Pure Mathematics 1 Quizzes: Test Your Understanding

Question 1

A ball is dropped from a height of 100 meters and rebounds to a height of 60% of its previous height on each subsequent bounce. What is the total distance the ball travels before coming to a rest?

Accepted Answer

166.67 meters

Answer

250 meters

Answer

400 meters

Question 2

Find the derivative of f(x) = x^3 - 2x^2 + 1.

Accepted Answer

3x^2 - 4x

Answer

x^2 - 4x + 1

Answer

3x - 4

Answer

x - 4

Question 3

Calculate the integral ∫x^2 dx.

Accepted Answer

x^3/3 + C

Answer

x^2 + C

Answer

x + C

Answer

1/x + C

Question 4

What is the period of the trigonometric function sin(x)?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

1

Question 5

Determine the derivative of the function y = x² + 2x.

Accepted Answer

y' = 2x + 2

Answer

y' = 2x - 2

Answer

y' = x² + 2

Answer

y' = x² - 2

Question 6

What is the domain of the function y = 1/(x - 2)?

Accepted Answer

All real numbers except 2

Answer

All real numbers except -2

Answer

All real numbers

Answer

All positive real numbers

Question 7

Find the value of cos(π/3).

Accepted Answer

1/2

Answer

-1/2

Answer

0

Answer

1

Question 8

What is the integral of the function y = x²?

Accepted Answer

y = x³/3 + C

Answer

y = 3x² + C

Answer

y = x² + C

Answer

y = 2x + C

Question 9

Find the derivative of the function: f(x) = x³ - 5x + 2

Accepted Answer

3x² - 5

Answer

3x² + 5

Answer

x² - 5

Answer

x² + 5

Question 10

Factor the polynomial: x³ + 2x² - 5x - 6

Accepted Answer

(x + 3)(x - 1)(x - 2)

Answer

(x - 3)(x + 1)(x + 2)

Answer

(x + 6)(x - 1)(x - 2)

Answer

(x - 6)(x + 1)(x + 2)

Question 11

Calculate the integral: ∫(x^2 + 3x - 4) dx?

Accepted Answer

x^3/3 + 3x^2/2 - 4x + C

Answer

x^3/3 + 3x^2/2 + 4x + C

Answer

x^2/3 + 3x/2 - 4x + C

Answer

x^2/3 + 3x/2 + 4x + C

Question 12

Which of the following is the equation of the circle with center (2, -3) and radius 5?

Accepted Answer

(x - 2)^2 + (y + 3)^2 = 5

Answer

(x + 2)^2 + (y - 3)^2 = 5

Answer

(x - 2)^2 + (y - 3)^2 = 25

Answer

(x + 2)^2 + (y + 3)^2 = 25

Question 13

Find the derivative of the function f(x) = x^3 - 2x^2 + 5x - 1

Accepted Answer

f'(x) = 3x^2 - 4x + 5

Answer

f'(x) = x^3 - 4x^2 + 10x - 1

Answer

f'(x) = 3x^2 - 4x + 1

Answer

f'(x) = x^2 - 4x + 5

Question 14

Find the complex conjugate of the number z = 3 + 4i

Accepted Answer

z̄ = 3 - 4i

Answer

z̄ = -3 - 4i

Answer

z̄ = 3 + 4i

Answer

z̄ = -3 + 4i

Question 15

Determine the derivative of f(x) = x^3 - 2x^2 + 5x - 7.

Accepted Answer

f'(x) = 3x^2 - 4x + 5

Answer

f'(x) = x^2 - 4x + 5

Answer

f'(x) = 3x^2 - 4x - 5

Answer

f'(x) = x^2 - 4x - 5

Question 16

Solve the trigonometric equation: sin(x) = 1/2.

Accepted Answer

x = 30° or x = 150°

Answer

x = 30° or x = 210°

Answer

x = 60° or x = 120°

Answer

There are no solutions

Question 17

Find the maximum value of the function f(x) = -x^2 + 4x - 3.

Accepted Answer

1

Answer

0

Answer

2

Answer

3

Question 18

Determine the derivative of the function f(x) = x^3 + 2x^2 - 5x + 1.

Accepted Answer

3x^2 + 4x - 5

Answer

x^2 + 2x - 5

Answer

3x^3 + 2x^2 - 5

Answer

x^3 + 2x^2 - 5x

Question 19

What is the domain of the function f(x) = 1 / (x - 2)?

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All positive real numbers

Answer

All real numbers greater than 2

Question 20

What is the value of sin(π/3)?

Accepted Answer

√3/2

Answer

1/2

Answer

1/4

Answer

√3/4

Question 21

What is the derivative of the function f(x) = e^x?

Accepted Answer

e^x

Answer

x*e^x

Answer

1/e^x

Answer

e/x

Question 22

Find the equation of the circle with radius 5 and centre at the origin.

Accepted Answer

x² + y² = 25

Answer

x² + y² = 10

Answer

x² - y² = 25

Answer

x² - y² = 10

Question 23

Determine the derivative of the function f(x) = x^3 + 2x^2 - 5.

Accepted Answer

3x^2 + 4x

Answer

3x + 2

Answer

x^2 + 2x

Answer

x^3 + 4x^2

Question 24

Solve the equation 2x^2 - 5x + 2 = 0.

Accepted Answer

x = 1 or x = 2

Answer

x = -1 or x = -2

Answer

x = 1/2 or x = 2

Answer

x = -1/2 or x = -2

Question 25

Determine the domain of the function f(x) = √(x - 2).

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 2

Answer

x < 2

Question 26

Identify the range of the function f(x) = |x|.

Accepted Answer

y ≥ 0

Answer

y > 0

Answer

y ≤ 0

Answer

y < 0

Question 27

Find the inverse of the function f(x) = 2x + 1.

