view all the answers

What is the purpose of the independence test in a contingency table?

To test if two events are independent Signup and view all the answers

What is the formula for calculating the conditional probability of event A given event B?

P(A|B) = P(A and B) / P(B) Signup and view all the answers

What is the formula for the probability of two events A and B occurring in a contingency table?

n(A and B) / n(Total) 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 in the numerator and the denominator Signup and view all the answers

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

√(a) Signup and view all the answers

What is the purpose of simplifying surds?

To express the radicand as a product of factors 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 definition of a surd?

A radical resulting in an irrational number 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 a^(m/n) where a > 0, m and n are integers, and n ≠ 0?

√(a^m) 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 power of a power rule in exponentiation?

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

What is the purpose of rationalising the denominator in surd equations?

To simplify the equation by removing the surd from the denominator Signup and view all the answers

What is the formula for solving exponential growth and decay problems?

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

What is the purpose of writing surds in exponential notation?

To make manipulation easier Signup and view all the answers

What is the first step in solving a surd equation?

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

What is the purpose of checking solutions in surd equations?

To verify the solution is correct and there are no extraneous solutions Signup and view all the answers

What is the result of a^0, where a ≠ 0?

1 Signup and view all the answers

What is the purpose of solving exponential problems?

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

What is the definition of a fractional exponent?

A power that is a fraction Signup and view all the answers

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

To simplify the equation by applying exponent laws 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))?

$\frac{f(a + h) - f(a)}{h}$ Signup and view all the answers

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

A vertical shift Signup and view all the answers

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

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

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

A horizontal shift Signup and view all the answers

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

x = -p Signup and view all the answers

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

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

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

A change in shape Signup and view all the answers

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

A vertical shift Signup and view all the answers

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

y = q 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 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 identify the repeated expression 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 type of roots does a quadratic equation have when Δ = 0?

Real and equal roots 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 set of real numbers represented by?

ℝ Signup and view all the answers

What is the step to find the original quadratic equation given its roots?

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

What is the formula for solving quadratic equations of the form ax² + bx + c = 0?

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

What is the purpose of identifying restrictions in solving quadratic equations by substitution?

To ensure the values do not make the denominator equal to zero Signup and view all the answers

What is the effect of the parameter b on the direction of the function f(x) if a > 0?

f(x) is increasing if b > 1, decreasing if 0 Signup and view all the answers

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

A horizontal shift Signup and view all the answers

What happens when Δ is a perfect square in a quadratic equation?

The roots are rational Signup and view all the answers

What is the result of a⁰, where a ≠ 0?

1 Signup and view all the answers

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

To convert the growth rate into a decimal form Signup and view all the answers

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

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

What type of roots does a quadratic equation have when Δ < 0?

Imaginary roots Signup and view all the answers

What is the formula for simple depreciation?

A = P(1 - in) Signup and view all the answers

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

Identify the restrictions Signup and view all the answers

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

Δ > 0 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 characteristic of compound depreciation?

The book value never reaches zero Signup and view all the answers

What is the notation for the set of irrational numbers?

ℚᶜ Signup and view all the answers

What is the purpose of using timelines in finance?

To visualize the periods and changes in compounding and interest rates Signup and view all the answers

What is the method used to solve quadratic equations by rewriting them in the form of a perfect square trinomial?

Completing the square Signup and view all the answers

What is the purpose of the quadratic formula?

To solve quadratic equations of the form ax² + bx + c = 0 Signup and view all the answers

How is the interest rate adjusted when compounding occurs more than once a year?

The interest rate is divided by the number of compounding periods Signup and view all the answers

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

y = q Signup and view all the answers

What is the difference between simple and compound depreciation?

Simple depreciation calculates depreciation on the initial principal amount, compound depreciation calculates depreciation on the remaining value Signup and view all the answers

What is the formula for compound depreciation?

A = P(1 - i)^n 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 roots Signup and view all the answers

What is the purpose of determining the critical values in solving quadratic inequalities?

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

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

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

What is the general method for solving quadratic inequalities?

Graphing the quadratic function and using a table of signs Signup and view all the answers

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

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

What is the result of solving a quadratic equation with a discriminant Δ equal to 0?

One real root Signup and view all the answers

What is the method mostly used for solving systems of simultaneous equations with linear and non-linear equations?

