POST UTME AFE BABALOLA UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. x^2 + y^2 - 6x - 4y + 12 = 0
B. x^2 + y^2 + 2x - 4y + 5 = 0
C. x^2 + y^2 + 4x + 2y - 6 = 0
D. x^2 + y^2 - 2x + 4y - 8 = 0
Question 2
A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even, the coin is flipped twice. If the number on the die is odd, the coin is flipped only once. What is the probability that at least one of the coin flips shows heads?
A. \frac{1}{2}
B. \frac{2}{3}
C. \frac{3}{4}
D. \frac{4}{5}
Question 3
Find the value of ( x ) in the equation \( x^2 + 2x - 3 = 0 \).
A. \( x = -3 \) or \( x = 1 \)
B. \( x = -1 \) or \( x = 3 \)
C. \( x = 1 \) or \( x = -3 \)
D. \( x = -1 \) or \( x = -3 \)
Question 4
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. 32
B. 64
C. 16
D. 128
Question 5
Solve for ( x ) in the equation \( x^2 + 4x + 4 = 0 \).
A. \( -2 \)
B. \( -1 \)
C. ( 1 )
D. ( 2 )
Question 6
Solve for y in the equation \( y = \frac{1}{2}x + 3 \) when x = 6.
A. 9
B. 10
C. 11
D. 12
Question 7
Find the surface area of the sphere with radius 5 cm.
A. ( 50pi ) cm²
B. ( 100pi ) cm²
C. ( 150pi ) cm²
D. ( 200pi ) cm²
Question 8
Find the area of the circle with radius ( 4 ) cm.
A. ( 16pi ) cm^2
B. ( 32pi ) cm^2
C. ( 64pi ) cm^2
D. ( 128pi ) cm^2
Question 9
Find the equation of the line pas\sing through the points (2,3) and (4,5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 10
Solve for ( x ) in the equation \( 2^x = 8 \).
A. ( 1 )
B. ( 2 )
C. ( 3 )
D. ( 4 )
Question 11
Determine the value of the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{array} ].
A. -10
B. 10
C. 20
D. 30
Question 12
A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.3. If Y is another random variable such that Y = 2X - 1, find P\( Y = 3 \).
A. 0.4
B. 0.3
C. 0.2
D. 0.1
Question 13
Evaluate the integral \int_0^1 \( 2x^3 - 5x^2 + 3x - 1 \) dx.
A. [1, 2, 3, 4]
B. [1, 2, 3, 4]
C. [1, 2, 3, 4]
D. [1, 2, 3, 4]
Question 14
If \vec{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} and \vec{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}, find the cross product \vec{a} \times \vec{b}.
A. \begin{pmatrix} -1 \ 8 \ -5 \end{pmatrix}
B. \begin{pmatrix} 1 \ -8 \ 5 \end{pmatrix}
C. \begin{pmatrix} -1 \ -8 \ 5 \end{pmatrix}
D. \begin{pmatrix} 1 \ 8 \ -5 \end{pmatrix}
Question 15
Find the determinant of the matrix \[\begin{bmatrix} 2 & 3 & 4 \\ 5 & 6 & 7 \\ 8 & 9 & 10 \end{bmatrix}\].
A. -120
B. 120
C. 0
D. 240

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