POST UTME AAUA 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. x^2 + y^2 - 6x - 2y + 12 = 0
B. x^2 + y^2 - 4x + 2y - 10 = 0
C. x^2 + y^2 + 2x - 4y + 15 = 0
D. x^2 + y^2 + 4x + 2y - 20 = 0
Question 2
A random sample of 16 students from a population of 50 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. Calculate the s\tandard error of the mean.
A. 2.5 cm
B. 3.5 cm
C. 4.5 cm
D. 5.5 cm
Question 3
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 36 )
Question 4
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{6} \)
Question 5
Solve for x in the equation \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. -1
D. 1
Question 6
A curve is defined by the equation y = x^2 + 2x + 1. Find the area under the curve between x = 0 and x = 2.
A. 6
B. 7
C. 8
D. 9
Question 7
Find the equation of the \tangent to the curve y = x^2 at the point (1, 1).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 8
Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2}{x^3} )
B. ( f'(x) = \frac{2}{x^3} )
C. ( f'(x) = -\frac{1}{x^3} )
D. ( f'(x) = \frac{1}{x^3} )
Question 9
Let \( vec{a} = egin{bmatrix} 1 \ 2 \ 3 \end{bmatrix} \) and \( vec{b} = egin{bmatrix} 4 \ 5 \ 6 \end{bmatrix} \). Find the cross product \( vec{a} \times vec{b} \).
A. \( egin{bmatrix} 3 \ 6 \ 9 \end{bmatrix} \)
B. \( egin{bmatrix} 6 \ 9 \ 12 \end{bmatrix} \)
C. \( egin{bmatrix} 9 \ 12 \ 15 \end{bmatrix} \)
D. \( egin{bmatrix} 12 \ 15 \ 18 \end{bmatrix} \)
Question 10
Solve for ( x ) in the equation \( egin{vmatrix} 1 & 2 \ 3 & 4 \end{vmatrix} = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -4 \)
D. \( x = 4 \)
Question 11
Let \( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find the product ( AB ).
A. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
B. \begin{bmatrix} 23 & 26 \ 47 & 54 \end{bmatrix}
C. \begin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix}
D. \begin{bmatrix} 25 & 28 \ 49 & 56 \end{bmatrix}
Question 12
A histogram is shown below. What is the mean of the data set?
A. 20
B. 22
C. 25
D. 30
Question 13
Let \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find the product ( AB ) if it exists.
A. \( egin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix} \)
B. \( egin{bmatrix} 17 & 20 \ 39 & 46 \end{bmatrix} \)
C. \( egin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix} \)
D. \( egin{bmatrix} 23 & 26 \ 47 & 54 \end{bmatrix} \)
Question 14
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 0
C. x = -1
D. x = 1
Question 15
A vector is represented by the equation \vec{a} = 2\hat{i} + 3\hat{j}. Find the magnitude of the vector.
A. 3.6
B. 4.2
C. 4.5
D. 5.1

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