Gr 11 Math Term 2 Test

What is the formula for the two-point form of a straight line equation?

(y - y1) / (x - x1) = (y2 - y1) / (x2 - x1) (correct)
y - y1 = m(x - x1)
y - y1 = (y2 - y1) / (x2 - x1)
y = mx + c

What is the definition of the gradient of a line?

The x-intercept of the line
The y-intercept of the line
Rise over run (correct)
Run over rise

What is the purpose of the gradient-point form of a straight line equation?

To find the equation of a line given its gradient and a point on the line (correct)
To find the y-intercept of a line
To find the x-intercept of a line
To find the gradient of a line

What is the standard form of the straight line equation?

y = mx + c (A) Signup and view all the answers

What information is required to use the two-point form of a straight line equation?

Two points on the line (D) Signup and view all the answers

What is the value of c in the equation y = mx + c?

The y-intercept of the line (C) Signup and view all the answers

What is the relationship between the gradient-point form and the two-point form of a straight line equation?

The gradient-point form is derived from the two-point form (A) Signup and view all the answers

What is the advantage of using the gradient-intercept form of a straight line equation?

It is easier to find the y-intercept (B) Signup and view all the answers

What is the angle of inclination for a horizontal line?

0° (D) Signup and view all the answers

What is the relationship between the gradient and the y-intercept of a line?

The y-intercept is the point where the line crosses the y-axis (C) Signup and view all the answers

What is the tangent of the angle of inclination for a line with a gradient of -0.5?

-30° (A) Signup and view all the answers

What is the equation form used when given two points on a line?

Two-Point Form (A) Signup and view all the answers

What is the measure of the steepness of a line?

Gradient (C) Signup and view all the answers

What is the characteristic of parallel lines?

Same gradient but different y-intercepts (D) Signup and view all the answers

What is the purpose of the point-slope form of a line?

To find the equation of a line given a point and a gradient (D) Signup and view all the answers

What is the relationship between the gradient and the inclination of a line?

The gradient is the tangent of the inclination (A) Signup and view all the answers

What is the inclination of a line with a gradient of 0?

0° (C) Signup and view all the answers

What is the characteristic of a vertical line?

Gradient is undefined (A) Signup and view all the answers

What is the condition for two lines to be parallel?

They have the same gradient (B) Signup and view all the answers

What is the relationship between the gradients of two perpendicular lines?

m1 × m2 = -1 (B) Signup and view all the answers

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

Vertical shift (C) Signup and view all the answers

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

Change in shape (D) Signup and view all the answers

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

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

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

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

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

x = -p (A) Signup and view all the answers

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

Horizontal shift (D) Signup and view all the answers

What is the condition for the graph of y = ax^2 + q to be a 'frown'?

a < 0 (B) Signup and view all the answers

What happens to the graph of y = ax^2 + q when a = 0?

It becomes a horizontal line (C) Signup and view all the answers

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

{y : y ≤ q, y ∈ ℝ} (C) Signup and view all the answers

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

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

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

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

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

x = -p (B) Signup and view all the answers

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

Replace x with x - m (B) Signup and view all the answers

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

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

What is the general form of a hyperbolic function?

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

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

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

What is the effect of a on the shape of a hyperbolic function?

It changes the shape and quadrants (A) Signup and view all the answers

What is the vertical asymptote of a hyperbolic function?

The line x = 0 (C) Signup and view all the answers

What is the period of the function y = sinθ?

360° (B) Signup and view all the answers

What is the effect of q on the graph of y = asinθ + q?

Vertical shift (B) Signup and view all the answers

What is the maximum value of the function y = sinθ?

1 (B) Signup and view all the answers

What is the range of the function y = sin(kθ)?

[-1, 1] (B) Signup and view all the answers

What is the effect of k on the period of the function y = sin(kθ)?

The period decreases (A) Signup and view all the answers

What is the effect of p on the graph of y = sin(θ + p)?

Horizontal shift (A) Signup and view all the answers

What is the period of the function y = cosθ?

360° (A) Signup and view all the answers

What is the y-intercept of the function y = cosθ?

(0°, 1) (D) Signup and view all the answers

What is the effect of a on the amplitude of the function y = acosθ?

The amplitude increases (C) Signup and view all the answers

What is the effect of k on the period of the function y = cos(kθ)?

The period decreases (B) Signup and view all the answers

What is the period of the tangent function?

180° (B) Signup and view all the answers

What is the effect of q on the graph of y = a tan(θ) + q?

Vertical shift (C) Signup and view all the answers

What is the range of the tangent function?

All real numbers (B) Signup and view all the answers

What is the effect of k on the period of the function y = tan(kθ)?

The period decreases (B) Signup and view all the answers

What is the formula for the area of a circle?

πr^2 (C) Signup and view all the answers

What is the formula for the area of a triangle?

1/2 bh (B) Signup and view all the answers

What is the definition of a right prism?

A geometric solid with a polygon as its base and vertical sides (D) Signup and view all the answers

What is the effect of p on the graph of the function y = tan(θ + p)?

Horizontal shift (D) Signup and view all the answers

What is the formula for the area of a trapezium?

1/2 (a + b)h (A) Signup and view all the answers

What is the formula for the circumference of a circle?

