POST UTME FUTO 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for y in the equation \( y = \frac{1}{2} \left\( \frac{1}{3} \right \ \)^x ).
A. \frac{1}{6}
B. \frac{1}{12}
C. \frac{1}{18}
D. \frac{1}{24}
Question 2
Solve the system of equations: x + y = 4 and xy = 5.
A. x = 1, y = 3
B. x = 2, y = 2
C. x = 3, y = 1
D. x = 4, y = 0
Question 3
A matrix A is given by \( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \ \). Find the determinant of A.
A. 0
B. 1
C. 2
D. 3
Question 4
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 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 1, \infty \)
Question 6
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 7
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x + 2
D. y = x - 2
Question 8
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{64}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{16}{3} \)
D. \( \frac{8}{3} \)
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 10
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. \( \frac{32}{15} pi \)
B. \( \frac{64}{15} pi \)
C. \( \frac{16}{3} pi \)
D. \( \frac{32}{3} pi \)
Question 11
A particle moves along the curve \( y = x^2 - 4x + 2 \). Find the rate of change of y with respect to x when x = 2.
A. 2
B. -2
C. 1
D. 0
Question 12
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 13
Solve the inequality $\frac{x^2 - 4x + 3}{x^2 - 4x + 2} > 0$.
A. \( -\infty, -1 \) \cup \( 2, \infty \)
B. \( -\infty, -2 \) \cup \( 1, \infty \)
C. \( -\infty, -3 \) \cup \( 2, \infty \)
D. \( -\infty, -1 \) \cup \( 1, \infty \)
Question 14
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 15
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

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