Substitution method Signup and view all the answers

What is the restriction to consider when solving inequalities with fractions?

Ensuring the denominator is not zero Signup and view all the answers

What is the purpose of graphing the quadratic function in solving quadratic inequalities?

To visualize the solution and identify the regions where the inequality holds true Signup and view all the answers

What is the number of independent equations required to solve for n unknown variables?

n equations Signup and view all the answers

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

To make the equation simpler Signup and view all the answers

What is the result of the second difference between any two consecutive terms in a quadratic sequence?

The difference is constant Signup and view all the answers

What is the purpose of solving systems of equations?

To find the value of multiple variables Signup and view all the answers

What is the general form of a quadratic sequence?

Tn = an^2 + bn + c Signup and view all the answers

What is the purpose of identifying the question and determining what needs to be solved in a word problem?

To identify the variables in the problem Signup and view all the answers

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

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

What is the purpose of setting up a system of equations in a word problem?

To solve for multiple variables Signup and view all the answers

What is the method of solving systems of equations that involves making one of the variables the subject of both equations?

Solving by equating Signup and view all the answers

What is the purpose of solving systems of equations in real-life problems?

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

What is the step in problem-solving strategies that involves translating the words into algebraic expressions?

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 f(x) = a(x + p)^2 + q?

The graph is a 'smile' if a > 0 and a 'frown' if a < 0 Signup and view all the answers

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

A horizontal shift Signup and view all the answers

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

All real numbers greater than or equal to q 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 of the graph of f(x) = a(x + p)^2 + q?

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

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

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

What is the purpose of shifting the equation of a parabola?

To change the position of the graph Signup and view all the answers

How do you find the equation of a parabola from the graph?

Use the formula y = a(x - x_1)(x - x_2) Signup and view all the answers

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

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

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

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

What is the formula for the probability of three events A, B, and C occurring?

P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C) Signup and view all the answers

What are events that cannot occur simultaneously?

Mutually exclusive events Signup and view all the answers

What is the purpose of a tree diagram?

To visualize and organize the outcomes of a sequence of events Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

P(A) × P(B) Signup and view all the answers

What is the purpose of a contingency table?

To compute probabilities and test for independence between events Signup and view all the answers

What is the formula for the probability of an event A given event B?

P(A and B) / P(B) Signup and view all the answers

What is the condition for two events A and B to be independent?

P(A) × P(B) = P(A and B) Signup and view all the answers

What is the purpose of determining a specific path in a tree diagram?

To calculate the probability of a specific sequence of events Signup and view all the answers

What is the formula for the probability of an event A?

P(A) = n(A) / n(Total) Signup and view all the answers

What is the purpose of calculating the sum of probabilities in a tree diagram?

To calculate the probability of multiple paths leading to a desired outcome Signup and view all the answers

What is the formula for calculating the accumulated value in compound interest?

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

What is the purpose of breaking down periods in compound interest calculations?

To calculate the accumulated value at the end of each segment Signup and view all the answers

What is the formula for calculating the effective interest rate?

1 + i_effective = (1 + i_nominal/m)^m Signup and view all the answers

What is the difference between independent and dependent events?

Independent events do not affect the probability of each other, while dependent events do affect the probability of each other Signup and view all the answers

What is the formula for the probability of two independent events?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the purpose of Venn diagrams?

To visualize the relationships between events Signup and view all the answers

What is the formula for the probability of two mutually exclusive events?

P(A or B) = P(A) + P(B) Signup and view all the answers

What is the concept of conditional probability?

The probability of an event occurring given that another event has occurred Signup and view all the answers

What is the formula for calculating the accumulated value in simple interest?

A = P(1 + in) Signup and view all the answers

What is the difference between nominal and effective interest rates?

Nominal interest rate is the interest rate per compounding period, while effective interest rate is the actual interest rate per year Signup and view all the answers

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

a^(m/n) 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 result of (√a)^m when a > 0 and m is an integer?

a^(m/2) 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 property of ∏(a) × ∏(b)?

∏(ab) Signup and view all the answers

What is the radical symbol ∏(a) equivalent to?

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

What is the law of exponents for the quotient of powers?

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

What is the result of ∏(a^m)?

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

What is the primary goal when solving equations involving surds?

