POST UTME AAUA 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 cm
B. 6 cm
C. 4 cm
D. 2 cm
Question 2
A set of 5 consecutive integers has a median of 9. What is the sum of the integers?
A. 45
B. 50
C. 55
D. 60
Question 3
Find the derivative of ( f(x) = \sin^2 x ) u\sing the chain rule.
A. 2 \sin x \cos x
B. -2 \sin x \cos x
C. \cos^2 x
D. \sin^2 x
Question 4
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?
A. 30 cm^3
B. 40 cm^3
C. 50 cm^3
D. 60 cm^3
Question 5
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
C. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 4
D. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 4
Question 6
Simplify the expression \( \frac{2x^2 - 5x + 3}{x^2 - 2x - 3} \).
A. \( \frac{2x - 1}{x + 1} \)
B. \( \frac{2x + 1}{x - 1} \)
C. \( \frac{2x - 3}{x + 1} \)
D. \( \frac{2x + 3}{x - 1} \)
Question 7
In a geometric sequence with first term 2 and common ratio 3, find the sum of the first 5 terms.
A. 2 + 6 + 18 + 54 + 162
B. 2 + 6 + 18 + 54 + 162 + 486
C. 2 + 6 + 18 + 54 + 162 + 486 + 1458
D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374
Question 8
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( mathrm{proj}_{mathbf{a}}mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{|mathbf{a}|^2} mathbf{a} \).
A. \begin{pmatrix} 0.8 \ 1.2 \end{pmatrix}
B. \begin{pmatrix} 1.6 \ 2.4 \end{pmatrix}
C. \begin{pmatrix} 2.4 \ 3.6 \end{pmatrix}
D. \begin{pmatrix} 3.2 \ 4.8 \end{pmatrix}
Question 9
Solve the inequality 2x^2 + 5x - 3 > 0.
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 10
A company produces x units of a product, where x is a multiple of 5. If the company produces 25 units, what is the value of x?
A. 20
B. 25
C. 30
D. 35
Question 11
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P\( A \cap B \).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 12
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.135
B. 0.225
C. 0.675
D. 0.975
Question 13
A circle has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 ). Find the equation of the \tangent line to the circle at the point ( (5, 7) ).
A. y = -1x + 12
B. y = x + 3
C. y = -x + 9
D. y = x - 5
Question 14
Solve for x in the matrix equation \( \begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. \( x = \frac{3 - 4}{2 - 1} \ \)
B. \( x = \frac{3 + 4}{2 + 1} \ \)
C. \( x = \frac{3 - 4}{2 + 1} \ \)
D. \( x = \frac{3 + 4}{2 - 1} \ \)
Question 15
Convert the decimal number 0.75 to a \fraction in simplest form.
A. \frac{1}{4}
B. \frac{2}{4}
C. \frac{3}{4}
D. \frac{4}{4}

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