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POST UTME LASU 2019 Mathematics | Objective

Are you preparing for POST UTME LASU 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

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is 6, what is the value of the mis\sing number in the data set?

Correct A. 12

B. 14

C. 16

D. 18

Correct Answer: A

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Question 2

Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...

Correct A. 59049

B. 59048

C. 59050

D. 59052

Correct Answer: A

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Question 3

Solve the system of linear equations u\sing matrices: \begin{align*} x + y &= 4 \ 2x - 3y &= -1 \end{align*}

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 4

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 5

A set of 10 numbers has a mean of 20. If 5 more numbers are added to the set, the mean becomes 22. What is the sum of the original 10 numbers?

A. 200

Correct B. 220

C. 240

D. 260

Correct Answer: B

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Question 6

Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 5x - 3} ) u\sing the quotient rule.

Correct A. \( \frac{-2x + 5}{\( 2x^2 + 5x - 3 \ \)^2} )

B. \( \frac{2x + 5}{\( 2x^2 + 5x - 3 \ \)^2} )

C. \( \frac{2x - 5}{\( 2x^2 + 5x - 3 \ \)^2} )

D. \( \frac{-2x - 5}{\( 2x^2 + 5x - 3 \ \)^2} )

Correct Answer: A

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Question 7

A circle with center ( C(2, 3) ) and radius \( r = 4 \) has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 ). Find the equation of the line pas\sing through the point ( P(6, 7) ) that is \tangent to the circle.

Correct A. \( y - 7 = \frac{1}{4}\( x - 6 \ \) )

B. \( y - 7 = -\frac{1}{4}\( x - 6 \ \) )

C. \( y - 7 = \frac{1}{2}\( x - 6 \ \) )

D. \( y - 7 = -\frac{1}{2}\( x - 6 \ \) )

Correct Answer: A

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Question 8

Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.

Correct A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{4} \)

C. \( x < -\frac{3}{2} \) or \( x < \frac{5}{4} \)

D. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)

Correct Answer: A

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Question 9

A population of bacteria grows according to the \logistic equation \( \frac{dP}{dt} = rP left\( 1 - \frac{P}{K} \right \ \) ), where \( r = 0.5 \) and \( K = 100 \). Find the equilibrium population.

A. \( P = 0 \)

B. \( P = 50 \)

Correct C. \( P = 100 \)

D. \( P = 200 \)

Correct Answer: C

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Question 10

A random variable ( X ) has probability density function ( f(x) = \frac{1}{2}e^{-|x|} ). Find the expected value of ( X ).

Correct A. ( E(X) = 0 )

B. ( E(X) = 1 )

C. ( E(X) = -1 )

D. ( E(X) = 2 )

Correct Answer: A

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Question 11

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 64\pi cm^3

B. 128\pi cm^3

Correct C. 192\pi cm^3

D. 256\pi cm^3

Correct Answer: C

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Question 12

Solve for x in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 13

A bakery sells 250 loaves of bread per day. If they make a profit of ₦2 per loaf, how much profit do they make in a day?

Correct A. ₦500

B. ₦5000

C. ₦50000

D. ₦500000

Correct Answer: A

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Question 14

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

Correct A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16

B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16

C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16

Correct Answer: A

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Question 15

Find the vector projection of vector \( mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \) onto vector \( mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \).

Correct A. egin{pmatrix} 0.8 \ 1 \ 1.2 \end{pmatrix}

B. egin{pmatrix} 1 \ 1.2 \ 1.6 \end{pmatrix}

C. egin{pmatrix} 1.2 \ 1.5 \ 2 \end{pmatrix}

D. egin{pmatrix} 1.5 \ 1.8 \ 2.4 \end{pmatrix}

Correct Answer: A

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Question 16

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

Correct A. \( x+2 \ \)^2 + \( y-3 \)^2 = 16 )

B. \( x-2 \ \)^2 + \( y+3 \)^2 = 16 )

C. \( x+2 \ \)^2 + \( y+3 \)^2 = 16 )

D. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )

Correct Answer: A

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Question 17

Solve for x in the equation \( 2^x + 2^{x+1} = 2^{x+2} + 1 \).

A. \( x = -1 \)

B. \( x = 0 \)

Correct C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: C

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Question 18

A fair six-sided die is rolled. What is the probability that the number rolled is either 1 or 6?

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 19

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. ( 0 )

B. ( 1 )

C. \( -1 \)

D. ( 2 )

Correct Answer: A

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Question 20

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

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

Correct B. \( \frac{2}{3} \)

C. \( \frac{3}{4} \)

D. \( \frac{4}{5} \)

Correct Answer: B

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Question 21

Let X be a random variable with probability density function (pdf) given by f(x) = \( \frac{1}{2} e^{-|x|} \) for -\( infty < x < infty \). Find the probability that X lies between -1 and 1.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 22

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -\( infty, -\frac{3}{2} \ \)) (cup) (1, (infty))

B. \( -\( infty, -\frac{3}{2} \ \)) (cap) (1, (infty))

C. \( -\( infty, -\frac{3}{2} \ \)) (cup) \( -1, \( infty \ \))

D. \( -\( infty, -\frac{3}{2} \ \)) (cap) \( -1, \( infty \ \))

Correct Answer: A

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Question 23

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

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

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

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

D. \( \frac{3pi}{4} \)

Correct Answer: A

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Question 24

Let A be a 2x2 matrix given by [A = egin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix}]. Find the determinant of A.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 25

Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

Correct A. 1, 2, 3

B. 1, 2, 4

C. 1, 3, 4

D. 2, 3, 4

Correct Answer: A

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