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

What is the purpose of writing surds in exponential notation?

To make manipulation easier Signup and view all the answers

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

The surd is eliminated Signup and view all the answers

What is the formula for exponential growth and decay?

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

What is the purpose of solving surd equations?

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

What is the result of applying the power of a power rule in exponentiation?

a^(mn) = (a^m)^n 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 result of applying the negative exponent rule in exponentiation?

a^(-m) = 1 / a^m 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 nature of exponential growth and decay models?

Exponential Signup and view all the answers

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

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

How can you determine the original quadratic equation given its roots?

By writing the roots as a product of two factors Signup and view all the answers

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

Imaginary Signup and view all the answers

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

Identify the restrictions Signup and view all the answers

What happens when the discriminant Δ is a perfect square in a quadratic equation?

The roots are rational Signup and view all the answers

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

To determine the nature of the roots 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 formula to calculate 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 Δ = 0?

Real and equal Signup and view all the answers

What is the purpose of factorizing the quadratic expression in solving quadratic inequalities?

To identify the regions where the quadratic expression is positive or negative 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 graphical representation of a quadratic function used for in solving quadratic inequalities?

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

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

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

What is the restriction to consider when solving inequalities with fractions?

To ensure the denominator is not zero Signup and view all the answers

What method is mostly used for solving systems of simultaneous equations with linear and non-linear equations?

Substitution Signup and view all the answers

What is the number of independent equations required to solve for n unknown variables?

n Signup and view all the answers

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

To solve the quadratic equation in standard form Signup and view all the answers

What is the general method for solving quadratic inequalities?

Factoring, solving for critical values, creating a table of signs, and graphing Signup and view all the answers

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

Solve for one of the variables in one of the equations Signup and view all the answers

What is the purpose of solving word problems?

To apply mathematical language to describe real-life contexts Signup and view all the answers

What is the definition of a quadratic sequence?

A sequence of numbers in which the second difference between any two consecutive terms is constant Signup and view all the answers

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

Vertical shift upwards by q units Signup and view all the answers

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

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

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

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

What is the general form of a quadratic sequence?

Tn = an^2 + bn + c Signup and view all the answers

What is the purpose of solving simultaneous equations?

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

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

The values of the unknown variables Signup and view all the answers

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

Horizontal shift Signup and view all the answers

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

{y : y ≥ q, y ∈ ℝ} 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 of the graph of f(x) = a(x + p)^2 + q?

x = -p Signup and view all the answers

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

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

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

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

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

The graph is shifted upward Signup and view all the answers

What is the purpose of sketching the graph of a quadratic function?

To determine the characteristics of the graph Signup and view all the answers

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

The graph is narrower for larger values of a Signup and view all the answers

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

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

What is the formula for solving quadratic equations of the form ax^2 + bx + c = 0?

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

What is the result of a^0, where a ≠ 0?

1 Signup and view all the answers

What is the set of rational numbers represented by?

ℚ Signup and view all the answers

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

To use the formula correctly Signup and view all the answers

What is the definition of a quadratic equation?

An equation of the form ax^2 + bx + c = 0 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 result of √(a^n), where n is a positive integer?

a^(n/2) 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?

Complex and distinct 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 average gradient of the curve at point P when h = 0?

2a Signup and view all the answers

What is the horizontal asymptote of the hyperbolic function y = a/x + q?

y = q Signup and view all the answers

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

A horizontal shift Signup and view all the answers

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

{x : x ∈ ℝ, x ≠ -p} Signup and view all the answers

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

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

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

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

If b > 1, what is the effect on the function f(x)?

f(x) is an increasing function Signup and view all the answers

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

For a > 0, the function is increasing, and for a < 0, the function is decreasing Signup and view all the answers

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

A horizontal shift Signup and view all the answers

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

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

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

A vertical shift Signup and view all the answers

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

y = q Signup and view all the answers

What is the formula for simple depreciation?

A = P(1 - in) Signup and view all the answers

What is the purpose of finding the axes of symmetry of a hyperbolic function?

To identify the axes of symmetry of the function Signup and view all the answers

What is the effect of compound depreciation on the depreciation amount?

The depreciation amount decreases every year Signup and view all the answers

What is the purpose of using timelines in finance?