2πr (A) Signup and view all the answers

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

A horizontal shift only (B) Signup and view all the answers

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

x = -p (A) Signup and view all the answers

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

A vertical shift (D) Signup and view all the answers

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

y = q (A) Signup and view all the answers

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

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

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

A change in the shape of the graph (C) Signup and view all the answers

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

A horizontal shift (D) Signup and view all the answers

What is the domain of y = ab^(x + p) + q?

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

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

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

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

y = q (B) Signup and view all the answers

What is the total area of the exposed or outer surfaces of a prism?

Surface area (C) Signup and view all the answers

How many rectangles are there in a rectangular prism unfolded into a net?

6 (C) Signup and view all the answers

What is the formula for the volume of a triangular prism?

1/2 × b × h × H (B) Signup and view all the answers

What is the formula for the surface area of a cylinder?

π r (r + h) (D) Signup and view all the answers

What is the formula for the volume of a sphere?

4/3 × π r^3 (A) Signup and view all the answers

What is the formula for the surface area of a right cone?

π r (r + h) (C) Signup and view all the answers

What happens to the surface area and volume when one or more dimensions of a prism or cylinder is multiplied by a constant factor?

They change according to the relationships between the original and new dimensions (A) Signup and view all the answers

What is the formula for the volume of a square pyramid?

1/3 × b^2 × H (D) Signup and view all the answers

What is the formula for the surface area of a triangular pyramid?

1/2 b (h_b + 3h_s) (B) Signup and view all the answers

What is the formula for the volume of a right cone?

1/3 × π r^2 × H (A) Signup and view all the answers

What is the formula for the surface area of a right prism?

2(lh + lb + bh) (C) Signup and view all the answers

If we multiply all three dimensions of a rectangular prism by a constant factor k, what is the effect on the volume?

The volume scales by k^3 (B) Signup and view all the answers

What is the formula for the surface area of a sphere?

4πr^2 (D) Signup and view all the answers

If we multiply one dimension of a rectangular prism by a constant factor k, what is the effect on the volume?

The volume scales by k (C) Signup and view all the answers

What is the formula for the volume of a triangular prism?

1/2lhH (C) Signup and view all the answers

If we multiply two dimensions of a rectangular prism by a constant factor k, what is the effect on the volume?

The volume scales by k^2 (B) Signup and view all the answers

What is the formula for the surface area of a right cone?

πr(r + h) (A) Signup and view all the answers

If we multiply all three dimensions of a rectangular prism by a constant factor k, what is the effect on the surface area?

The surface area scales by k^2 (A) Signup and view all the answers

What is the formula for the volume of a cylinder?

πr^2h (D) Signup and view all the answers

What is the formula for the surface area of a triangular pyramid?

bh + 3/2bh_s (C) Signup and view all the answers

In a cyclic quadrilateral, what can be said about the opposite angles?

They are supplementary (C) Signup and view all the answers

What is the relationship between the exterior angle of a cyclic quadrilateral and the interior opposite angle?

They are equal (B) Signup and view all the answers

What is the tangent-chord theorem?

The angle between a tangent and a chord is equal to the angle in the alternate segment. (A) Signup and view all the answers

What can be said about two tangents drawn from the same point outside a circle?

They are equal in length (D) Signup and view all the answers

What is the angle at the center of a circle when subtended by a chord?

Twice the angle at the circumference subtended by the same chord (A) Signup and view all the answers

What is the relationship between equal chords of a circle?

They subtend equal angles at the center (B) Signup and view all the answers

What is the relationship between a diameter and the circle?

It subtends a right angle on the circle (C) Signup and view all the answers

When a line segment subtends equal angles on the same side, what can be said about the four points?

They are cyclic (B) Signup and view all the answers

Which equation form is used when the gradient and a point on the line are known?

Gradient-point form (A) Signup and view all the answers

What is the value of y when x = 0 in the equation y = mx + c?

c (B) Signup and view all the answers

Which equation form is also known as the standard form of the straight line equation?

Gradient-intercept form (B) Signup and view all the answers

What is the name of the form derived from the definition of gradient and the two-point form?

Gradient-point form (D) Signup and view all the answers

What information is required to use the gradient-point form of a straight line equation?

The gradient and a point on the line (A) Signup and view all the answers

What is the relationship between the gradient and the y-intercept of a line in the equation y = mx + c?

The gradient is independent of the y-intercept (C) Signup and view all the answers

What is the equation of the line that passes through two points (x_1, y_1) and (x_2, y_2)?

y - y_1 = (y_2 - y_1)/(x_2 - x_1)(x - x_1) (D) Signup and view all the answers

What is the advantage of using the gradient-intercept form of a straight line equation?

It is easier to graph the line (D) Signup and view all the answers

What is the relationship between the gradient of a line and the angle of inclination?

m = tan(θ) (B) Signup and view all the answers

What is the condition for two lines to be parallel?

m₁ = m₂ (A) Signup and view all the answers

What is the equation form used when given a gradient and a point on a line?

Gradient-Point Form (B) Signup and view all the answers

What is the angle of inclination for a vertical line?

