POST UTME UI 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the vector \(\mathbf{a} \cdot \mathbf{b}\) given \(\mathbf{a} = \begin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} 4 \ 5 \end{pmatrix}\).
A. 23
B. 29
C. 31
D. 37
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 3
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{2}{6}
C. \frac{3}{6}
D. \frac{4}{6}
Question 4
Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).
A. 4
B. 6
C. 8
D. 10
Question 5
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. \frac{2x^2 - 4}{\( x - 2 \)^2}
B. \frac{2x^2 + 4}{\( x - 2 \)^2}
C. \frac{2x^2 - 4x}{\( x - 2 \)^2}
D. \frac{2x^2 + 4x}{\( x - 2 \)^2}
Question 6
Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 7
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 114,273
B. 114,274
C. 114,275
D. 114,276
Question 8
Find the equation of the line pas\sing through the points (1, 2) and (3, 4).
A. \boxed{y = x + 1}
B. \boxed{y = x - 1}
C. \boxed{y = -x + 2}
D. \boxed{y = x - 2}
Question 9
Solve the system of linear equations \begin{align*} x + y &= 4 \ x - 2y &= -2 \end{align*}.
A. \begin{pmatrix} 2 \ 2 \end{pmatrix}
B. \begin{pmatrix} 1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 3 \ 1 \end{pmatrix}
D. \begin{pmatrix} 4 \ 0 \end{pmatrix}
Question 10
In the diagram below, a circle with center O passes through points A, B, and C. If the radius of the circle is 6 units, what is the area of the shaded region?
A. 36π
B. 72π
C. 108π
D. 144π
Question 11
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 12
A histogram of exam scores for a class of 50 students is shown below. What is the mean score?
A. 70
B. 75
C. 80
D. 85
Question 13
Solve the equation \( 2x^3 - 5x^2 + 3x - 1 = 0 \) u\sing the Rational Root Theorem.
A. \boxed{r = \pm 1}
B. \boxed{r = \pm 2}
C. \boxed{r = \pm 3}
D. \boxed{r = \pm 1/2}
Question 14
Find the derivative of the function \( f(x) = \frac{x^2 + 3x - 2}{x + 1} \) u\sing the Quotient Rule.
A. \boxed{f'(x) = \frac{2x + 3}{\( x + 1 \)^2}}
B. \boxed{f'(x) = \frac{2x - 3}{\( x + 1 \)^2}}
C. \boxed{f'(x) = \frac{2x + 2}{\( x + 1 \)^2}}
D. \boxed{f'(x) = \frac{2x - 2}{\( x + 1 \)^2}}
Question 15
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24π cm^3
B. 48π cm^3
C. 72π cm^3
D. 96π cm^3

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