POST UTME FUTO 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -3 \) \cup \( 1, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -3 \) \cup \( -1, \infty \)
D. \( -\infty, 1 \) \cup \( -3, \infty \)
Question 3
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.
A. \frac{64}{3}
B. \frac{32}{3}
C. \frac{16}{3}
D. \frac{8}{3}
Question 4
A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?
A. 22
B. 25
C. 28
D. 30
Question 5
Let $A = \begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix}$. Find the inverse of $A$.
A. \begin{pmatrix} 1 & -1 \ -1 & 1 \end{pmatrix}
B. \begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix}
C. \begin{pmatrix} 1 & 1 \ 1 & 2 \end{pmatrix}
D. \begin{pmatrix} 2 & -1 \ -1 & 1 \end{pmatrix}
Question 6
Solve for x in the equation \( \log_{10}\( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 7
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. x^{-3/2}
B. -x^{-3/2}
C. x^{-1/2}
D. x^{1/2}
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )
B. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 3 )
C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - 2 )
D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 2 )
Question 9
A binary operation \(*\) on the set \( \{0, 1\} \) is defined as follows: \( 0*0 = 0, 0*1 = 1, 1*0 = 1, 1*1 = 0 \). Find the value of \( 1*0 \)*\( 1*1 \).
A. 0
B. 1
C. 10
D. 01
Question 10
Find the area under the curve \( y = x^3 - 2x^2 + x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. \frac{23}{2}
B. \frac{25}{2}
C. \frac{27}{2}
D. \frac{29}{2}
Question 11
Find the determinant of the matrix $\begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}$.
A. -1
B. 1
C. 2
D. 3
Question 12
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases} \).
A. \( x = \frac{7}{5}, y = \frac{17}{5} \)
B. \( x = \frac{7}{5}, y = -\frac{17}{5} \)
C. \( x = -\frac{7}{5}, y = \frac{17}{5} \)
D. \( x = -\frac{7}{5}, y = -\frac{17}{5} \)
Question 13
A circle with center $C$ passes through points $A$ and $B$. If $AB = 6$ and $CA = 3$, find the area of the circle.
A. 9\pi
B. 12\pi
C. 18\pi
D. 24\pi
Question 14
A sequence is defined by the formula an = 2n + 1. Find the sum of the first 5 terms.
A. 15
B. 17
C. 19
D. 21
Question 15
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( x < -1 \) or \( x > 5 \)
B. \( x < -5 \) or \( x > 1 \)
C. \( x < -1 \) or \( x < 5 \)
D. \( x < -5 \) or \( x > 1 \)

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