POST UTME SUMMIT UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A company produces two products, A and B. The profit from the sale of one unit of product A is ₦100, and the profit from the sale of one unit of product B is ₦120. If the company produces 20 units of product A and 15 units of product B, what is the total profit?
A. ₦3500
B. ₦4000
C. ₦4500
D. ₦5000
Question 2
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. \frac{64}{3}
B. \frac{32}{3}
C. \frac{16}{3}
D. \frac{8}{3}
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \)
Question 4
Solve the inequality \( x^2 - 6x + 8 > 0 \).
A. \( x < 2 \) or \( x > 4 \)
B. \( x > 2 \) and \( x < 4 \)
C. \( x < 2 \) and \( x > 4 \)
D. \( x = 2 \) or \( x = 4 \)
Question 5
Find the sum of the first 5 terms of the geometric series \( 2x + 4x^2 + 8x^3 + ... \).
A. \( 2x + 4x^2 + 8x^3 + 16x^4 + 32x^5 \)
B. \( 2x + 4x^2 + 8x^3 + 16x^4 + 32x^5 + 64x^6 \)
C. \( 2x + 4x^2 + 8x^3 + 16x^4 + 32x^5 + 64x^6 + 128x^7 \)
D. \( 2x + 4x^2 + 8x^3 + 16x^4 + 32x^5 \)
Question 6
A right-angled triangle has a hypotenuse of length 10 cm. If the ratio of the lengths of the two legs is 3:4, what is the length of the longer leg?
A. 6
B. 8
C. 10
D. 12
Question 7
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 12 \) and \( mathbf{a} cdot mathbf{c} = 20 \), where \( mathbf{b} = 2mathbf{i} + 3mathbf{j} \) and \( mathbf{c} = mathbf{i} - 2mathbf{j} \).
A. \( 6mathbf{i} + 4mathbf{j} \)
B. \( 4mathbf{i} + 6mathbf{j} \)
C. \( 3mathbf{i} + 5mathbf{j} \)
D. \( 5mathbf{i} + 3mathbf{j} \)
Question 8
A polynomial function f(x) has a degree of 3 and a leading coefficient of 1. If f(0) = 2 and f(1) = 5, what is the value of f\( -1 \)?
A. 2
B. 3
C. 4
D. 5
Question 9
A vector has a magnitude of 5 units and makes an angle of 60 degrees with the positive x-axis. Find the x and y components of the vector.
A. 2.5 \hat{i} + 4.33 \hat{j}
B. 4.33 \hat{i} + 2.5 \hat{j}
C. 2.5 \hat{i} - 4.33 \hat{j}
D. 4.33 \hat{i} - 2.5 \hat{j}
Question 10
Solve the system of equations: \[ \begin{cases} x + y + z = 6 \\ x + 2y + 3z = 14 \end{cases} \]
A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}
B. \begin{pmatrix} 2 \ 1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 1 \ 3 \ 2 \end{pmatrix}
D. \begin{pmatrix} 3 \ 2 \ 1 \end{pmatrix}
Question 11
Find the derivative of the function f(x) = \frac{x^2 + 1}{x^2 - 1} u\sing the quotient rule.
A. \frac{2x}{\( x^2 - 1 \)^2}
B. \frac{2x^3 - 2x}{\( x^2 - 1 \)^2}
C. \frac{2x^3 + 2x}{\( x^2 - 1 \)^2}
D. \frac{2x^3 - 2x}{\( x^2 - 1 \)^2}
Question 12
A right circular cone has a height of 12 cm and a base radius of 6 cm. Find the volume of the cone.
A. \frac{1}{3} \pi (6)^2 (12)
B. \frac{1}{3} \pi (6)^2 (8)
C. \frac{1}{3} \pi (8)^2 (12)
D. \frac{1}{3} \pi (8)^2 (6)
Question 13
A right-angled triangle has sides of length 3, 4, and 5. Find the area of the triangle.
A. \( \frac{1}{2} \times 3 \times 4 \)
B. \( \frac{1}{2} \times 3 \times 5 \)
C. \( \frac{1}{2} \times 4 \times 5 \)
D. \( \frac{1}{2} \times 3 \times 5 \)
Question 14
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = -\frac{1}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{1}{\( x^2 + 1 \)^2} )
Question 15
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi

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