POST UTME AL-HIKMAH UNIVERSITY 2018 Mathematics | Objective

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Question 1
In the diagram below, ( ABC ) is a right-angled triangle with \( angle B = 90^circ \). If \( AB = 6 \) cm and \( BC = 8 \) cm, find the length of side ( AC ).
A. 10 cm
B. 12 cm
C. 15 cm
D. 18 cm
Question 2
A circle with center O and radius 4 units is inscribed in a square with side length 8 units. Find the area of the shaded region.
A. 16 square units
B. 32 square units
C. 48 square units
D. 64 square units
Question 3
A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has a total of 20 bars, find the sum of the products of the heights and widths of the bars.
A. ( 500 )
B. ( 1000 )
C. ( 1500 )
D. ( 2000 )
Question 4
Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \) u\sing integration.
A. \( int_{1}^{2} \frac{1}{x} dx = ln 2 - ln 1 \)
B. \( int_{1}^{2} \frac{1}{x} dx = ln 1 - ln 2 \)
C. \( int_{1}^{2} \frac{1}{x} dx = ln 2 + ln 1 \)
D. \( int_{1}^{2} \frac{1}{x} dx = ln 1 + ln 2 \)
Question 5
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. ( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )
B. ( f'(x) = \frac{1}{2}x^{-\frac{3}{2}} )
C. ( f'(x) = -\frac{1}{2}x^{-\frac{1}{2}} )
D. ( f'(x) = \frac{1}{2}x^{-\frac{1}{2}} )
Question 6
A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed of the car for the entire trip?
A. 45
B. 50
C. 55
D. 60
Question 7
Determine the mean of the data set {2, 4, 6, 8, 10} u\sing the formula for population mean.
A. \( \frac{2+4+6+8+10}{5} = 6 \)
B. \( \frac{2+4+6+8+10}{4} = 6.5 \)
C. \( \frac{2+4+6+8+10}{3} = 6.67 \)
D. \( \frac{2+4+6+8+10}{2} = 6 \)
Question 8
Solve for x in the equation \( \log_{2} \( x^2 \ \) = 4 ).
A. 16
B. 32
C. 64
D. 128
Question 9
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 192\pi cm^3
D. 256\pi cm^3
Question 10
A survey of 50 students found that 30 students preferred Mathematics, 15 preferred Science, and 5 preferred both subjects. What is the probability that a randomly selected student prefers Mathematics?
A. 0.6
B. 0.7
C. 0.8
D. 0.9
Question 11
A polynomial function is defined by ( f(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of \( f\( -1 \ \) ).
A. 2
B. 3
C. 4
D. 5
Question 12
A circle has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the circle passes through the point ( (6, 8) ) and has a center at ( (3, 4) ), find the radius.
A. \( \sqrt{5} \)
B. \( \sqrt{10} \)
C. \( \sqrt{15} \)
D. \( \sqrt{20} \)
Question 13
A set of 5 numbers has a mean of 10. If the largest number is 20, find the sum of the remaining 4 numbers.
A. \( 4 \times 10 + 20 = 48 \)
B. \( 4 \times 10 - 20 = 28 \)
C. \( 4 \times 10 + 20 = 28 \)
D. \( 4 \times 10 - 20 = 48 \)
Question 14
Simplify the expression \( \sqrt[3]{64x^3y^3} \).
A. \( 4x^1y^1 \)
B. \( 4x^3y^3 \)
C. \( 4x^3y^1 \)
D. \( 4x^1y^3 \)
Question 15
In the diagram below, the circle with center A passes through points B and C. Find the length of arc BC.
A. 10
B. 20
C. 30
D. 40

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