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POST UTME LEAD CITY UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME LEAD CITY UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

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

Correct Answer: A

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Question 2

If \( y = \frac{1}{x} \), find \( \frac{dy}{dx} \) at \( x = 2 \).

A. \( -\frac{1}{4} \)

Correct B. \( \frac{1}{4} \)

C. \( -\frac{1}{2} \)

D. \( \frac{1}{2} \)

Correct Answer: B

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Question 3

Solve the system of equations u\sing matrices: [ egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} ]

Correct A. \( x = 1, y = 2 \)

B. \( x = 2, y = 1 \)

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 4

Find the area of the triangle with vertices ( A(1,2) ), ( B(3,4) ), and ( C(2,1) ).

A. ( 5 )

B. ( 10 )

Correct C. ( 15 )

D. ( 20 )

Correct Answer: C

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Question 5

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \( \frac{1}{6} \)

B. \( \frac{1}{3} \)

C. \( \frac{2}{3} \)

Correct D. \( \frac{5}{6} \)

Correct Answer: D

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Question 6

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 7

Solve for ( x ) in the equation \( 2^x + 5^x = 7^x \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8

A cylindrical \tank with a radius of 4m and a height of 10m is filled with water. Find the volume of water in the \tank.

A. 800\pi

Correct B. 1000\pi

C. 1200\pi

D. 1500\pi

Correct Answer: B

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Question 9

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

Correct A. 6x + 2

B. 3x^2 + 2

C. 6x - 2

D. 3x^2 - 2

Correct Answer: A

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Question 10

A rec\tangular prism with a length of 5m, a width of 3m, and a height of 2m is placed on a table. Find the surface area of the prism.

A. 62

Correct B. 64

C. 66

D. 68

Correct Answer: B

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Question 11

In a circle of radius 8 cm, a chord of length 12 cm subt\ends an angle of 60° at the centre. Find the area of the sector.

A. 48π cm²

Correct B. 64π cm²

C. 72π cm²

D. 80π cm²

Correct Answer: B

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Question 12

A matrix A has the following form: [ A = egin{bmatrix} 2 & 1 & 3 \ 4 & 3 & 5 \ 6 & 2 & 1 \end{bmatrix} ]. Find the determinant of A.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 13

A histogram represents the distribution of exam scores of 20 students. The scores are: 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230. Find the mean of the scores.

A. 100

B. 110

Correct C. 120

D. 130

Correct Answer: C

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Question 14

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the prism.

A. 400 cm³

B. 500 cm³

C. 600 cm³

Correct D. 800 cm³

Correct Answer: D

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Question 15

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

Correct A. 5 cm

B. 7.5 cm

C. 10 cm

D. 12.5 cm

Correct Answer: A

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Question 16

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. \( egin{pmatrix} 0.8 \ 1.2 \end{pmatrix} \)

B. \( egin{pmatrix} 1.2 \ 1.8 \end{pmatrix} \)

C. \( egin{pmatrix} 0.4 \ 0.6 \end{pmatrix} \)

D. \( egin{pmatrix} 1.6 \ 2.4 \end{pmatrix} \)

Correct Answer: A

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Question 17

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).

Correct A. \( x = \frac{pi}{4} \)

B. \( x = \frac{pi}{2} \)

C. \( x = \frac{3pi}{4} \)

D. \( x = \frac{5pi}{4} \)

Correct Answer: A

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Question 18

Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^3 + 8x^4 + ldots \).

Correct A. \( 2048x^{20} \)

B. \( 1024x^{20} \)

C. \( 512x^{20} \)

D. \( 256x^{20} \)

Correct Answer: A

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Question 19

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \( \frac{1}{6} \)

B. \( \frac{1}{3} \)

C. \( \frac{2}{3} \)

Correct D. \( \frac{5}{6} \)

Correct Answer: D

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Question 20

Find the derivative of the function ( f(x) = 3x^2 \sin x ) u\sing the product rule.

A. \( 6x \sin x + 3x^2 \cos x \)

Correct B. \( 3x^2 \cos x + 6x \sin x \)

C. \( 6x^2 \sin x + 3x \cos x \)

D. \( 3x^2 \sin x + 6x \cos x \)

Correct Answer: B

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Question 21

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 2 & 3 \ 1 & 2 & 4 \end{pmatrix} ].

A. 4

Correct B. -2

C. 6

D. 8

Correct Answer: B

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Question 22

A coin is tossed three times. What is the probability that at least two of the tosses result in heads?

A. 1/4

B. 1/2

Correct C. 3/4

D. 7/8

Correct Answer: C

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Question 23

The equation of a circle is given by \( x^2 + y^2 = 16 \). Find the equation of the line that passes through the point ( (4, 0) ) and is perp\endicular to the given circle.

Correct A. x + y = 4

B. x - y = 4

C. x + y = 8

D. x - y = 8

Correct Answer: A

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Question 24

Simplify the expression \( \frac{3x^2 + 2x - 1}{2x^2 - 5x + 1} \).

Correct A. x + 1

B. x - 1

C. 3x - 2

D. 2x + 1

Correct Answer: A

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Question 25

Find the value of ( x ) in the equation \( 2^x + 5^x = 10^x \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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