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POST UTME BABCOCK UNIVERSITY 2024 Mathematics | Objective

Are you preparing for POST UTME BABCOCK UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

In a triangle $ABC$, if $\tan A = \frac{1}{3}$ and $\tan B = \frac{1}{2}$, find $\tan C$.

Correct A. \frac{\sqrt{5}}{5}

B. \frac{5}{\sqrt{5}}

C. \frac{\sqrt{5}}{2}

D. \frac{2}{\sqrt{5}}

Correct Answer: A

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Question 2

Find the volume of the solid formed by revolving the region bounded by $y = x^2$ and $y = 4 - x$ about the $x$-axis.

Correct A. \frac{256}{15}\pi

B. \frac{256}{3}\pi

C. \frac{256}{5}\pi

D. \frac{256}{7}\pi

Correct Answer: A

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Question 3

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 4

Solve the equation $\log_{10} $ x^2 $ = 4$ for $x$.

Correct A. \pm 4

B. \pm 2

C. \pm 1

D. \pm 3

Correct Answer: A

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Question 5

Find the surface area of the sphere with radius 5 cm.

A. 250\pi cm^2

Correct B. 500\pi cm^2

C. 750\pi cm^2

D. 1000\pi cm^2

Correct Answer: B

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Question 6

Find the equation of the circle with centre at ((2,3)) and radius (5).

Correct A. $ x-2 \ $^2 + $ y-3 $^2 = 25 )

B. $ x+2 \ $^2 + $ y+3 $^2 = 25 )

C. $ x-3 \ $^2 + $ y-2 $^2 = 25 )

D. $ x+3 \ $^2 + $ y+2 $^2 = 25 )

Correct Answer: A

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Question 7

Solve the inequality $ |x-2| geq 3 $.

Correct A. $ x leq -1 $ or ( x geq 5 )

B. ( x leq 1 ) or ( x geq 5 )

C. $ x leq -1 $ or ( x geq 4 )

D. ( x leq 1 ) or ( x geq 4 )

Correct Answer: A

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Question 8

Find the value of $ \sin 2\theta $ given that $ \sin \theta = \frac{3}{5} $ and $ \cos \theta = \frac{4}{5} $.

Correct A. $ \frac{24}{25} $

B. $ \frac{16}{25} $

C. $ \frac{12}{25} $

D. $ \frac{20}{25} $

Correct Answer: A

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Question 9

A rec\tangular box has a length of ( 6 ) cm, a width of ( 4 ) cm, and a height of ( 3 ) cm. Find the volume of the box.

Correct A. ( 72 ) cm$ ^3 $

B. ( 48 ) cm$ ^3 $

C. ( 36 ) cm$ ^3 $

D. ( 24 ) cm$ ^3 $

Correct Answer: A

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Question 10

Solve the equation $ x^2 + 4x + 4 = 0 $.

Correct A. $ x = -2 $

B. $ x = 2 $

C. $ x = -1 $

D. $ x = 1 $

Correct Answer: A

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Question 11

Find the equation of the circle with center at (2, 3) and radius 4.

Correct A. \text{Equation: } $ x - 2 $^2 + $ y - 3 $^2 = 16

B. \text{Equation: } $ x + 2 $^2 + $ y - 3 $^2 = 16

C. \text{Equation: } $ x - 2 $^2 + $ y + 3 $^2 = 16

D. \text{Equation: } $ x + 2 $^2 + $ y + 3 $^2 = 16

Correct Answer: A

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Question 12

Solve the system of linear equations: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}

Correct A. \text{Solution: } x = 2, y = 2

B. \text{Solution: } x = 1, y = 3

C. \text{Solution: } x = 3, y = 1

D. \text{Solution: } x = 4, y = 0

Correct Answer: A

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Question 13

Find the volume of the solid formed by revolving the region bounded by the parabola $ y = x^2 $ and the line $ y = 2x $ about the x-axis.

Correct A. \text{Volume: } \frac{16}{3} \pi

B. \text{Volume: } \frac{32}{3} \pi

C. \text{Volume: } \frac{64}{3} \pi

D. \text{Volume: } \frac{128}{3} \pi

Correct Answer: A

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Question 14

Solve the inequality $ 2x^2 + 5x - 3 \geq 0 $.

Correct A. \text{Solution: } x \leq -1 \text{ or } x \geq \frac{3}{2}

B. \text{Solution: } x < -1 \text{ or } x > \frac{3}{2}

C. \text{Solution: } x \leq -1 \text{ or } x < \frac{3}{2}

D. \text{Solution: } x > -1 \text{ or } x \geq \frac{3}{2}

Correct Answer: A

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Question 15

Find the value of $ \log_{10} \( x^2 $ given that $ \log_{10} x = 2 $.

Correct A. \text{Value: } 4

B. \text{Value: } 6

C. \text{Value: } 8

D. \text{Value: } 10

Correct Answer: A

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Question 16

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.

Correct A. ( f'(x) = \frac{-2x}{$ x^2 + 1 $^2} )

B. ( f'(x) = \frac{2x}{$ x^2 + 1 $^2} )

C. ( f'(x) = \frac{2}{$ x^2 + 1 $^2} )

D. ( f'(x) = \frac{-2}{$ x^2 + 1 $^2} )

Correct Answer: A

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Question 17

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the surface area of the prism.

Correct A. $ 2\( 5 \times 3 + 3 \times 2 + 5 \times 2 \ $ )

B. $ 2\( 5 \times 3 + 3 \times 2 + 5 \times 3 \ $ )

C. $ 2\( 5 \times 3 + 3 \times 5 + 2 \times 5 \ $ )

D. $ 2\( 5 \times 3 + 3 \times 5 + 2 \times 3 \ $ )

Correct Answer: A

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Question 18

Find the volume of the solid formed by revolving the region bounded by the curve $ y = x^2 $ and the line $ y = 2 $ about the x-axis.

A. $ \frac{8}{3} pi $

Correct B. $ \frac{16}{3} pi $

C. $ \frac{32}{3} pi $

D. $ \frac{64}{3} pi $

Correct Answer: B

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Question 19

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. ( 16 pi )

B. ( 32 pi )

C. ( 64 pi )

D. ( 128 pi )

Correct Answer: A

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Question 20

Find the derivative of the function ( f(x) = \sin^2(x) ) u\sing the chain rule.

Correct A. ( f'(x) = 2 \sin(x) \cos(x) )

B. ( f'(x) = 2 \cos(x) \sin(x) )

C. ( f'(x) = 2 \sin^2(x) \cos(x) )

D. ( f'(x) = 2 \cos^2(x) \sin(x) )

Correct Answer: A

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Question 21

Let $ mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} $ and $ mathbf{b} = egin{pmatrix} 1 \ -1 \end{pmatrix} $. Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula $ mathrm{proj}_{mathbf{a}} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{| mathbf{a} |^2} mathbf{a} $.

Correct A. 0.6

B. 0.8

C. 1.2

D. 1.5

Correct Answer: A

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Question 22

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3 or 5?

A. 1/3

B. 1/2

Correct C. 2/3

D. 5/6

Correct Answer: C

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Question 23

The volume of a cube is given by $ V = s^3 $, where ( s ) is the length of a side. If the volume of the cube is 216 cubic units, what is the length of a side?

A. 3

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 24

Solve the equation $ x^2 + 4x + 4 = 0 $ u\sing the quadratic formula.

A. 0

Correct B. -2

C. -4

D. 2

Correct Answer: B

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Question 25

A right triangle has a hypotenuse of length 10 and one leg of length 6. Find the length of the other leg.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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