POST UTME AAUA 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the \tangent line to the curve y = x^2 + 2x - 3 at the point (1, 2).
A. y = 4x - 1
B. y = 4x + 1
C. y = 4x - 3
D. y = 4x + 3
Question 2
A set ( A ) contains the elements ( 1, 2, 3, 4, 5 ). Find the number of subsets of ( A ) that contain exactly three elements.
A. 10
B. 15
C. 20
D. 25
Question 3
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 4
Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ 11 \end{bmatrix}.
A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}
Question 5
Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 4 \\ 5 & 6 & 7 \\ 8 & 9 & 10 \end{bmatrix}.
A. -120
B. 120
C. 240
D. -240
Question 6
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 7
A circle has a radius of 4 cm. Find the area of the circle.
A. 16π
B. 20π
C. 24π
D. 32π
Question 8
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 9
Find the vector equation of the line pas\sing through the points (1, 2) and (3, 4).
A. \vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t\begin{bmatrix} 1 \\ 1 \end{bmatrix}
B. \vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t\begin{bmatrix} 2 \\ 3 \end{bmatrix}
C. \vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t\begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t\begin{bmatrix} 4 \\ 5 \end{bmatrix}
Question 10
Solve for x in the equation 2^x + 3^x = 5^x.
A. 1
B. 2
C. 3
D. 4
Question 11
Solve the equation \sin^2 x + \cos^2 x = 1 for x in the interval [0, 2\pi].
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{3\pi}{4}
D. \frac{5\pi}{4}
Question 12
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 104,843
B. 104,843
C. 104,843
D. 104,843
Question 13
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 14
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 15
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 17
B. 19
C. 21
D. 23

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