POST UTME CALEB UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. \( y = \frac{1}{2}x + 1 \)
B. \( y = 2x - 1 \)
C. \( y = \frac{1}{2}x - 1 \)
D. \( y = 2x + 1 \)
Question 2
Find the surface area of the sphere with radius ( 6 ).
A. ( 4 pi (6)^2 )
B. ( 4 pi (6) )
C. ( 2 pi (6)^2 )
D. ( 2 pi (6) )
Question 3
Solve the inequality \( \frac{x}{x-1} > 0 \) for ( x in mathbb{R} setminus {1} ).
A. \( -∞, 0 \) ∪ (1, ∞)
B. \( -∞, 1 \) ∪ (1, ∞)
C. \( -∞, 0 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (1, ∞)
Question 4
Solve the system of equations \\begin{align*} x + y &= 2 \\ x - y &= 1 \\end{align*} u\sing matrices.
A. x = 1, y = 1
B. x = 2, y = 0
C. x = 0, y = 2
D. x = 1, y = 2
Question 5
A circle with center ( O(0, 0) ) and radius 4 passes through the point ( P(3, 4) ). Find the equation of the circle.
A. \( x^2 + y^2 = 16 \)
B. \( x^2 + y^2 = 20 \)
C. \( x^2 + y^2 = 24 \)
D. \( x^2 + y^2 = 28 \)
Question 6
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the population mean.
A. 169.1 cm, 181.9 cm
B. 170.5 cm, 180.5 cm
C. 171.5 cm, 179.5 cm
D. 172.5 cm, 178.5 cm
Question 7
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 10 \) and \( mathbf{a} cdot mathbf{c} = 5 \), given that \( mathbf{b} = 2mathbf{i} + 3mathbf{j} \) and \( mathbf{c} = mathbf{i} - 2mathbf{j} \).
A. \( 5mathbf{i} - mathbf{j} \)
B. \( 2mathbf{i} + mathbf{j} \)
C. \( 3mathbf{i} + 2mathbf{j} \)
D. \( mathbf{i} - 3mathbf{j} \)
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -3 \) ∪ (1, ∞)
D. \( -∞, -1 \) ∪ (3, ∞)
Question 9
Find the volume of the sphere with radius ( 6 ).
A. \( \frac{4}{3} pi \( 6 \ \)^3 )
B. \( \frac{4}{3} pi \( 6 \ \)^2 )
C. \( \frac{4}{3} pi \( 6 \ \) )
D. \( \frac{4}{3} pi \( 6 \ \)^2 )
Question 10
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. \( y = \frac{2}{2} x + \frac{1}{2} \)
B. \( y = \frac{2}{2} x + \frac{3}{2} \)
C. \( y = \frac{2}{2} x + \frac{5}{2} \)
D. \( y = \frac{2}{2} x + \frac{1}{2} \)
Question 11
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant method.
A. \( egin{pmatrix} 6 \ -2 \end{pmatrix} \)
B. \( egin{pmatrix} -6 \ 2 \end{pmatrix} \)
C. \( egin{pmatrix} 0 \ 0 \end{pmatrix} \)
D. \( egin{pmatrix} 3 \ -6 \end{pmatrix} \)
Question 12
Find the equation of the circle with center (2,3) and radius 4.
A. \( x-2 \)^2+\( y-3 \)^2=16
B. \( x-2 \)^2+\( y-3 \)^2=4
C. \( x-2 \)^2+\( y-3 \)^2=9
D. \( x-2 \)^2+\( y-3 \)^2=25
Question 13
A quadratic equation is given by \[x^2 + 4x + 4 = 0\]. Solve for x.
A. \[x = -2\]
B. \[x = -1\]
C. \[x = 0\]
D. \[x = 1\]
Question 14
Find the area under the curve \[y = \frac{1}{x^2 + 1}\] from \[x = 0\] to \[x = 1\].
A. \[\frac{\pi}{4}\]
B. \[\frac{\pi}{2}\]
C. \[\frac{\pi}{6}\]
D. \[\frac{\pi}{3}\]
Question 15
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8

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