POST UTME FUTO 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \). If \( a_1 = 2 \), find the value of \( a_5 \).
A. 31
B. 32
C. 33
D. 34
Question 2
If f(x) = x^3 - 2x^2 + x - 1, find f'(x) u\sing the chain rule.
A. \frac{d}{dx} \( x^3 - 2x^2 + x - 1 \) = 3x^2 - 4x + 1
B. \frac{d}{dx} \( x^3 - 2x^2 + x - 1 \) = 3x^2 - 4x - 1
C. \frac{d}{dx} \( x^3 - 2x^2 + x - 1 \) = 3x^2 + 4x - 1
D. \frac{d}{dx} \( x^3 - 2x^2 + x - 1 \) = 3x^2 + 4x + 1
Question 3
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \frac{1}{2}
B. \frac{2}{7}
C. \frac{3}{8}
D. \frac{5}{8}
Question 4
Simplify the expression \( \sqrt{\frac{4}{9}} \ \).
A. \frac{2}{3}
B. \frac{4}{9}
C. \frac{2}{9}
D. \frac{4}{3}
Question 5
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 6
Find the value of x in the quadratic equation \( x^2 + 5x - 6 = 0 \).
A. 2
B. -3
C. 1
D. -2
Question 7
A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. $1500
B. $2000
C. $2500
D. $3000
Question 8
Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \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 9
Solve the system of linear equations u\sing matrices: \( egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 10
A vector ( mathbf{a} ) has magnitude 5 and direction \( 30^circ \) from the positive x-axis. Find the vector ( mathbf{a} ) in component form.
A. \( mathbf{a} = egin{pmatrix} 4 \ 3 \end{pmatrix} \)
B. \( mathbf{a} = egin{pmatrix} 3 \ 4 \end{pmatrix} \)
C. \( mathbf{a} = egin{pmatrix} 5 \ 0 \end{pmatrix} \)
D. \( mathbf{a} = egin{pmatrix} 0 \ 5 \end{pmatrix} \)
Question 11
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y - 3 = \frac{2}{2} \( x - 2 \)
B. y - 3 = \frac{2}{4} \( x - 2 \)
C. y - 3 = \frac{4}{2} \( x - 2 \)
D. y - 3 = \frac{4}{4} \( x - 2 \)
Question 12
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 13
Find the surface area of the sphere with radius \( r = 4 \) cm.
A. ( 32 pi ) cm^2
B. ( 64 pi ) cm^2
C. ( 128 pi ) cm^2
D. ( 256 pi ) cm^2
Question 14
Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. -1
C. 2
D. -2
Question 15
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 4.
A. 40
B. 50
C. 60
D. 70

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