POST UTME FUTA 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram shows the distribution of exam scores with a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find 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 2
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing the definite integral.
A. 64
B. 128
C. 256
D. 512
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
A random experiment consists of rolling a fair six-sided die. What is the probability that the number rolled is greater than 4?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 5
In a circle of radius 8 cm, a chord of length 12 cm subt\ends an angle of 60° at the centre. Find the area of the sector formed by the chord and the radii drawn to the \ends of the chord.
A. 48\pi cm^2
B. 64\pi cm^2
C. 72\pi cm^2
D. 80\pi cm^2
Question 6
A circle with center ( C(2,3) ) and radius \( r = 4 \) has equation \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). Find the equation of the circle.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 7
A probability distribution is given by the function ( f(x) = \frac{1}{2}x ) for ( 0 leq x leq 2 ). Find the expected value of the random variable.
A. 1
B. 1.5
C. 2
D. 2.5
Question 8
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 9
Let ( f(x) = \frac{x^2 - 4}{x^2 - 9} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. \( f'(x) = \frac{2x\( x^2 - 9 \) - 2x\( x^2 - 4 \)}{\( x^2 - 9 \)^2} \)
B. \( f'(x) = \frac{2x\( x^2 - 9 \) + 2x\( x^2 - 4 \)}{\( x^2 - 9 \)^2} \)
C. \( f'(x) = \frac{2x\( x^2 - 9 \) - 2x\( x^2 - 4 \)}{\( x^2 - 9 \)^2} \)
D. \( f'(x) = \frac{2x\( x^2 - 9 \) + 2x\( x^2 - 4 \)}{\( x^2 - 9 \)^2} \)
Question 10
Let \( S = {1, 2, 3, 4, 5} \) and \( T = {2, 3, 4, 5, 6} \). Find the symmetric difference of ( S ) and ( T ).
A. S \cup T
B. S \cap T
C. S \triangle T
D. S \oplus T
Question 11
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 12
Solve the system of equations \( egin{cases} x^2 + y^2 = 4 \ x + y = 2 \end{cases} \).
A. \( x = 1, y = 1 \)
B. \( x = 2, y = 0 \)
C. \( x = 0, y = 2 \)
D. \( x = 1, y = 2 \)
Question 13
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 14
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 15
A sequence is defined recursively as \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the value of \( a_5 \).
A. 31
B. 33
C. 35
D. 37

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