POST UTME UNIOSUN 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 2
Solve the system of equations: \( egin{cases} 2x + 3y = 7 \ 4x - 2y = - 3 \end{cases} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 3
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 4
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 cross product formula.
A. \( egin{pmatrix} 0 \ 0 \ 0 \end{pmatrix} \)
B. \( egin{pmatrix} 6 \ -4 \ 0 \end{pmatrix} \)
C. \( egin{pmatrix} 0 \ 0 \ 6 \end{pmatrix} \)
D. \( egin{pmatrix} 0 \ 0 \ -6 \end{pmatrix} \)
Question 5
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. -\frac{2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 6
Find the derivative of the function \( y = \sin^2\( x \ \) ) u\sing the chain rule.
A. \( 2 \sin\( x \ \) \cos(x) )
B. \( \cos^2\( x \ \) )
C. \( \sin^2\( x \ \) )
D. \( \sin\( x \ \) )
Question 7
A vector \overrightarrow{a} has magnitude 5 and direction 60°. Find the magnitude of the vector \overrightarrow{a} + \overrightarrow{b}, where \overrightarrow{b} has magnitude 3 and direction 120°.
A. 4
B. 5
C. 6
D. 7
Question 8
A rec\tangular box has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the surface area of the box.
A. 88
B. 96
C. 104
D. 112
Question 9
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first 5 terms of the sequence.
A. \( 2 + 7 + 17 + 37 + 79 \)
B. \( 2 + 5 + 13 + 29 + 61 \)
C. \( 2 + 7 + 17 + 37 + 79 \)
D. \( 2 + 5 + 13 + 29 + 61 \)
Question 10
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3/2.
A. 2047
B. 2048
C. 2049
D. 2050
Question 11
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 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 12
Solve the quadratic equation $x^2 + 4x + 4 = 0$.
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 13
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).
A. \( -infty, -2 \ \) cup (2, infty) )
B. \( -infty, -2 \ \) cup (2, infty) cup { 0 } )
C. \( -infty, -2 \ \) cup (2, infty) cup { 4 } )
D. \( -infty, -2 \ \) cup (2, infty) cup { -4 } )
Question 14
Find the determinant of the matrix \( egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{pmatrix} \).
A. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) - 1 \times \( 4 \times 2 - 3 \times 1 \) + 3 \times \( 4 \times 1 - 3 \times 2 \) )
B. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) - 1 \times \( 4 \times 2 - 3 \times 1 \) - 3 \times \( 4 \times 1 - 3 \times 2 \) )
C. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) + 1 \times \( 4 \times 2 - 3 \times 1 \) + 3 \times \( 4 \times 1 - 3 \times 2 \) )
D. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) - 1 \times \( 4 \times 2 - 3 \times 1 \) - 3 \times \( 4 \times 1 - 3 \times 2 \) )
Question 15
A cone has a height of 10 cm and a radius of 5 cm. Find the volume of the cone.
A. 500\pi
B. 1000\pi
C. 2000\pi
D. 3000\pi

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