POST UTME LAUTECH 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for $x$ in the equation $\tan x = \sqrt{3}$.
A. \frac{\pi}{3}
B. \frac{\pi}{6}
C. \frac{\pi}{4}
D. \frac{\pi}{2}
Question 2
Find the equation of the \tangent to the curve y = \frac{1}{x+1} at the point where x = -2.
A. y = -2x - 5
B. y = 2x - 3
C. y = -\frac{1}{2}x + 1
D. y = \frac{1}{2}x - 1
Question 3
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 4
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 6 \) and \( mathbf{a} cdot mathbf{c} = 3 \), given that \( mathbf{b} = 2mathbf{i} + 3mathbf{j} \) and \( mathbf{c} = mathbf{i} - 2mathbf{j} \).
A. 3mathbf{i} + 2mathbf{j}
B. 2mathbf{i} + 3mathbf{j}
C. 4mathbf{i} + mathbf{j}
D. 5mathbf{i} - 2mathbf{j}
Question 5
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) in the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ).
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 7
A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 3. If a_1 = 2, find the sum of the first 5 terms of the sequence.
A. 2 + 7 + 17 + 37 + 79
B. 2 + 5 + 13 + 29 + 61
C. 2 + 7 + 15 + 31 + 63
D. 2 + 5 + 13 + 27 + 55
Question 8
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If they sell 30 more whole wheat loaves than white bread loaves, and they sell a total of 240 whole wheat loaves, how many white bread loaves do they sell?
A. 120
B. 150
C. 180
D. 200
Question 9
Solve the inequality \( 2x - 5 > 9 \).
A. x > 7
B. x < 7
C. x > 2
D. x < 2
Question 10
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. 4
B. 6
C. 8
D. 10
Question 11
Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).
A. 62
B. 64
C. 66
D. 68
Question 12
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. 1
B. -2
C. 3
D. -3
Question 13
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A. \frac{2}{3}
B. \frac{3}{4}
C. \frac{4}{5}
D. \frac{5}{6}
Question 14
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. -1
B. 1
C. 2
D. 3
Question 15
Find the area under the curve y = \sin x from x = 0 to x = \frac{\pi}{2}.
A. \boxed{1}
B. \frac{\pi}{2}
C. \frac{1}{2}
D. \frac{\pi}{4}

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