90° (B) Signup and view all the answers

What is the formula for the gradient of a line?

m = Δy/Δx (C) Signup and view all the answers

What is the significance of the y-intercept in the equation of a line?

It represents the point where the line crosses the y-axis (A) Signup and view all the answers

What is the formula for finding the equation of a line parallel to a given line and passing through a specific point?

y - y₁ = m(x - x₁) (B) Signup and view all the answers

What is the characteristic of a line with a negative gradient?

The line falls from left to right (A) Signup and view all the answers

What is the relationship between the gradient and the inclination of a line for obtuse angles?

m = -tan(θ) and θ is obtuse (B) Signup and view all the answers

What is the purpose of the point-slope form of a line?

To find the equation of a line given a gradient and a point (C) Signup and view all the answers

What is the condition for two lines to be perpendicular?

Their gradients multiply to -1. (A) Signup and view all the answers

Given a line with equation y = mx + c, what does the gradient m represent?

The rate of change of the line. (C) 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. (D) Signup and view all the answers

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

x = -p (A) Signup and view all the answers

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

{y : y ≤ q, y ∈ ℝ} (D) Signup and view all the answers

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

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

What is the characteristic of the graph of y = ax^2 + q when a > 0?

It is a 'smile' shape. (A) Signup and view all the answers

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

It affects the shape of the graph. (C) Signup and view all the answers

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

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

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

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

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

A horizontal shift to the left by p units (C) Signup and view all the answers

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

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

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

The line y = q (B) Signup and view all the answers

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

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

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

A vertical shift by q units (C) Signup and view all the answers

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

The graph is stretched or compressed (A) Signup and view all the answers

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

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

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

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

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

A horizontal shift to the right by p units (D) Signup and view all the answers

If a < 0, what is the range of the function f(x) = ax^2 + q?

{y : y ≤ q, y ∈ ℝ} (D) Signup and view all the answers

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

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

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

All real numbers (A) Signup and view all the answers

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

x = -p (A) Signup and view all the answers

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

The line y = q (A) Signup and view all the answers

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

Shifts the graph horizontally to the right by p units (C) Signup and view all the answers

What is the average gradient of a curve between two points A(x_A, y_A) and C(x_C, y_C)?

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

What is the effect of a > 0 on the graph of y = ax^2 + q?

The graph is a 'smile' shape (A) Signup and view all the answers

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

Shifts the graph vertically upwards by q units (A) Signup and view all the answers

What is the general form of a hyperbolic function?

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

What is the vertical asymptote of a hyperbolic function?

x = 0 (B) Signup and view all the answers

What is the amplitude of the function y = sinθ?

1 (C) Signup and view all the answers

What is the effect of a on the amplitude of the function y = acosθ?

The amplitude is multiplied by a (C) Signup and view all the answers

What is the period of the function y = sin(kθ)?

360°/k (B) Signup and view all the answers

What is the effect of p on the graph of y = sin(θ + p)?

The graph shifts to the left by p units (A) Signup and view all the answers

What is the x-intercept of the function y = cosθ?

(270°, 0) (A), (90°, 0) (C) Signup and view all the answers

What is the range of the function y = cos(kθ)?

[-1, 1] (D) Signup and view all the answers

What is the effect of q on the graph of y = acosθ + q?

The graph shifts vertically up by q units (A), The graph shifts vertically down by q units (D) Signup and view all the answers

What is the maximum value of the function y = cosθ?

1 (D) Signup and view all the answers

What is the y-intercept of the function y = sinθ?

(0, 0) (C) Signup and view all the answers

What is the domain of the function y = coskθ?

{θ: θ ∈ ℝ} (A) Signup and view all the answers

In a cyclic quadrilateral, what is the relationship between the opposite angles?

Supplementary (C) Signup and view all the answers

What is the angle between a tangent to a circle and a chord drawn from the point of contact equal to?

The angle which the chord subtends in the alternate segment (D) Signup and view all the answers

What is the formula for the surface area of a rectangular prism?

2[lh + lb + bh] (C) Signup and view all the answers

If the dimensions of a rectangular prism are multiplied by a factor k, what is the effect on the volume?

The volume is multiplied by k^3 (A) Signup and view all the answers

What is the length of two tangents drawn from the same point outside a circle?

Equal (C) Signup and view all the answers

What is the formula for the volume of a triangular prism?

1/2 b × h × H (C) Signup and view all the answers

What is the angle at the center of a circle when subtended by a chord?

Twice the angle on the circle (C) Signup and view all the answers

What can be said about the angles on a circle subtended by the same arc?

They are equal (D) Signup and view all the answers

What is the formula for the surface area of a sphere?

4πr^2 (D) Signup and view all the answers

What is the characteristic of a diameter in a circle?

It is the longest chord (C) Signup and view all the answers

What is the effect on the surface area of a rectangular prism if its dimensions are multiplied by a factor k?

The surface area is multiplied by k^2 (A) Signup and view all the answers

What is the formula for the volume of a cylinder?

πr^2 × h (D) Signup and view all the answers

What can be said about the perpendicular bisector of a chord?

It passes through the center of the circle (A) Signup and view all the answers

What is the relationship between equal chords in a circle?

They subtend equal angles at the center (C) Signup and view all the answers

What is the formula for the area of a circle?

