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POST UTME ACHIEVERS UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Solve for x in the equation $\log_{10} x^2 \$$= 4 )$

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 2 View Details

Find the value of y in the equation (y = $\frac{1}{2}$ $x^2 + 3x - 4$\) when \$(y = frac{1}{2} x^2 + 3x - 4\(x = 2$

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 3 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, -3$ ∪ (1, ∞)

C. $-∞, 1$ ∪ (3, ∞)

D. $-∞, -3$ ∪ (1, ∞)

Correct Answer: A

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Question 4 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5)

Correct A. $y = x + 1$

B. $y = x - 1$

C. $y = -x + 1$

D. $y = x + 2$

Correct Answer: A

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Question 5 View Details

A survey of 100 students found that 70% preferred pizza, 20% preferred burgers, and 10% preferred sandwiches. What is the probability that a randomly selected student prefers pizza or burgers?

Correct A. 0.9

B. 0.8

C. 0.7

D. 0.6

Correct Answer: A

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Question 6 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} ].

Correct A. 25

B. 30

C. 35

D. 40

Correct Answer: A

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Question 7 View Details

A polynomial has roots at x = -2, $x = 3$, and $x = 4$. What is the polynomial in factored form?

Correct A. $x + 2$, x - 3\)$x - 4$

B. $x + 2$, x - 3\)$x - 4$

C. $x + 2$, x - 3\)$x - 4$

D. $x + 2$, x - 3\)$x - 4$

Correct Answer: A

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Question 8 View Details

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.

Correct A. 16π

B. 32π

C. 64π

D. 128π

Correct Answer: A

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Question 9 View Details

A set A has 5 elements, and a set B has 3 elements. What is the number of elements in the union of sets A and B?

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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Question 10 View Details

A sequence is defined by the formula $an = 2n + 1$. What is the sum of the first 5 terms of the sequence?

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 11 View Details

Solve the inequality ($\frac{x}{x-2}\(> 1$\) for \$(frac{x}{x-2} > 1\(x > 2$\).

Correct A. $2 < x$$< 4$

B. $x > 4$

C. $x > 2$

D. $x < 2$

Correct Answer: A

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Question 12 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi $cm^3$

Correct B. 48\pi $cm^3$

C. 72\pi $cm^3$

D. 96\pi $cm^3$

Correct Answer: B

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Question 13 View Details

Find the area under the curve $y = x^2 + 2x - 3$ from $x = 1$ to $x = 4$.

A. 20

B. 30

Correct C. 40

D. 50

Correct Answer: C

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Question 14 View Details

Solve the trigonometric equation $2 \sin^2 x + 3 $1x - 1 = 0$ for ( 0 leq x leq 2 pi ).

Correct A. $\frac{\pi}{6}$\), $\frac{5\pi}{6}$\)

B. $\frac{\pi}{4}$\), $\frac{3\pi}{4}$\)

C. $\frac{\pi}{3}$\), $\frac{2\pi}{3}$\)

D. $\frac{\pi}{2}$\), \pi

Correct Answer: A

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Question 15 View Details

A right-angled triangle has a hypotenuse of length 10 cm and one of its legs is 6 cm. Find the length of the other leg.

Correct A. 8 cm

B. 6 cm

C. 4 cm

D. 2 cm

Correct Answer: A

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Question 16 View Details

Find the volume of the solid formed by revolving the region bounded by the parabola (y = $x^2$\) and the line $y = 4\\((y = x^2) and the line$ about the x-axis.

Correct A. $\frac{64}{5} \pi$

B. $\frac{32}{3} \pi$

C. $\frac{16}{3} \pi$

D. $\frac{8}{3} \pi$

Correct Answer: A

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Question 17 View Details

Solve the inequality $|2x - 3| \geq 5$.

Correct A. $x \leq -1$ or ( x geq 4 )

B. $x \leq -4$ or ( x geq 1 )

C. ( x leq 1 ) or ( x geq 4 )

D. $x \leq -4$ or ( x geq 1 )

Correct Answer: A

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Question 18 View Details

Find the area of the triangle with vertices (A(1, 2)), (B(4, 6)), and (C(2, 1)).

A. $5 \sqrt{3}$

B. $10 \sqrt{3}$

Correct C. $15 \sqrt{3}$

D. $20 \sqrt{3}$

Correct Answer: C

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Question 19 View Details

Solve the system of linear equations $2x + 3y = 7$ and $x - 2y = -3$.

Correct A. $x = 1, y = 2$

B. $x = 2, y = 1$

C. $x = 3, y = 4$

D. $x = 4, y = 3$

Correct Answer: A

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Question 20 View Details

Find the determinant of the matrix $egin{bmatrix} 2 & 1 & 4 \ 3 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}$.

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 21 View Details

A polynomial $p(x)$ has degree 4 and has roots $x = 1, x = -2, x = 3,$ and (x = -4\). Find the value of $p(0)\\((x = -4). Find the value of$.

Correct A. 0

B. 24

C. -24

D. 48

Correct Answer: A

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Question 22 View Details

A solid right circular cone has a height of 12 cm and a base radius of 6 cm. Find the volume of the cone.

Correct A. 288\pi

B. 288\$\pi/3$

C. 288\$\pi/2$

D. 288\$\pi/4$

Correct Answer: A

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Question 23 View Details

Solve for $x$: $\log_{10} x^2$$= 4$\).

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 24 View Details

A matrix (A\) is given by $\\((A) is given by \begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}$. Find the determinant of $A$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 25 View Details

A histogram is given below. Find the mean of the data.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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