Pure Mathematics 1 Quizzes: Test Your Understanding

Question 1

Find the value of sin(π/3).

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

0

Question 2

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

Accepted Answer

3x^2 + 4x - 5

Answer

3x^2 - 4x + 5

Answer

x^3 + 4x^2 - 10x + 1

Answer

x^2 + 4x - 5

Question 3

Find the equation of the line passing through the points (2, 3) and (4, 7).

Accepted Answer

y = 2x - 1

Answer

y = x + 1

Answer

y = x - 1

Answer

y = 2x + 1

Question 4

Find the probability of rolling a 6 on a standard six-sided die.

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 5

Which of the following is the inverse function of f(x) = x^2?

Accepted Answer

f^-1(x) = √x

Answer

f^-1(x) = x

Answer

f^-1(x) = 2x

Answer

f^-1(x) = x^3

Question 6

What is the cosine of a π/3 radian angle?

Accepted Answer

√3/2

Answer

0

Answer

1/2

Answer

1

Question 7

Solve the inequality |x - 2| < 3.

Accepted Answer

{x | -1 < x < 5}

Answer

{x | x < -1 or x > 5}

Answer

{x | -5 < x < 1}

Answer

{x | x < -5 or x > 1}

Question 8

Which of the following is the equation of the straight line with a gradient of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = -2x - 3

Answer

y = 3x - 2

Answer

y = -3x - 2

Question 9

Solve the equation: 3x^2 - 5x + 2 = 0

Accepted Answer

x = 1, x = 2/3

Answer

x = -1, x = -2/3

Answer

x = 1, x = -2/3

Answer

x = -1, x = 2/3

Question 10

Evaluate sin(π/3)

Accepted Answer

√3/2

Answer

1/2

Answer

-1/2

Answer

-√3/2

Question 11

Convert 30 degrees into radians

Accepted Answer

π/6

Answer

π/3

Answer

π/2

Answer

π

Question 12

Calculate the gradient of the line passing through the points (2, 3) and (5, 11).

Accepted Answer

4

Answer

2

Answer

8

Answer

16

Question 13

Determine the equation of the tangent to the curve y = x³ - 2x at the point (1, -1).

Accepted Answer

y = 3x - 4

Answer

y = x + 1

Answer

y = 2x - 3

Answer

y = -x + 1

Question 14

Identify the graph of the function f(x) = |x - 2| + 1.

Accepted Answer

V-shaped graph with vertex at (2, 1)

Answer

U-shaped graph with vertex at (2, -1)

Answer

Straight line with gradient 1 and y-intercept 1

Answer

Straight line with gradient -1 and y-intercept 1

Question 15

Calculate the area of the region bounded by the curves y = x² and y = 4 - x².

Accepted Answer

16/3

Answer

8/3

Answer

32/3

Answer

64/3

Question 16

Solve the equation 2cos(3x) - 1 = 0 for 0 ≤ x ≤ π.

Accepted Answer

x = π/6, 5π/6

Answer

x = π/3, 2π/3

Answer

x = 0, π

Answer

The equation has no solution.

Question 17

Expand and simplify the expression (2x - 3)(x + 4).

Accepted Answer

2x² + 5x - 12

Answer

2x² - 5x - 12

Answer

2x² + 11x - 12

Answer

2x² - 11x - 12

Question 18

Solve the system of equations: 2x + y = 5, x - 2y = 3.

Accepted Answer

x = 2, y = 1

Answer

x = 4, y = -1

Answer

x = 1, y = 2

Answer

x = -1, y = 4

Question 19

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

Accepted Answer

3x^2 - 4x + 5

Answer

x^3 - 2x^2 + 5x

Answer

3x^2 - 2x + 5

Answer

x^3 - 4x + 5

Question 20

Find the area of the triangle with vertices A(1, 2), B(3, 5), and C(5, 2)

Accepted Answer

12 square units

Answer

6 square units

Answer

18 square units

Answer

24 square units

Question 21

The sum of the interior angles of a quadrilateral is:

Accepted Answer

360 degrees

Answer

180 degrees

Answer

540 degrees

Answer

720 degrees

Question 22

Which of the following is a rational function?