πr^2 (A) Signup and view all the answers

What is the formula for the volume of a cone?

1/3 πr^2 × H (C) Signup and view all the answers

What is the formula for the surface area of a triangular pyramid?

b(l + h_s) (C) Signup and view all the answers

What is the formula for the volume of a sphere?

4/3 πr^3 (C) Signup and view all the answers

What is the total area of the exposed or outer surfaces of a prism?

Surface area (A) Signup and view all the answers

What is the formula to calculate the volume of a triangular prism?

1/2 × b × h × H (A) Signup and view all the answers

What is the surface area of a sphere?

4 × π × r^2 (A) Signup and view all the answers

What is the formula to calculate the volume of a right cone?

1/3 × π × r^2 × H (C) Signup and view all the answers

What happens to the surface area and volume of a prism or cylinder when one or more dimensions are multiplied by a constant factor?

They change according to the relationships between the original and new dimensions (C) Signup and view all the answers

What is the formula to calculate the surface area of a rectangular prism?

2 × (l × b + b × h + l × h) (A) Signup and view all the answers

What is the formula to calculate the volume of a cube?

b^3 (D) Signup and view all the answers

What is the formula to calculate the surface area of a triangular pyramid?

1/2 × b × (h_b + 3h_s) (B) Signup and view all the answers

What is the formula to calculate the volume of a sphere?

4/3 × π × r^3 (C) Signup and view all the answers

What is the formula to calculate the surface area of a right cone?

π × r × (r + h) (C) Signup and view all the answers

What is the period of the function y = tan(kθ)?

180°/k (B) Signup and view all the answers

What is the effect of a on the shape of the function y = a tan(θ)?

a > 1: the graph is steeper, a < 1: the graph is less steep (D) Signup and view all the answers

What is the y-intercept of the function y = tan(θ)?

(0, 0) (A) Signup and view all the answers

What is the effect of p on the graph of the function y = tan(θ + p)?

For p > 0, the graph is shifted to the right, for p < 0, the graph is shifted to the left (D) Signup and view all the answers

What is the domain of the function y = tan(kθ)?

{θ: -90°/k < θ < 90°/k, θ ∈ ℝ} (A) Signup and view all the answers

What is the formula for the area of a trapezium?

A = (a + b) × h (C) Signup and view all the answers

What is the formula for the area of a circle?

A = πr^2 (A) Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2πr (A) Signup and view all the answers

What is the definition of a right prism?

A geometric solid with a polygon as its base and vertical sides perpendicular to the base (A) Signup and view all the answers

What is the characteristic of parallel lines?

They have the same gradient but different y-intercepts (B) Signup and view all the answers

What is the primary purpose of the gradient-point form of a straight line equation?

To determine the equation of a line given its gradient and a point on the line (B) Signup and view all the answers

Given a line with a gradient of 3 and passing through the point (2, 5), what is the equation of the line in gradient-intercept form?

y = 3x + 1 (A) Signup and view all the answers

What is the relationship between the gradient and y-intercept of a line in gradient-intercept form?

The gradient is independent of the y-intercept (A) Signup and view all the answers

Given two points (3, 4) and (5, 6), what is the equation of the line passing through these points in two-point form?

y - 4 = (6 - 4)/(5 - 3)(x - 3) (B) Signup and view all the answers

What is the primary advantage of using the gradient-intercept form of a straight line equation?

It is easier to find the y-intercept of the line (A) Signup and view all the answers

What is the equation of the line passing through the point (2, 3) with a gradient of -2?

y - 3 = -2(x - 2) (A) Signup and view all the answers

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

The gradient is directly proportional to the steepness (A) Signup and view all the answers

Given a line with a gradient of 1/2 and passing through the point (4, 3), what is the equation of the line in gradient-intercept form?

y = (1/2)x + 1 (A) Signup and view all the answers

What is the relationship between the gradient and the inclination of a line?

m = tan(θ) for 0° ≤ θ < 180° (D) Signup and view all the answers

What is the inclination of a line with a gradient of -2?

150° (C) Signup and view all the answers

What is the equation of a line that is parallel to the line y = 2x + 3 and passes through the point (1, 4)?

y = 2x + 1 (C) Signup and view all the answers

What is the characteristic of parallel lines?

They have the same gradient (A) Signup and view all the answers

What is the angle of inclination of a vertical line?

90° (B) Signup and view all the answers

What is the relationship between the gradient and the y-intercept of a line?

m is independent of c (C) Signup and view all the answers

What is the effect of a negative gradient on the angle of inclination?

The angle of inclination is obtuse (D) Signup and view all the answers

What is the purpose of the point-slope form of a line?

To find the equation of a line given a point and a gradient (A) Signup and view all the answers

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

{y : y ≤ q, y ∈ ℝ} (C) Signup and view all the answers

What is the effect of shifting the graph of y = a(x+p)^2 + q m units to the left?

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

What is the relationship between the gradient and the inclination of a horizontal line?

m = 0 (D) Signup and view all the answers

What is the condition for two lines to be parallel?

They have the same gradient (D) 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 (C) Signup and view all the answers

What is the formula to find the average gradient of a curve between two points A(x_A, y_A) and C(x_C, y_C)?

