Pure Mathematics 2 Quizzes: Master Key Concepts and Excel in Exams

Question 1

Find the area of the region bounded by the curves y = x^2 and y = 4.

Accepted Answer

16/3

Answer

8/3

Answer

32/3

Answer

64/3

Question 2

When a quadratic equation has complex roots, what is the value of its discriminant?

Accepted Answer

Negative

Answer

Positive

Answer

Zero

Answer

Undefined

Question 3

What is the derivative of the function f(x) = sin(2x + 1)?

Accepted Answer

2cos(2x + 1)

Answer

cos(2x + 1)

Answer

-2cos(2x + 1)

Answer

-cos(2x + 1)

Question 4

Which of the following is a necessary condition for the geometric series ∑^{∞}_{n=1} ar^(n-1) to converge?

Accepted Answer

a > 0 and |r| < 1

Answer

a < 0 and |r| > 1

Answer

a ≠ 0 and |r| = 1

Answer

a ≠ 0 and |r| > 2

Question 5

Which of the following is NOT a trigonometric identity?

Accepted Answer

cos(2x) = cos^2(x) - sin^2(x)

Answer

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

Answer

tan(x) = sin(x)/cos(x)

Answer

sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

Question 6

Find the sum of the first 10 terms of the arithmetic sequence: 5, 10, 15, ...

Accepted Answer

550

Answer

500

Answer

600

Answer

650

Question 7

If sin(theta) = 0.5, what is the value of cos(theta)?

Accepted Answer

0.866

Answer

0.5

Answer

1

Answer

-0.866

Question 8

Find the sum of the first n terms of the geometric sequence a, ar, ar^2, ...

Accepted Answer

a(1 - r^n)/(1 - r)

Answer

a(1 + r^n)/(1 + r)

Answer

ar(1 - r^n)/(1 - r)

Answer

ar(1 + r^n)/(1 + r)

Question 9

Find the derivative of the function f(x) = e^(ax + b).

Accepted Answer

ae^(ax + b)

Answer

be^(ax + b)

Answer

a/e^(ax + b)

Answer

b/e^(ax + b)

Question 10

Find the inverse of the function f(x) = mx + c, where m ≠ 0.

Accepted Answer

f^(-1)(x) = (x - c)/m

Answer

f^(-1)(x) = (x + c)/m

Answer

f^(-1)(x) = mx - c

Answer

f^(-1)(x) = -mx + c

Question 11

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

Accepted Answer

The function is one-to-one.

Answer

The function is continuous on its domain.

Answer

The function is differentiable on its domain.

Answer

The function is increasing on its domain.

Question 12

If A is a 3x3 matrix and B is a 2x3 matrix, what is the size of the product AB?

Accepted Answer

3x2

Answer

2x3

Answer

3x3

Answer

2x2

Question 13

The equation y = e^(2x + 1) has which type of graph?

Accepted Answer

Exponential and increasing

Answer

Logarithmic and increasing

Answer

Exponential and decreasing

Answer

Logarithmic and decreasing

Question 14

The area of the region bounded by the curves y = x^2 and y = 4 is:

Accepted Answer

32/3

Answer

8/3

Answer

16/3

Answer

24/3

Question 15

Which of the following is a valid proof technique in mathematics?

Accepted Answer

Proof by contradiction

Answer

Proof by magic

Answer

Proof by intimidation

Answer

Proof by example

Question 16

Calculate the value of sin(30°) + cos(60°).

Accepted Answer

1

Answer

-1

Answer

2

Answer

0

Question 17

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

Accepted Answer

2x + 3

Answer

x^2 - 5

Answer

x^2 + 3

Answer

2x - 5

Question 18

Identify the correct definition of a proof by contradiction.

Accepted Answer

Assuming the opposite of the statement and demonstrating that it leads to a contradiction.

Answer

Using an indirect argument to prove the statement false.

Answer

Using a direct argument to prove the statement true.

