POST UTME CRAWFORD UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area of the triangle formed by the points ( A(2,3) ), ( B(4,5) ), and ( C(6,7) ).
A. 10
B. 20
C. 30
D. 40
Question 2
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 = 4 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
Question 3
A die is rolled. What is the probability that the number obtained is a multiple of 3?
A. 1/6
B. 1/3
C. 2/3
D. 5/6
Question 4
Find the equation of the circle with center (1, 2) and radius 3.
A. \( x - 1 \)^2 + \( y - 2 \)^2 = 9
B. \( x + 1 \)^2 + \( y - 2 \)^2 = 9
C. \( x - 1 \)^2 + \( y + 2 \)^2 = 9
D. \( x + 1 \)^2 + \( y + 2 \)^2 = 9
Question 5
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 6
A circle has a radius of 4 cm. Find the area of the circle.
A. \( 16\pi \text{ cm}^2 \)
B. \( 32\pi \text{ cm}^2 \)
C. \( 64\pi \text{ cm}^2 \)
D. \( 128\pi \text{ cm}^2 \)
Question 7
A circle has a radius of 4 cm and passes through the points (0, 0) and (3, 4). Find the equation of the circle in the form \( x - h \)^2 + \( y - k \)^2 = r^2.
A. \( x - 1 \)^2 + \( y - 2 \)^2 = 16
B. \( x + 1 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 1 \)^2 + \( y + 2 \)^2 = 16
D. \( x + 1 \)^2 + \( y + 2 \)^2 = 16
Question 8
A particle moves in a plane with its position given by the equation \( x = 2 \cos t \) and \( y = 3 \sin t \). Find the equation of the \tangent line at the point where \( t = \frac{\pi}{2} \).
A. y = -3x + 6
B. y = 3x - 6
C. y = 3x + 6
D. y = -3x - 6
Question 9
Find the area under the curve y = 2x^2 - 3x + 1 from x = 0 to x = 2.
A. \frac{13}{3}
B. \frac{23}{3}
C. \frac{33}{3}
D. \frac{43}{3}
Question 10
Solve the inequality \( 2x - 5 > 3 \).
A. \( x > 4 \)
B. \( x < 4 \)
C. \( x > 2 \)
D. \( x < 2 \)
Question 11
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 12
A histogram shows the distribution of exam scores for a class of 100 students. The histogram has 5 bars, each representing a different score range. If the tallest bar represents 30 students, what is the probability that a randomly selected student scored between 70 and 80?
A. 0.3
B. 0.4
C. 0.5
D. 0.6
Question 13
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x + 2
D. y = x - 2
Question 14
Find the sum of the first 10 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ldots \).
A. 2x + 3x^2 + 4x^3 + ldots + 20x^9
B. 2x + 3x^2 + 4x^3 + ldots + 21x^9
C. 2x + 3x^2 + 4x^3 + ldots + 22x^9
D. 2x + 3x^2 + 4x^3 + ldots + 23x^9
Question 15
Find the vector equation of the line pas\sing through the points (2, 3) and (4, 5).
A. \\vec{r} = \\vec{a} + t\\vec{b}
B. \\vec{r} = \\vec{a} - t\\vec{b}
C. \\vec{r} = \\vec{a} + t\\vec{c}
D. \\vec{r} = \\vec{a} - t\\vec{c}

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