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

What is the relationship between the gradients of two lines that are perpendicular to each other?

The product of the gradients is equal to -1. (D) Signup and view all the answers

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

Vertical shift by q units. (D) Signup and view all the answers

What is the effect of a on the shape of a hyperbolic function y = a/x + q if a > 1?

The graph moves further away from the axes. (C) Signup and view all the answers

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

A horizontal shift. (D) Signup and view all the answers

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

x = 0 (C) Signup and view all the answers

What is the characteristic of a quadratic function with a > 0?

A minimum turning point. (B) Signup and view all the answers

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

A vertical shift. (D) Signup and view all the answers

What is the average gradient of a curve between points A(a, g(a)) and Q(a + h, g(a + h))?

(g(a + h) - g(a)) / h (B) 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. (A) Signup and view all the answers

What is the effect of h on the average gradient formula?

As h tends to 0, the average gradient approaches the gradient at point P. (C) Signup and view all the answers

What is the general form of a hyperbolic function?

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

What is the range of a quadratic function with a < 0?

{y : y ≤ q, y ∈ ℝ}. (D) Signup and view all the answers

What is the relationship between the gradient of a line and its inclination?

The gradient is the tangent of the inclination. (C) Signup and view all the answers

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

It affects the steepness of the graph. (B) Signup and view all the answers

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

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

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

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

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

A horizontal shift occurs (A) Signup and view all the answers

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

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

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

x = -p (A) Signup and view all the answers

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

y = q and x = -p (B) Signup and view all the answers

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

A vertical shift occurs (D) Signup and view all the answers

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

y > q if a > 0, y < q if a < 0 (C) Signup and view all the answers

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

A horizontal shift occurs (A) Signup and view all the answers

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

All real numbers (C) Signup and view all the answers

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

The graph is increasing if a > 0, decreasing if a < 0 (A) Signup and view all the answers

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

y = q (C) Signup and view all the answers

What is the relationship between the interior opposite angle and the exterior angle of a cyclic quadrilateral?

They are supplementary (D) Signup and view all the answers

What is the angle between a tangent to a circle and a chord drawn from the point of contact?

It is equal to the angle which the chord subtends in the alternate segment (D) Signup and view all the answers

What is the relationship between two tangents drawn from the same point outside a circle?

They are equal in length (D) Signup and view all the answers

What is the angle subtended by a diameter at the circumference of a circle?

Right angle (B) Signup and view all the answers

What is the relationship between the angles subtended by the same arc at the center and on the circle?

They are equal (D) Signup and view all the answers

What is the condition for a line segment to be a perpendicular bisector of a chord?

All of the above (D) Signup and view all the answers

What is the relationship between the length of two tangents drawn from the same point to a circle?

They are equal in length (D) Signup and view all the answers

What is the angle at the center of a circle subtended by an arc?

It is twice the angle on the circle subtended by the same arc (B) Signup and view all the answers

What is the effect of a on the graph of y = a sin(θ) + q?

The amplitude increases and the graph is not reflected about the x-axis. (B) Signup and view all the answers

What is the period of the function y = sin(2θ)?

180° (A) Signup and view all the answers

What is the effect of p on the graph of y = sin(θ + p)?

The graph shifts horizontally to the left by p units. (D) Signup and view all the answers

What is the maximum value of the function y = cos(θ)?

1 (D) Signup and view all the answers

What is the range of the function y = a cos(kθ)?

[-1, 1] (D) Signup and view all the answers

What is the effect of k on the period of the function y = cos(kθ)?

The period decreases when k > 1. (A) Signup and view all the answers

What is the x-intercept of the function y = sin(θ) for 0° ≤ θ ≤ 360°?

(180°, 0) (A) Signup and view all the answers

What is the y-intercept of the function y = cos(θ) for 0° ≤ θ ≤ 360°?

(0°, 1) (B) Signup and view all the answers

What is the domain of the function y = sin(kθ)?

{θ: θ ∈ ℝ} (C) Signup and view all the answers

What is the effect of a on the graph of y = a cos(θ) + q?

The amplitude increases and the graph is not reflected about the x-axis. (A) Signup and view all the answers

What is the effect of k on the period of the function y = tan(kθ)?

The period decreases by a factor of k (D) Signup and view all the answers

What is the domain of the function y = tan(kθ)?

All real numbers except multiples of 90 degrees (D) Signup and view all the answers

What is the effect of a on the graph of y = a tan(θ)?

The graph is stretched vertically by a factor of a (C) Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p)?

The graph is shifted horizontally by p units (D) Signup and view all the answers

What is the formula for the area of a trapezium?

A = (a + b)h/2 (A) Signup and view all the answers

What is the formula for the area of a circle?

A = πr^2 (C) Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2πr (D) Signup and view all the answers

What is the definition of a right prism?

A geometric solid with a polygon as its base and vertical sides (A) Signup and view all the answers

What is the characteristic of a right prism?

The base and top surface are the same shape and size (B) Signup and view all the answers

What is the formula for the area of a triangle?

A = bh/2 (D) Signup and view all the answers

What is the surface area of a triangular prism unfolded into a net?