Question 19

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 20

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

Accepted Answer

6x + 2

Answer

6x - 1

Answer

9x

Answer

3x

Question 21

Find the indefinite integral of f(x) = 2x + 1.

Accepted Answer

x^2 + x + C

Answer

x^2 + 2x + C

Answer

2x^2 + x + C

Answer

2x^2 + 2x + C

Question 22

The sum of the first 10 terms of an arithmetic series is 150, and the first term is 5. What is the common difference?

Accepted Answer

2

Answer

1

Answer

4

Answer

3

Question 23

What is 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 + 1

Answer

y = x + 1

Question 24

Simplify the expression (x^2 - 4) / (x - 2).

Accepted Answer

x + 2

Answer

x - 2

Answer

x^2 - 2

Answer

x - 4

Question 25

What is the value of log2(8)?

Accepted Answer

3

Answer

1

Answer

4

Answer

2

Question 26

Find the equation of the tangent line to the curve y = x^3 - 2x + 1 at the point x = 1.

Accepted Answer

y = 2x - 1

Answer

y = 3x - 2

Answer

y = x

Answer

y = x + 1

Question 27

Which method would you use to prove that the sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6?

Accepted Answer

Mathematical induction

Answer

Binomial theorem

Answer

Formula for the sum of an arithmetic series

Answer

Formula for the sum of a geometric series

Question 28

What is the value of sin(60°)?

Accepted Answer

√3/2

Answer

1

Answer

1/2

Answer

√2/2

Question 29

Find the area of the region bounded by the curve y = x^2, the x-axis, and the lines x = 1 and x = 2.

Accepted Answer

7/3

Answer

4/3

Answer

8/3

Answer

5/3

Question 30

Find the equation of the tangent to the curve y = x² + 3x - 2 at the point where x = 1.

Accepted Answer

y = 5x - 4

Answer

y = 4x - 3

Answer

y = 3x - 2

Answer

y = 2x + 1

Question 31

Evaluate the definite integral of the function f(x) = 2x + 1 from x = 0 to x = 2.

Accepted Answer

6

Answer

8

Answer

4

Answer

10

Question 32

The sum of the first n terms of an arithmetic series is given by Sn = 2n² + 3n. Find the common difference of the series.

Accepted Answer

4

Answer

2

Answer

5

Answer

3

Question 33

Solve the equation 2^(x+1) = 8.

Accepted Answer

x = 2

Answer

x = 1

Answer

x = 3

Question 34

The points A(1, 2) and B(3, 4) are the endpoints of a diameter of a circle. Find the equation of the circle.

Accepted Answer

(x - 2)² + (y - 3)² = 2

Answer

(x - 3)² + (y - 4)² = 2

Answer

(x - 2)² + (y - 3)² = 1

Answer

(x - 1)² + (y - 2)² = 2

Question 35

Prove that the sum of the squares of the first n natural numbers is given by the formula:  ∑(i²) = n(n+1)(2n+1)/6

Accepted Answer

Use mathematical induction.

Answer

Use the formula for the sum of a geometric series.

Answer

Use the binomial theorem.

Answer

Use the formula for the sum of an arithmetic series.

Question 36

Find the derivative of the function f(x) = sin(2x) + cos(x).

Accepted Answer

f'(x) = 2cos(2x) - sin(x)

Answer

f'(x) = cos(2x) - sin(x)

Answer

f'(x) = 2sin(2x) - cos(x)

Answer

f'(x) = cos(2x) + sin(x)

Question 37

Solve the equation sin(2θ) = 1/2 for 0 ≤ θ ≤ 2π.

Accepted Answer

θ = π/12, 5π/12, 13π/12, 17π/12

Answer

θ = π/4, 3π/4, 5π/4, 7π/4

Answer

θ = π/3, 2π/3, 4π/3, 5π/3

Answer

θ = π/6, 5π/6, 13π/6, 17π/6

Question 38

Find the limit as x approaches 0 of the function f(x) = (sin(x))/x.

Accepted Answer

1

Answer

∞

Answer

0

Answer

-1

Question 39

Find 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

4/3