To visualize the periods and changes in compounding and interest rates Signup and view all the answers

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

A vertical shift Signup and view all the answers

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

y = q Signup and view all the answers

What is the formula to find the annual depreciation rate (i) for compound decay?

A = P(1 - i)^n Signup and view all the answers

What is the effect of compounding more than once a year on the interest rate?

The interest rate is divided by p Signup and view all the answers

What is the formula for calculating the accumulated value in compound interest?

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

What is the purpose of breaking down periods in compound interest calculations?

To calculate the accumulated value at the end of each period Signup and view all the answers

What is the formula for calculating the effective interest rate?

1 + i_effective = (1 + i_nominal/m)^m Signup and view all the answers

What is the definition of independent events in probability?

Two events are independent if the occurrence of one does not affect the probability of the other Signup and view all the answers

What is the formula for calculating the probability of two independent events?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the purpose of using Venn diagrams in probability?

To visualize the sample space and events Signup and view all the answers

What is the formula for calculating the union of two events?

P(A or B) = P(A) + P(B) - P(A and B) Signup and view all the answers

What is the formula for calculating the conditional probability of an event?

P(A|B) = P(A and B) / P(B) Signup and view all the answers

What is the definition of mutually exclusive events in probability?

Two events are mutually exclusive if they cannot occur at the same time Signup and view all the answers

What is the formula for calculating the probability of two mutually exclusive events?

P(A or B) = P(A) + P(B) Signup and view all the answers

What is the formula for the general addition rule for three events?

P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) Signup and view all the answers

What is the definition of mutually exclusive events?

Events that cannot occur simultaneously Signup and view all the answers

What is the purpose of a tree diagram?

To organise and visualise the different possible outcomes of a sequence of events Signup and view all the answers

What is the formula for the probability of a path in a tree diagram?

P(A) × P(B) × ... Signup and view all the answers

What is the purpose of a contingency table?

To test for independence between two events Signup and view all the answers

What is the formula for the conditional probability P(A|B) ?

P(A and B) / P(B) Signup and view all the answers

What is the definition of independent events?

The occurrence of one event does not affect the probability of the other Signup and view all the answers

What is the formula for the probability of two independent events A and B?

P(A) × P(B) Signup and view all the answers

What is the purpose of calculating the probability of an event using a tree diagram?

To calculate the probability of a specific sequence of events Signup and view all the answers

What is the definition of a dependent event?

The occurrence of one event affects the probability of the other 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 value of $a^{-rac{1}{n}}$?

$\sqrt[n]{a^{-1}}$ 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 result of multiplying $\sqrt[n]{a}$ and $\sqrt[n]{b}$?

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

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

What is the result of raising $\sqrt[n]{a}$ to the power of $m$?

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

What is the purpose of converting surds to exponential notation?

To make it easier to manipulate expressions Signup and view all the answers

What is the main goal when solving surd equations?

To isolate 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 should you do after eliminating the surd in a surd equation?

Solve the resulting equation Signup and view all the answers

Why do you need to check the solution in a surd equation?

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

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

To make the expression easier to manipulate 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?

Eliminating the surd Signup and view all the answers

What is the purpose of applying the rules of exponents in surd equations?

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

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

Verifying the solution is correct Signup and view all the answers

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

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

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

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

What is the formula for exponential growth and decay?

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

What is the result of a^0, where a ≠ 0?

1 Signup and view all the answers

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

To simplify the equation Signup and view all the answers

What is the definition of a quadratic equation?

An equation of the form ax^2 + bx + c = 0 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 purpose of the quadratic formula?

To solve quadratic equations Signup and view all the answers

What is the definition of a rational exponent?

A fractional exponent Signup and view all the answers

What is the purpose of simplifying surds?

To simplify the equation Signup and view all the answers

What is the definition of a surd?

A root of a number that is not a perfect square Signup and view all the answers

What is the quadratic formula used to determine?

The roots of a quadratic equation Signup and view all the answers

What does the discriminant Δ represent in a quadratic equation?

The type of roots of a quadratic equation Signup and view all the answers

What is the condition for a quadratic equation to have two distinct real 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 solving a quadratic equation by substitution?

Identify the repeated expression Signup and view all the answers

What happens when Δ is a perfect square in a quadratic equation?

The equation has two rational roots 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 nature of the roots of a quadratic equation when Δ = 0?