The sum of the areas of the two triangles and the three rectangles (B) Signup and view all the answers

What is the formula for the volume of a cylinder?

πr^2 × h (B) Signup and view all the answers

What is the surface area of a right cone?

πr^2 + πr × h (D) Signup and view all the answers

What is the volume of a sphere?

4/3 πr^3 (A) Signup and view all the answers

What happens to the surface area and volume of a prism or cylinder when one or more dimensions are multiplied by a constant factor?

The surface area and volume both change (A) Signup and view all the answers

What is the formula for the surface area of a square pyramid?

b^2 + 2bh_s (B) Signup and view all the answers

What is the formula for the volume of a triangular pyramid?

1/3 × b × h × H (A) Signup and view all the answers

What is the formula for the surface area of a sphere?

4πr^2 (B) Signup and view all the answers

What is the formula for the volume of a right cone?

1/3 × πr^2 × h (B) Signup and view all the answers

What is the surface area of a rectangular prism unfolded into a net?

2(l × b) + 2(l × h) + 2(b × h) (C) Signup and view all the answers

If a rectangular prism has a length of 6 cm, a breadth of 4 cm, and a height of 3 cm, and its dimensions are multiplied by a factor of 2, what will be its new surface area?

176 cm² (B) Signup and view all the answers

What is the effect of multiplying the dimensions of a rectangular prism by a factor of k on its volume?

The volume is multiplied by k³ (B) Signup and view all the answers

If a sphere has a radius of 4 cm, what is its surface area?

160π cm² (B) Signup and view all the answers

What is the formula for the surface area of a triangular pyramid?

½ b (h_b + 3h_s) (D) Signup and view all the answers

What is the formula for the volume of a right cone?

⅓ πr²h (C) Signup and view all the answers

What is the effect of multiplying the dimensions of a rectangular prism by a factor of k on its surface area?

The surface area is multiplied by k² (C) Signup and view all the answers

What is the formula for the volume of a sphere?

⅔ πr³ (A) Signup and view all the answers

What is the formula for the surface area of a right cylinder?

2πr² + 2πrh (D) Signup and view all the answers

What is the effect of multiplying the dimensions of a rectangular prism by a factor of k on its volume and surface area?

The volume is multiplied by k³, and the surface area is multiplied by k² (D) Signup and view all the answers

What is the formula for the surface area of a square pyramid?

b² + 2bh_s (C) Signup and view all the answers

What is the primary difference between the two-point form and the gradient-point form of a straight line equation?

The two-point form is used when the gradient is known, while the gradient-point form is used when two points are known. (C) Signup and view all the answers

Which of the following statements is true about the gradient-intercept form of a straight line equation?

The gradient-intercept form is used when the equation of the line is in the form y = mx + c. (C) Signup and view all the answers

What is the condition for two lines to be perpendicular?

m1 × m2 = -1 (B) Signup and view all the answers

What is the main advantage of using the gradient-intercept form of a straight line equation?

It is easier to find the y-intercept of a line using the gradient-intercept form. (C) Signup and view all the answers

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

It affects the shape of the graph. (C) Signup and view all the answers

What is the relationship between the gradient of a line and the y-intercept of a line?

The gradient of a line is unrelated to the y-intercept of a line. (A) Signup and view all the answers

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

x = -p (B) Signup and view all the answers

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

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

What is the equation of the line that passes through the points (2, 3) and (4, 5)?

y = x + 1 (B) Signup and view all the answers

What is the gradient of the line that passes through the points (1, 2) and (3, 4)?

2/3 (A) Signup and view all the answers

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

It affects the horizontal shift of the graph. (D) Signup and view all the answers

What is the condition for the graph of y = ax^2 + q to be a 'frown'?

a < 0 (D) Signup and view all the answers

What is the y-intercept of the line that passes through the point (2, 3) with a gradient of 2?

3 (D) Signup and view all the answers

What is the equation of the line that passes through the point (1, 2) with a gradient of 1/2?

y = 1/2x + 3/2 (A) Signup and view all the answers

What happens to the graph of y = ax^2 + q when a = 0?

The graph becomes a horizontal line. (A) Signup and view all the answers

What is the relationship between the gradient of a line and its inclination?

The gradient of a line is equal to the tangent of its inclination (A) Signup and view all the answers

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

{y : y ≤ q, y ∈ ℝ} (B) Signup and view all the answers

What is the condition for two lines to be parallel?

They have the same gradient (C) Signup and view all the answers

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

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

What is the equation of a line that is parallel to a given line and passes through a specific point?

y - y1 = m(x - x1) (B) Signup and view all the answers

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

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

What is the inclination of a line with a gradient of -1?

135° (B) Signup and view all the answers

What is the characteristic of a vertical line?

It has an undefined gradient (A) Signup and view all the answers

What is the relationship between the gradient of a line and its y-intercept?

The gradient of a line has no relation to its y-intercept (A) Signup and view all the answers

What is the equation form used to find the equation of a line that is parallel to a given line and passes through a specific point?

Point-slope form (B) Signup and view all the answers

What is the inclination of a horizontal line?

0° (A) Signup and view all the answers

What is the tangent of the angle of inclination for a line with a gradient of 0.5?

