POST UTME UNIOSUN 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a geometric sequence with first term (a) and common ratio (r), the sum of the first (n) terms is given by the formula \( S_n = \frac{a\( r^n - 1 \ \)}{r - 1}). If the sum of the first 8 terms of the sequence is 512, and the 9th term is 256, what is the value of (a)?
A. 128
B. 256
C. 512
D. 1024
Question 2
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x + 2
C. 6x + 2
D. 6x + 2
Question 3
A company produces two products, X and Y. The profit on product X is ₦50 per unit, and the profit on product Y is ₦30 per unit. If the company produces 200 units of product X and 300 units of product Y, what is the total profit?
A. ₦25,000
B. ₦30,000
C. ₦35,000
D. ₦40,000
Question 4
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 104,783
B. 104,783
C. 104,783
D. 104,783
Question 5
A sequence is defined by $a_n = 2n + 1$. Find the sum of the first $5$ terms of the sequence.
A. 30
B. 35
C. 40
D. 45
Question 6
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. 256\pi cm^3
B. 512\pi cm^3
C. 768\pi cm^3
D. 1024\pi cm^3
Question 7
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi cm^2
B. 32\pi cm^2
C. 64\pi cm^2
D. 128\pi cm^2
Question 8
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.
A. 6 cdot 4 cdot 3
B. 6 cdot 4 cdot 3 + 2
C. 6 cdot 4 cdot 3 - 2
D. 6 cdot 4 cdot 3 + 4
Question 9
A polynomial function f(x) has zeros at x = -2, x = 1, and x = 3. Write the function in factored form.
A. f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \)
B. f(x) = a\( x + 2 \)\( x - 1 \)\( x - 3 \)
C. f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \) + 2
D. f(x) = a\( x + 2 \)\( x - 1 \)\( x - 3 \) + 2
Question 10
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. If the other leg is denoted by (x), what is the value of (x)?
A. 4
B. 6
C. 8
D. 12
Question 11
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = x + 1
B. y = x - 1
C. y = -x + 5
D. y = x - 5
Question 12
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 4 cm
B. 6 cm
C. 8 cm
D. 12 cm
Question 13
A geometric sequence has first term \( a = 2 \) and common ratio \( r = 3 \). Find the sum of the first 5 terms.
A. \( 2 + 6 + 18 + 54 + 162 = 242 \)
B. \( 2 + 6 + 18 + 54 + 162 = 242 \)
C. \( 2 + 6 + 18 + 54 + 162 = 242 \)
D. \( 2 + 6 + 18 + 54 + 162 = 242 \)
Question 14
Solve the inequality $\log_2\( x-1 \) > 2$.
A. \( 4, \infty \)
B. \( 2, \infty \)
C. \( 1, \infty \)
D. \( 0, \infty \)
Question 15
A binary operation \ast is defined as: a \ast b = a^2 + b^2. Find the value of \( 2 \ast 3 \) \ast 4.
A. 25
B. 37
C. 49
D. 65

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