POST UTME ESUT 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle passes through the points (2,3), (4,5), and (6,7). Find the equation of the circle.
A. \( x - 4 \)^2 + \( y - 3 \)^2 = 5
B. \( x - 3 \)^2 + \( y - 4 \)^2 = 5
C. \( x - 5 \)^2 + \( y - 3 \)^2 = 5
D. \( x - 3 \)^2 + \( y - 5 \)^2 = 5
Question 2
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. \frac{128\pi}{3}
B. \frac{64\pi}{3}
C. \frac{32\pi}{3}
D. \frac{16\pi}{3}
Question 3
Solve the equation \[\sin^2 x + \cos^2 x = 1\].
A. \sin x = 0
B. \cos x = 0
C. \sin x = \cos x
D. \sin x = -\cos x
Question 4
A polynomial function f(x) = x^3 - 2x^2 - 5x + 6 has a root at x = -1. Find the other two roots of the function.
A. 2, 3
B. 1, 2
C. 1, 3
D. 2, 4
Question 5
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 6
Find the surface area of the sphere with radius 4cm.
A. 256\pi cm^2
B. 512\pi cm^2
C. 768\pi cm^2
D. 1024\pi cm^2
Question 7
Solve the system of equations \[\begin{cases} x + y = 2 \ 2x - 3y = - 3 \end{cases}\].
A. \begin{cases} x = 1 \ y = 1 \end{cases}
B. \begin{cases} x = 1 \ y = -1 \end{cases}
C. \begin{cases} x = -1 \ y = 1 \end{cases}
D. \begin{cases} x = -1 \ y = -1 \end{cases}
Question 8
Find the value of x in the equation \( \sin^2 x + \cos^2 x = 1 \) if \( \sin x = \frac{3}{5} \).
A. 0
B. \frac{\pi}{4}
C. \frac{\pi}{2}
D. \frac{3\pi}{4}
Question 9
Find the equation of the line pas\sing through the points (2,3) and (4,5).
A. y = \frac{2}{3}x + 1
B. y = \frac{3}{2}x - 1
C. y = \frac{4}{3}x - 1
D. y = \frac{5}{4}x + 1
Question 10
A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 1, with a_1 = 3. Find the value of a_5.
A. 31
B. 32
C. 33
D. 34
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. 0.2
B. 0.24
C. 0.28
D. 0.32
Question 12
The mean of 5 numbers is 12. If one of the numbers is 15, find the sum of the remaining 4 numbers.
A. 45
B. 50
C. 55
D. 60
Question 13
Solve the matrix equation \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 7 \\ 10 \end{bmatrix}.
A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}
Question 14
A car travels from city A to city B at an average speed of 60 km/h. On the return trip, the car travels at an average speed of 40 km/h. What is the average speed of the car for the entire trip?
A. 40
B. 50
C. 60
D. 70
Question 15
A bakery sells a total of 250 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?
A. 50
B. 75
C. 100
D. 125

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