0.5 (D) Signup and view all the answers

What is the relationship between the gradient of a line and its inclination for obtuse angles?

The gradient of a line is equal to the negative of the tangent of its inclination (B) Signup and view all the answers

If the quadratic function f(x) = ax^2 + q has a range of {y : y ≤ q, y ∈ ℝ}, what is the sign of a?

a < 0 (B) Signup and view all the answers

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

-p (B) Signup and view all the answers

If the graph of a quadratic function is shifted horizontally by 2 units to the right, what is the new equation of the function?

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

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

x = -p (D) Signup and view all the answers

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

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

What is the average gradient of the curve between two points A(x_A, y_A) and C(x_C, y_C)?

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

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

The graph is closer to the axes for larger values of a (B) Signup and view all the answers

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

x = 0 (C) Signup and view all the answers

What is the equation of the hyperbolic function that has a horizontal asymptote at y = 2 and a vertical asymptote at x = 0?

f(x) = 2/x + 2 (D) Signup and view all the answers

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

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

What is the effect of a on the graph of y = \frac{a}{x + p} + q?

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

What is the equation of the vertical asymptote of the graph of y = \frac{a}{x + p} + q?

x = -p (C) Signup and view all the answers

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

The graph is shifted horizontally by p units. (B) Signup and view all the answers

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

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

What is the axes of symmetry of the graph of y = \frac{a}{x + p} + q?

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

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

The graph is shifted vertically by q units. (D) Signup and view all the answers

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

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

What is the equation of the horizontal asymptote of the graph of y = ab^{x + p} + q?

y = q (D) Signup and view all the answers

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

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

What is the characteristic of the graph of y = \frac{a}{x + p} + q?

The graph is a hyperbola. (C) Signup and view all the answers

What is the domain of the function y = sin(kθ)?

(-∞, ∞) (A) Signup and view all the answers

What is the effect of a < 0 on the graph of y = a sin(θ)?

The graph is reflected about the x-axis. (A) Signup and view all the answers

What is the period of the function y = cos(2θ)?

180° (D) Signup and view all the answers

What is the x-intercept of the function y = sin(θ)?

(270°, 0) (B), (180°, 0) (C) Signup and view all the answers

What is the effect of q on the graph of y = a cos(θ) + q?

The graph is shifted vertically by q units. (A) Signup and view all the answers

What is the range of the function y = a sin(θ)?

[-a, a] (A) Signup and view all the answers

What is the maximum value of the function y = cos(θ)?

1 (B) Signup and view all the answers

What is the effect of p on the graph of y = sin(θ + p)?

The graph is shifted horizontally by p units. (B) Signup and view all the answers

What is the minimum value of the function y = a cos(θ)?

-a (A) Signup and view all the answers

What is the y-intercept of the function y = cos(θ)?

(0, 1) (B) Signup and view all the answers

What is the formula to calculate the surface area of a triangular prism?

b(h_b + 3h_s) (D) Signup and view all the answers

What is the formula to calculate the volume of a cylinder?

πr^2h (C) Signup and view all the answers

What is the formula to calculate the surface area of a right cone?

πr(r + h) (D) Signup and view all the answers

What is the formula to calculate the volume of a sphere?

4/3πr^3 (D) Signup and view all the answers

What happens to the surface area and volume of a rectangular prism when one of its dimensions is multiplied by a constant factor?

The surface area is multiplied by the square of the factor and the volume is multiplied by the cube of the factor. (B) Signup and view all the answers

What is the formula to calculate the surface area of a square pyramid?

b(b + 2h_s) (B) Signup and view all the answers

What is the formula to calculate the volume of a triangular pyramid?

1/3(bh_bH) (A) Signup and view all the answers

What is the formula to calculate the surface area of a cylinder?

2πr(h + r) (D) Signup and view all the answers

What is the formula to calculate the volume of a square pyramid?

1/3(b^2H) (A) Signup and view all the answers

What is the formula to calculate the surface area of a sphere?

4πr^2 (A) Signup and view all the answers

What is the relationship between the opposite angles of a cyclic quadrilateral?

They are supplementary. (A) Signup and view all the answers

If a tangent is drawn to a circle at a point, what is the angle between the tangent and the chord drawn from the point of contact?

The angle is equal to the angle subtended by the chord in the alternate segment. (A) Signup and view all the answers

What is the relationship between the length of two tangents drawn from the same point outside a circle?

The tangents are equal in length. (C) Signup and view all the answers

What is the relationship between the angle at the center of a circle and the angle subtended by the same arc?

The angle at the center is twice the angle subtended by the same arc. (A) Signup and view all the answers

What is the relationship between the chords of a circle that subtend equal angles at the center?

The chords are equal in length. (B) Signup and view all the answers

What is the relationship between the angles subtended by the same arc on the same side of a circle?

The angles are equal. (D) Signup and view all the answers

What is the characteristic of a diameter of a circle?

It is a chord that passes through the center. (C) Signup and view all the answers

What is the period of the function y = tan(2θ)?

90°/2 (D) Signup and view all the answers

What is the condition for four points to be cyclic?

When a line segment subtends equal angles on the same side. (D) Signup and view all the answers

What is the effect of a on the graph of y = a tan(θ)?