Accepted Answer

x/(x-1)

Answer

x^2 + 2x - 3

Answer

sin(x)

Answer

e^x

Question 23

Solve the equation 2cos(θ) = 1 for θ.

Accepted Answer

θ = π/3, 5π/3

Answer

θ = 0, π

Answer

θ = π/6, 5π/6

Answer

no solution

Question 24

Differentiate the function f(x) = x^2 + 2x - 1 with respect to x.

Accepted Answer

2x + 1

Answer

2x - 1

Answer

2x

Answer

x^2 - 1

Question 25

Solve the quadratic equation: 2x^2 + 5x - 3 = 0

Accepted Answer

x = -1 or x = 3/2

Answer

x = 1 or x = -3/2

Answer

x = -2 or x = 4

Answer

x = 0 or x = 6

Question 26

What is the gradient of the line represented by the equation y = -2x + 5?

Accepted Answer

-2

Answer

2

Answer

1

Answer

-1

Question 27

Evaluate the trigonometric expression: sin(30°)

Accepted Answer

0.5

Answer

1

Answer

2

Answer

0

Question 28

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

Accepted Answer

3x^2 + 2

Answer

x^3 + 1

Answer

3x^2 - 2x

Answer

x^3

Question 29

Calculate the volume of a sphere with a radius of 4 cm.

Accepted Answer

(32/3)π cm^3

Answer

(4/3)π cm^3

Answer

16π cm^3

Answer

64π cm^3

Question 30

Calculate the derivative of the function sin(x).

Accepted Answer

cos(x)

Answer

-sin(x)

Answer

sin(x)

Answer

-cos(x)

Question 31

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 32

Which equation represents a circle with center (2, 3) and radius 5?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 33

Find the value of log base 2 of 16.

Accepted Answer

4

Answer

2

Answer

16

Answer

8

Question 34

Determine the derivative of the function f(x) = e^x.

Accepted Answer

e^x

Answer

x * e^x

Answer

e^(x^2)

Answer

1 / e^x

Question 35

Find the derivative of the function f(x) = 3x² + 2x - 1.

Accepted Answer

6x + 2

Answer

6x² + 2x - 1

Answer

9x + 2

Answer

3x + 2

Question 36

Solve the linear equation: 2x + 5 = 11.

Accepted Answer

x = 3

Answer

x = -3

Answer

x = 8

Answer

x = 2

Question 37

What is the sine of 60 degrees?

Accepted Answer

√3 / 2

Answer

√2 / 2

Answer

1

Answer

1/2

Question 38

Determine the equation of the line passing through the points (2, 3) and (4, 7).

Accepted Answer

y = 2x - 1

Answer

y = x + 1

Answer

y = -2x + 7

Answer

y = x - 1

Question 39

Simplify the algebraic expression: (x² + 3x - 4) / (x - 1).

Accepted Answer

x + 4

Answer

x + 1

Answer

x - 4

Answer

x² + 4

Question 40

Calculate the area of a triangle with a base of 10 cm and a height of 8 cm.

Accepted Answer

40 cm²

Answer

20 cm²

Answer

80 cm²

Answer

18 cm²

Question 41

What is the value of the logarithm base 2 of 8?

Accepted Answer

3

Answer

2

Answer

4

Answer

1

Question 42

Find the indefinite integral of the function f(x) = 4x³ - 2x.

Accepted Answer

x⁴ - x² + C

Answer

x³ - x + C

Answer

4x⁴ - 2x² + C

Answer

12x² - 2 + C

Question 43

Solve the linear inequality: 3x - 5 > 7.

Accepted Answer

x > 4

Answer

x < 4

Answer

x > -4

Answer

x < -4

Question 44

Evaluate the cosine of 45 degrees.

Accepted Answer

√2 / 2

Answer

1

Answer

√3 / 2

Answer

1/2