One real root Signup and view all the answers

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

To work backwards and find the original equation Signup and view all the answers

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

x = (-b ± √(b^2 - 4ac)) / 2a 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 (one root) 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 completing a table of signs in solving quadratic inequalities?

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

What is the method mostly used for solving systems of simultaneous equations with linear and non-linear equations?

Substitution method Signup and view all the answers

What is the general method for solving quadratic inequalities?

All of the above Signup and view all the answers

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

Δ > 0 Signup and view all the answers

What happens when Δ is a perfect square in a quadratic equation?

The roots are rational Signup and view all the answers

What is the purpose of the critical values in solving quadratic inequalities?

To determine the regions where the quadratic expression is positive or negative 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 considering restrictions when solving inequalities with fractions?

To avoid undefined expressions Signup and view all the answers

What happens to the graph of f(x) = a(x + p)^2 + q when a > 0?

The graph becomes a 'smile' and has a minimum turning point. Signup and view all the answers

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

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

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

A horizontal shift. 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 main purpose of using mathematical models to solve real-world problems?

To describe real-life contexts and make predictions. Signup and view all the answers

What is the definition of a quadratic sequence?

A sequence of numbers in which the second difference between any two consecutive terms is constant. 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 purpose of setting up a system of equations to solve a word problem?

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

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

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

What is the result of shifting the graph of y = ax^2 vertically upwards by q units?

The turning point of the graph is above the x-axis. Signup and view all the answers

How do you find the y-intercept of the function f(x) = a(x + p)^2 + q?

Set x = 0 and solve for y. 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 purpose of solving systems of linear equations?

To find the solution to a real-world problem. Signup and view all the answers

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

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

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

Gradient = (yA - yC) / (xA - xC) Signup and view all the answers

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

A vertical shift Signup and view all the answers

What is the general form of a quadratic sequence?

Tn = an^2 + bn + c. Signup and view all the answers

What is the first step in solving a word problem using mathematical models?

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

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

x = -p Signup and view all the answers

What is the purpose of shifting the equation of a parabola?

To change the position of the parabola. Signup and view all the answers

What is the purpose of solving systems of linear equations graphically?

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

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

{x : x ∈ ℝ, x ≠ -p} Signup and view all the answers

What is the formula for finding the equation of a parabola from the graph?

y = a(x - x1)(x - x2) Signup and view all the answers

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

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

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

The graph moves closer to or further away from the axes 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 range of the function y = ab^x + q?

{y : y ∈ ℝ, y ≠ q} 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 effect of a change in a on the shape of the graph of y = ab^x + q?

The graph becomes increasing or decreasing Signup and view all the answers

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

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

What is the effect of b on the direction of the graph of f(x) = ab^x when a > 0?

If b > 1, the graph is increasing; if 0 Signup and view all the answers

What happens to the graph of f(x) = ab^(x+p) + q when p > 0?

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

What is the range of the graph of f(x) = ab^x + q when a > 0?

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

What type of depreciation reduces the value of an asset by a constant amount each year?

Simple depreciation Signup and view all the answers

What is the formula for compound depreciation?

A = P(1 - i)^n Signup and view all the answers

What is the purpose of using timelines in finance?

To visualize the periods and changes in compounding and interest rates over time Signup and view all the answers

What happens when an investment is compounded more than once a year?

The number of years is multiplied by the compounding frequency Signup and view all the answers

What is the horizontal asymptote of the graph of f(x) = ab^x + q?

y = q Signup and view all the answers

What is the domain of the graph of f(x) = ab^x + q?

All real numbers Signup and view all the answers

What is the formula for simple depreciation?

A = P(1 - in) Signup and view all the answers

What is the purpose of breaking down periods in compound interest calculations?

To account for changes in interest rates or additional deposits/withdrawals Signup and view all the answers

What is the formula for compound interest?

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

What is the difference between nominal and effective interest rates?

Nominal interest rate is the interest rate per year, while effective interest rate is the interest rate per compounding period Signup and view all the answers

What is the formula for independent events?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the purpose of the addition rule for mutually exclusive events?

To find the probability of the union of two mutually exclusive events Signup and view all the answers

What is the definition of conditional probability?

The probability of event A occurring given that event B has occurred Signup and view all the answers

What is the formula for the effective interest rate?

