POST UTME UI 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Evaluate the integral \( int_{0}^{1} \frac{1}{x^2 + 1} dx \).
A. \( \frac{1}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{2} \)
D. \( \frac{3pi}{4} \)
Question 2
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3/4.
A. 2.9375
B. 3.09375
C. 3.21875
D. 3.34375
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 4
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. 1/6
B. 1/3
C. 2/3
D. 5/6
Question 5
Solve the inequality \( \frac{x - 2}{x + 1} > 0 \).
A. \( -∞, -1 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (1, 2)
C. \( -∞, -1 \) ∪ (2, ∞)
D. \( -∞, 1 \) ∪ (2, ∞)
Question 6
Find the equation of the line pas\sing through the points (1,2) and (3,4).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 2 \)
D. \( y = 2x + 2 \)
Question 7
Solve the system of linear equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \).
A. \( x = 1, y = 1 \)
B. \( x = 1, y = 3 \)
C. \( x = 3, y = 1 \)
D. \( x = 3, y = 3 \)
Question 8
A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?
A. 8
B. 10
C. 12
D. 14
Question 9
Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.
A. \frac{4}{3}
B. \frac{2}{3}
C. \frac{1}{3}
D. \frac{1}{2}
Question 10
A set of 5 points is chosen at random from the set ( {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ). Find the probability that the 5 points form an arithmetic sequence.
A. \( \frac{1}{252} \)
B. \( \frac{1}{126} \)
C. \( \frac{1}{63} \)
D. \( \frac{1}{32} \)
Question 11
A matrix A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} has an inverse A^{-1}. Find the value of A^{-1} cdot A.
A. \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}
B. \begin{bmatrix} 0 & 1 \ 1 & 0 \end{bmatrix}
C. \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}
D. \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}
Question 12
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{pi}{2} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 13
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?
A. ₦1250
B. ₦12500
C. ₦125000
D. ₦1250000
Question 14
Solve the inequality $|x - 2| > 3$.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, 1 \) \cup \( 5, \infty \)
C. \( -\infty, -1 \) \cup (2, 5)
D. \( -\infty, 1 \) \cup (2, 5)
Question 15
Solve the inequality \( \frac{1}{x+1} - \frac{1}{x-1} > 0 \).
A. \( -∞, -1 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (1, 2)
C. \( -∞, -1 \) ∪ (2, ∞)
D. \( -∞, 1 \) ∪ (2, ∞)

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