Accepted Answer

f^-1(x) = (x - 1)/2

Answer

f^-1(x) = (x + 1)/2

Answer

f^-1(x) = 2x - 1

Answer

f^-1(x) = 1/2x + 1

Question 28

Find the derivative of f(x) = x^3 - 2x^2 + 1. Explain the method you use.

Accepted Answer

3x^2 - 4x

Answer

3x^2 + 4x

Answer

x^3 - 4x

Answer

x^3 + 4x

Question 29

Which of the following functions is odd? Explain your reasoning.

Accepted Answer

f(x) = sin(x)

Answer

f(x) = x^2

Answer

f(x) = cos(x)

Answer

f(x) = e^x

Question 30

Which of the following sequences is convergent?

Accepted Answer

aₘ = 1/n

Answer

aₘ = n²

Answer

aₘ = (-1)ⁿ¹

Answer

aₘ = n + 1

Question 31

Find the equation of the tangent line to the curve y = x³ + 2x² - 1 at the point (1, 2).

Accepted Answer

y = 6x - 4

Answer

y = 5x - 3

Answer

y = 4x - 2

Answer

y = 3x - 1

Question 32

Which of the following is a valid trigonometric identity?

Accepted Answer

cos^2(x) + sin^2(x) = 1

Answer

tan(x + y) = tan(x) + tan(y)

Answer

sin(x - y) = sin(x) - sin(y)

Answer

cot(x) = tan(x)

Question 33

Evaluate the integral ∫(x² + 3x) dx.

Accepted Answer

x³/3 + (3/2)x² + C

Answer

(1/3)x³ + (3/2)x² + C

Answer

x³/3 - (3/2)x² + C

Answer

(1/3)x³ - (3/2)x² + C

Question 34

Find the exact value of sin(π/3).

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

0

Question 35

Solve the inequality x² - 4 < 0.

Accepted Answer

x < -2 or x > 2

Answer

x < 2 or x > -2

Answer

x > -2 and x < 2

Answer

x < -2 and x > 2

Question 36

Determine the equation of the circle with center (3, -2) and radius 5.

Accepted Answer

(x - 3)² + (y + 2)² = 5

Answer

(x + 3)² + (y - 2)² = 5

Answer

(x - 3)² + (y - 2)² = 25

Answer

(x + 3)² + (y + 2)² = 25

Question 37

Determine the period of the trigonometric function y = 3sin(2x + π/3)

Accepted Answer

π/3

Answer

π

Answer

π/2

Answer

2π

Question 38

Which of the following is an example of an implicit function?

Accepted Answer

sin(x) + cos(y) = 0

Answer

y = x^2

Answer

x + y = 5

Answer

xy = 1

Question 39

Find the derivative of the function f(x) = x^3 + 2x^2 - 1

Accepted Answer

3x^2 + 4x

Answer

x^3 + 2x

Answer

3x^2 - 1

Answer

x^3 + 4x

Question 40

Solve the system of linear equations using matrices:
2x + 3y = 11
x - y = 1

Accepted Answer

Calculate the inverse of [2, 3; 1, -1] and multiply it by [11; 1]

Answer

Multiply [2, 3; 1, -1] by [11; 1]

Answer

Leave the system of equations unsolved

Question 41

Expand and simplify: 2x(x - 3) + 5

Accepted Answer

2x^2 - 6x + 5

Answer

2x^2 + 6x + 5

Answer

x^2 + 6x + 5

Answer

x^2 - 6x + 5

Question 42

Find the derivative of the function f(x) = x^3 - 2x + 5.

Accepted Answer

3x^2 - 2

Answer

x^2 - 2

Answer

3x^2 + 5

Answer

2x - 5

Question 43

Identify the graph of the quadratic function y = -x^2.

Accepted Answer

A parabola opening downwards

Answer

An ellipse

Answer

A straight line with positive slope

Answer

A circle

Question 44

What is the derivative of the function f(x) = 3x² - 2x + 1?

Accepted Answer

6x - 2

Answer

9x - 2

Answer

3x - 2

Answer

6x² - 2

Question 45

Find the equation of the line passing through the points (2, 1) and (4, 5).

Accepted Answer

y = 2x - 3

Answer

y = -2x + 5

Answer

y = x + 1

Answer

y = 3x - 5

Question 46

Simplify the expression (x² + 2x - 3) / (x - 1).

Accepted Answer

x + 3

Answer

x² - 3

Answer

x - 3

Answer

x² + 3

Question 47

Solve the equation 2x² + 5x - 3 = 0.

Accepted Answer

x = -3 or x = 1/2

Answer

x = 3 or x = -1/2

Answer

x = -3 or x = -1/2

Answer

x = 3 or x = 1/2

Question 48

What is the value of sin(60°)?

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

√2/2

Question 49

Find the integral of the function f(x) = 2x.

Accepted Answer

x² + C

Answer

x + C

Answer

2x + C

Answer

2x² + C

Question 50

If a = 3 and b = -2, what is the value of 2a + 3b?

Accepted Answer

0

Answer

-12

Answer

12

Answer

6

Question 51

What is the value of log₂(8)?

Accepted Answer

3

Answer

4

Answer

8

Answer

2

Question 52

Find the equation of the circle with center (3, -2) and radius 5.

Accepted Answer

(x - 3)² + (y + 2)² = 25

Answer

(x + 3)² + (y - 2)² = 5

Answer

(x + 3)² + (y - 2)² = 25

Answer

(x - 3)² + (y + 2)² = 5

Question 53

What is the value of sin⁻¹(1/2)?

Accepted Answer

30°

Answer

60°

Answer

90°

Answer

45°