POST UTME BABCOCK UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \( \sin 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \).
A. \( \frac{24}{25} \)
B. \( \frac{16}{25} \)
C. \( \frac{12}{25} \)
D. \( \frac{20}{25} \)
Question 2
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the surface area of the prism.
A. \( 2\( 5 \times 3 + 3 \times 2 + 5 \times 2 \ \) )
B. \( 2\( 5 \times 3 + 3 \times 2 + 5 \times 3 \ \) )
C. \( 2\( 5 \times 3 + 3 \times 5 + 2 \times 5 \ \) )
D. \( 2\( 5 \times 3 + 3 \times 5 + 2 \times 3 \ \) )
Question 3
The volume of a cube is given by \( V = s^3 \), where ( s ) is the length of a side. If the volume of the cube is 216 cubic units, what is the length of a side?
A. 3
B. 4
C. 6
D. 8
Question 4
A circle has a radius of 4. Find the area of the circle.
A. 16
B. 25.13
C. 50.27
D. 100.54
Question 5
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the value of \( a_{10} \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 6
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 7
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 8
In a triangle $ABC$, if $\tan A = \frac{1}{3}$ and $\tan B = \frac{1}{2}$, find $\tan C$.
A. \frac{\sqrt{5}}{5}
B. \frac{5}{\sqrt{5}}
C. \frac{\sqrt{5}}{2}
D. \frac{2}{\sqrt{5}}
Question 9
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 10
A rec\tangular prism has a length of 8, a width of 5, and a height of 3. Find the volume of the prism.
A. 120
B. 150
C. 180
D. 200
Question 11
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) 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{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
Question 12
Find the volume of the solid formed by revolving the region bounded by $y = x^2$ and $y = 4 - x$ about the $x$-axis.
A. \frac{256}{15}\pi
B. \frac{256}{3}\pi
C. \frac{256}{5}\pi
D. \frac{256}{7}\pi
Question 13
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. 30
B. 40
C. 50
D. 60
Question 14
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \text{Volume: } \frac{16}{3} \pi
B. \text{Volume: } \frac{32}{3} \pi
C. \text{Volume: } \frac{64}{3} \pi
D. \text{Volume: } \frac{128}{3} \pi
Question 15
A right triangle has a hypotenuse of length 10 and one leg of length 6. Find the length of the other leg.
A. 4
B. 6
C. 8
D. 10

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