1 + i_effective = (1 + i_nominal/m)^m Signup and view all the answers

What is the purpose of Venn diagrams in probability?

To visualize the sample space and events Signup and view all the answers

What is the definition of dependent events?

Two events that affect the probability of each other Signup and view all the answers

What is the addition rule for non-mutually exclusive events?

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) Signup and view all the answers

What is the formula for the probability of the union of three events A, B, and C?

P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C) Signup and view all the answers

What is the definition of mutually exclusive events?

Events that cannot occur simultaneously Signup and view all the answers

What is the purpose of a tree diagram?

To organize and visualize the different possible outcomes of a sequence of events Signup and view all the answers

What is the formula for the probability of two independent events A and B?

P(A) × P(B) Signup and view all the answers

What is the structure of a two-way contingency table?

Rows represent one event and its complement, columns represent another event Signup and view all the answers

What is the formula for the probability of an event A given event B?

P(A and B) / P(B) Signup and view all the answers

What is the purpose of a contingency table?

To test for independence between events Signup and view all the answers

What is the formula for the probability of a specific path in a tree diagram?

P(Event 1) × P(Event 2) × ... Signup and view all the answers

What is the purpose of calculating the probability of a desired outcome in a tree diagram?

To find the probability of a specific sequence of events Signup and view all the answers

What is the condition for two events A and B to be independent?

P(A and B) = P(A) × P(B) Signup and view all the answers

Gr 11 Math Nov P1 (Easy)

Choose a study mode

Podcast

Questions and Answers

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

What is the value of a^(1/n)?

What is the value of a^(-1/n)?

What is the purpose of rationalising the denominator?

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

What is the result of dividing √(a) by √(b)?

What is the result of raising √(a) to the power of m?

What is the power of a power rule in exponentiation?

What is the definition of a negative exponent?

What is the purpose of rationalizing denominators?

What is the first step in solving a surd equation?

What is the purpose of checking solutions in surd equations?

What is the formula for exponential growth and decay?

What is the purpose of compound interest in finance?

What is the definition of a fractional exponent?

What is the purpose of writing surds in exponential notation?

What is the formula for solving quadratic surd equations?

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

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

What is the set of whole numbers represented by?

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

What is the formula for a⁻ⁿ?

What is the first step in solving a quadratic inequality?

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

What is the formula for solving quadratic equations of the form ax² + bx + c = 0?

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

What is the graphical representation of a quadratic function used for in solving quadratic inequalities?

What is the result of a⁰, where a ≠ 0?

What is the restriction to consider when solving inequalities with fractions?

What is the notation for the set of rational numbers?

What is the number of independent equations required to solve for n unknown variables?

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

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

What method is mostly used for solving systems of simultaneous equations with linear and non-linear equations?

What is the result of √(aⁿ), where n is a positive integer?

What is the purpose of the critical values in solving quadratic inequalities?

What is the general method for solving quadratic inequalities?

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 purpose of making a substitution in solving quadratic equations?

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

How can you determine the original quadratic equation given its roots?

What is the discriminant of a quadratic equation?

What type of roots does a quadratic equation have when Δ < 0?

What type of roots does a quadratic equation have when Δ = 0?

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

What happens when Δ is a perfect square in a quadratic equation?

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

What is the purpose of solving word problems?

What is the definition of a quadratic sequence?

What is the general form of the nth term of a quadratic sequence?

What is the effect of q > 0 on a parabolic function?

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

What is the purpose of solving systems of equations graphically?

What is the role of problem-solving strategies in natural sciences and engineering disciplines?

What is the final step in solving a word problem?

What is the purpose of finding the general term of a quadratic sequence?

What is the effect of a > 0 on the graph of f(x)?

What is the effect of p on the graph of f(x)?

What is the domain of the function f(x)?

What is the axis of symmetry of the graph of f(x)?

What is the formula to find the y-intercept of the graph of f(x)?

What is the turning point of the graph of f(x)?

What is the range of the function f(x) when a > 0?

What is the formula to shift the graph of f(x) to the right by m units?

What is the formula to calculate the average gradient of a curve?

What is the method to find the equation of a parabola from the graph?

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

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

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

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

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

What is the formula for the hyperbolic function of the form y = a/(x + p) + q?

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

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

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