POST UTME ABU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation: \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{\pi}{6}
Question 2
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is 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 3
Determine the value of $\log_{10} \left\( \frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}} \right \)$.
A. -1
B. 1
C. 2
D. 3
Question 4
Solve the system of equations u\sing matrices: [ egin{cases} x + 2y = 6 \ 3x - 2y = -3 \end{cases} ].
A. \( x = 3, y = 1.5 \)
B. \( x = 1.5, y = 3 \)
C. \( x = 2, y = 2 \)
D. \( x = 4, y = 1 \)
Question 5
Find the area of the triangle with vertices at ((0,0)), ((3,0)), and ((0,4)).
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 6
Find the vector ( mathbf{v} ) that is orthogonal to both \( mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \).
A. \( mathbf{v} = egin{pmatrix} -10 \ 15 \ -6 \end{pmatrix} \)
B. \( mathbf{v} = egin{pmatrix} 10 \ -15 \ 6 \end{pmatrix} \)
C. \( mathbf{v} = egin{pmatrix} -15 \ 10 \ 6 \end{pmatrix} \)
D. \( mathbf{v} = egin{pmatrix} 15 \ -10 \ -6 \end{pmatrix} \)
Question 7
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, what is their total daily profit?
A. ₦1,250
B. ₦1,500
C. ₦1,750
D. ₦2,000
Question 8
A vector \overrightarrow{a} has a magnitude of 5 and makes an angle of 60^\circ with the positive x-axis. What is the x-component of this vector?
A. 2.5
B. 4.33
C. 5
D. 7.07
Question 9
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 10
Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].
A. 0
B. -1
C. 1
D. 2
Question 11
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 12
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x > \frac{3}{2}
D. x > -1 or x < \frac{3}{2}
Question 13
Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \) for ( x ) and ( y ).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 14
Find the sum of the first 10 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = 3 \).
A. \( 2\( 3^{10} - 1 \ \) )
B. \( 2\( 3^{10} + 1 \ \) )
C. \( 2\( 3^{10} - 2 \ \) )
D. \( 2\( 3^{10} + 2 \ \) )
Question 15
Solve for $x$: $\sqrt{2x + 5} - 3 = 2$.
A. -1
B. 1
C. 2
D. 3

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: