Pure Mathematics 2 Quizzes: Test Your Skills and Prepare for Exams

Question 1

Calculate the derivative of the function f(x) = ln(x^2 + 1) using the chain rule.

Accepted Answer

2x/(x^2 + 1)

Answer

1/(x^2 + 1)

Answer

(x^2 + 1)/x

Answer

x/(x^2 + 1)

Question 2

Given the equation y = e^(2x) + ln(x), determine the derivative of y with respect to x.

Accepted Answer

2e^(2x) + 1/x

Answer

2e^(2x) - 1/x

Answer

e^(2x) + 1/x

Answer

e^(2x) - 1/x

Question 3

Find the domain of the function f(x) = log_2(x - 3).

Accepted Answer

(3, ∞)

Answer

(0, 3]

Answer

(-∞, 3)

Answer

(0, ∞)

Question 4

Which of the following is the derivative of the function f(x) = xe^x?

Accepted Answer

e^x + xe^x

Answer

(x + 1)e^x

Answer

xe^x + e^x

Answer

(x - 1)e^x

Question 5

In triangle ABC, AB = 6 cm, BC = 8 cm and AC = 10 cm. What is the cosine of angle ABC?

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

1/3

Question 6

Which of the following is the indefinite integral of the function f(x) = 2x + 1?

Accepted Answer

x^2 + x + C

Answer

2x^2 + C

Answer

x^2/2 + x + C

Answer

x^2 + 2x + C

Question 7

Which of the following statements is true for any two sets A and B?

Accepted Answer

A ∩ B ⊆ A ∪ B

Answer

A ∪ B = A ∩ B

Answer

A - B = A ∪ B

Answer

B - A = A ∪ B

Question 8

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

Accepted Answer

f^-1(x) = (x - 3) / 2

Answer

f^-1(x) = (x + 3) / 2

Answer

f^-1(x) = 2x - 3

Answer

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

Question 9

Find the equation of the tangent line to the curve y = x^2 + 1 at the point (1, 2).

Accepted Answer

y = 2x + 1

Answer

y = 2x − 1

Answer

y = x + 1

Answer

y = −x + 3

Question 10

Which of the following topics is NOT covered in Pure Mathematics 2?

Accepted Answer

Probability

Answer

Proof

Answer

Trigonometry

Answer

Integration

Question 11

Determine the derivative of the function f(x) = sin(x) + cos(x).

Accepted Answer

cos(x) + sin(x)

Answer

sin(x) - cos(x)

Answer

cos(x) - sin(x)

Answer

sin(x) + cos(x)

Question 12

Find the solution to the differential equation y' - 2y = 0.

Accepted Answer

y = Ce^(-2x)

Answer

y = Ce^(2x)

Answer

y = xCe^(2x)

Answer

y = xCe^(-2x)

Question 13

Solve the equation 2cos(x) + 1 = 0.

Accepted Answer

x = π/3 - 2πn, x = 5π/3 - 2πn

Answer

x = π/3 + 2πn, x = 5π/3 + 2πn

Answer

x = π/3 - 2πn, x = 5π/3 + 2πn

Answer

x = π/3 + 2πn, x = 5π/3 - 2πn

Question 14

Which of the following accurately describes the derivative of a function?

Accepted Answer

It provides the gradient of the tangent line to the function's graph at a specific point.

Answer

It indicates whether a function is increasing or decreasing.

Answer

It reveals the function's local and global maximum and minimum values.

Answer

It's solely applicable for functions involving polynomials.

Question 15

Solve the equation sin(x) = 0.5.

Accepted Answer

x = π/6

Answer

x = π/3

Answer

x = π/2

Answer

x = π

Question 16

Which of the following is a crucial condition for a function to have an inverse?

Accepted Answer

The function must be one-to-one.

Answer

The function must be monotonically increasing or decreasing.

Answer

The function must be continuous.

Answer

The function must be differentiable.

Question 17

Find the equation that represents the circle with a radius of 5 centered at the origin.

Accepted Answer

x^2 + y^2 = 25

Answer

x^2 + y^2 = 5

Answer

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

Answer

(x + 5)^2 + (y + 5)^2 = 25

Question 18

Evaluate the integral ∫(x² + 2x + 1) dx.

Accepted Answer

x³/3 + 2x² + x + C

Answer

x³ + x² + x + C

Answer

x³ + 2x² + x + C

Answer

x³/3 + x² + x + C

Question 19

Evaluate sin(π/6) + cos(π/3).

Accepted Answer

√3/2

Answer

1

Answer

√2

Answer

2

Question 20

Calculate the value of sin(60°).

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

√2/2

Question 21

Solve the equation 2^x = 16.

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 8

Answer

x = 1

Question 22

Calculate the area enclosed by the curve y = x^2, the x-axis, and the lines x = 0 and x = 2.

Accepted Answer

8/3

Answer

2

Answer

4/3

Answer

4