POST UTME FUTA 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 2
Solve the inequality \( |x - 2| geq 3 \).
A. \( x leq -1 \) or ( x geq 5 )
B. ( x leq 1 ) or ( x geq 5 )
C. \( x leq -1 \) or ( x geq 4 )
D. ( x leq 1 ) or ( x geq 4 )
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{16}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{64}{3} \)
D. \( \frac{128}{3} \)
Question 4
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = -1 \end{cases} \).
A. \( x = 1, y = 3 \)
B. \( x = 2, y = 2 \)
C. \( x = 3, y = 1 \)
D. \( x = 4, y = 0 \)
Question 5
A binary operation ( odot ) on the set ( mathbb{R} ) is defined as \( a odot b = a^2 + b^2 \). Find the value of ( 2 odot 3 ).
A. 13
B. 14
C. 15
D. 16
Question 6
A rec\tangular box has dimensions ( x ), ( 2x ), and ( 3x ). If the surface area of the box is ( 120 ) square units, find the value of ( x ).
A. ( 2 )
B. ( 3 )
C. ( 4 )
D. ( 5 )
Question 7
A vector ( mathbf{a} ) has magnitude 5 and direction \( 30^circ \) counterclockwise from the positive x-axis. Find the x-component of ( mathbf{a} ).
A. 4
B. 4.33
C. 4.64
D. 5
Question 8
The sum of the first ( n ) terms of an arithmetic progression is given by \( S_n = \frac{n}{2} [2a + \( n - 1 \ \)d] ). If the first term is 5 and the common difference is 2, find the sum of the first 10 terms.
A. 105
B. 110
C. 115
D. 120
Question 9
A histogram of exam scores is shown below. Find the mean of the scores.
A. 60
B. 70
C. 80
D. 90
Question 10
Let ( f(x) = \frac{1}{x^2 + 1} ). Find the derivative of ( f(x) ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} \)
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} \)
C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^2} \)
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} \)
Question 11
Let ( P(x) = 2x^3 - 5x^2 + x - 1 ). Find the derivative of ( P(x) ) u\sing the power rule.
A. ( P'(x) = 6x^2 - 10x + 1 \)
B. ( P'(x) = 6x^2 - 10x - 1 \)
C. ( P'(x) = 6x^2 + 10x - 1 \)
D. ( P'(x) = 6x^2 + 10x + 1 \)
Question 12
A geometric progression has first term 2 and common ratio 3. Find the sum of the first 5 terms.
A. 731
B. 733
C. 735
D. 737
Question 13
A company produces ( x ) units of a product, where ( x ) is a random variable with a probability density function ( f(x) = \frac{1}{2}x ) for ( 0 leq x leq 2 ). Find the expected value of ( x ).
A. \( \frac{4}{3} \)
B. \( \frac{5}{3} \)
C. \( \frac{6}{3} \)
D. \( \frac{7}{3} \)
Question 14
A right-angled triangle has sides of length 3 cm, 4 cm, and 5 cm. Find the area of the triangle.
A. 6 cm^2
B. 8 cm^2
C. 10 cm^2
D. 12 cm^2
Question 15
Find the value of ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000

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