POST UTME UNIOSUN 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for $x$: $\log_{10} \( x^2 \) = 4$.
A. 10
B. 100
C. 1000
D. 10000
Question 2
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )
Question 3
A car travels from city A to city B at an average speed of 60 km/h. On the return trip, the car travels at an average speed of 40 km/h. What is the average speed for the entire trip?
A. 48 km/h
B. 50 km/h
C. 52 km/h
D. 54 km/h
Question 4
Find the area under the curve \( y = x^2 + 2x - 3 \) from x = 0 to x = 4.
A. 40
B. 60
C. 80
D. 100
Question 5
Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \].
A. 0
B. 1
C. 2
D. 3
Question 6
Solve the equation [ x^2 + 4x + 4 = 0 ].
A. -2
B. -1
C. 0
D. 1
Question 7
Solve the system of linear equations \( egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -2 \ 3x + y + 2z = 5 \end{cases} \).
A. \( x = 1, y = 2, z = 3 \)
B. \( x = 2, y = 3, z = 4 \)
C. \( x = 3, y = 4, z = 5 \)
D. \( x = 4, y = 5, z = 6 \)
Question 8
Find the equation of the circle pas\sing through the points (2,3), (4,5), and \( -1,2 \).
A. \( x^2 + y^2 - 4x - 6y + 5 = 0 \)
B. \( x^2 + y^2 + 4x + 6y + 5 = 0 \)
C. \( x^2 + y^2 - 4x + 6y + 5 = 0 \)
D. \( x^2 + y^2 + 4x - 6y + 5 = 0 \)
Question 9
A sequence is defined by the formula \( a_n = 2n^2 + 3n - 1 \). Find the sum of the first 5 terms of the sequence.
A. 55
B. 65
C. 75
D. 85
Question 10
A histogram has class boundaries 0, 5, 10, 15, 20 and class marks 2.5, 7.5, 12.5, 17.5. If the frequency of the class 5-10 is 8, find the mean of the histogram.
A. 10
B. 12
C. 14
D. 16
Question 11
In a certain number base, the number 1010 is equivalent to 12 in base 10. What is the value of the number base?
A. 4
B. 5
C. 6
D. 7
Question 12
Find the value of ( x ) in the equation \( 2^x + 5^x = 7^x \).
A. 1
B. 2
C. 3
D. 4
Question 13
Find the volume of the frustum of a cone with height $h$, base radii $r_1$ and $r_2$, and slant height $l$.
A. \frac{1}{3}\pi h\( r_1^2+r_2^2+r_1r_2 \)
B. \frac{1}{3}\pi h\( r_1^2-r_2^2+r_1r_2 \)
C. \frac{1}{3}\pi h\( r_1^2+r_2^2-r_1r_2 \)
D. \frac{1}{3}\pi h\( r_1^2-r_2^2-r_1r_2 \)
Question 14
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 15
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. 30
B. 32
C. 34
D. 36

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