It makes the branches steeper. (D) Signup and view all the answers

What is the domain of one branch of the function y = tan(kθ)?

{θ: -90°/k < θ < 90°/k, θ ∈ ℝ} (C) Signup and view all the answers

What is the range of the function y = tan(θ)?

(-∞, ∞) (D) Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p)?

It shifts the graph horizontally to the left. (A) Signup and view all the answers

What is the area of a polygon with a base of 5 units and a height of 6 units?

30 (A) Signup and view all the answers

What is the formula for the area of a circle?

πr^2 (D) Signup and view all the answers

What is the characteristic of a right prism?

It has a polygon as its base and vertical sides perpendicular to the base. (A) Signup and view all the answers

What is the formula for the area of a trapezium?

½(a + b)h (D) Signup and view all the answers

What is the characteristic of a cylinder?

It has a circle as its base and vertical sides perpendicular to the base. (B) Signup and view all the answers

If a rectangular prism has dimensions of length 8, breadth 6, and height 4, what is the volume of the prism if all its dimensions are multiplied by a factor of 2?

768 (A) Signup and view all the answers

What is the surface area of a sphere with a radius of 4 cm?

256π (A) Signup and view all the answers

A rectangular prism has dimensions of length 10, breadth 8, and height 6. If the length and breadth are multiplied by a factor of 3, what is the surface area of the new prism?

720 (C) Signup and view all the answers

What is the volume of a cone with a radius of 3 cm and a height of 6 cm?

54π (C) Signup and view all the answers

If the dimensions of a rectangular prism are multiplied by a factor of 4, what is the scale factor of the surface area?

16 (A) Signup and view all the answers

What is the surface area of a triangular prism with base dimensions of 5 cm and 6 cm, and a height of 8 cm?

140 (B) Signup and view all the answers

If the radius of a sphere is doubled, what is the scale factor of the surface area?

8 (A) Signup and view all the answers

What is the volume of a cylinder with a radius of 2 cm and a height of 10 cm?

80π (D) Signup and view all the answers

A triangular pyramid has a base area of 20 cm² and a height of 8 cm. What is the volume of the pyramid?

80 (C) Signup and view all the answers

What is the scale factor of the volume of a rectangular prism when its dimensions are multiplied by a factor of 3?

27 (C) Signup and view all the answers

Gr 11 Math Term 2 Test

Choose a study mode

Podcast

Questions and Answers

What is the formula for the two-point form of a straight line equation?

What is the definition of the gradient of a line?

What is the purpose of the gradient-point form of a straight line equation?

What is the standard form of the straight line equation?

What information is required to use the two-point form of a straight line equation?

What is the value of c in the equation y = mx + c?

What is the relationship between the gradient-point form and the two-point form of a straight line equation?

What is the advantage of using the gradient-intercept form of a straight line equation?

What is the angle of inclination for a horizontal line?

What is the relationship between the gradient and the y-intercept of a line?

What is the tangent of the angle of inclination for a line with a gradient of -0.5?

What is the equation form used when given two points on a line?

What is the measure of the steepness of a line?

What is the characteristic of parallel lines?

What is the purpose of the point-slope form of a line?

What is the relationship between the gradient and the inclination of a line?

What is the inclination of a line with a gradient of 0?

What is the characteristic of a vertical line?

What is the condition for two lines to be parallel?

What is the relationship between the gradients of two perpendicular lines?

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

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

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

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

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

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

What is the condition for the graph of y = ax^2 + q to be a 'frown'?

What happens to the graph of y = ax^2 + q when a = 0?

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

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

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

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

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

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

What is the general form of a hyperbolic function?

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

What is the effect of a on the shape of a hyperbolic function?

What is the vertical asymptote of a hyperbolic function?

What is the period of the function y = sinθ?

What is the effect of q on the graph of y = asinθ + q?

What is the maximum value of the function y = sinθ?

What is the range of the function y = sin(kθ)?

What is the effect of k on the period of the function y = sin(kθ)?

What is the effect of p on the graph of y = sin(θ + p)?

What is the period of the function y = cosθ?

What is the y-intercept of the function y = cosθ?

What is the effect of a on the amplitude of the function y = acosθ?

What is the effect of k on the period of the function y = cos(kθ)?

What is the period of the tangent function?

What is the effect of q on the graph of y = a tan(θ) + q?

What is the range of the tangent function?

What is the effect of k on the period of the function y = tan(kθ)?

What is the formula for the area of a circle?

What is the formula for the area of a triangle?

What is the definition of a right prism?

What is the effect of p on the graph of the function y = tan(θ + p)?

What is the formula for the area of a trapezium?

What is the formula for the circumference of a circle?

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

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

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

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

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

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

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

What is the domain of y = ab^(x + p) + q?

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

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

What is the total area of the exposed or outer surfaces of a prism?

How many rectangles are there in a rectangular prism unfolded into a net?

What is the formula for the volume of a triangular prism?

What is the formula for the surface area of a cylinder?

What is the formula for the volume of a sphere?

What is the formula for the surface area of a right cone?

What happens to the surface area and volume when one or more dimensions of a prism or cylinder is multiplied by a constant factor?

What is the formula for the volume of a square pyramid?