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POST UTME LASU 2024 Mathematics | Objective

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Question 1 View Details

Find the area under the curve $y = \frac{1}{2}x^2$ from $x = 0$ to $x = 4$.

Correct A. $\frac{16}{3}$

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

C. $\frac{64}{3}$

D. $\frac{128}{3}$

Correct Answer: A

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Question 2 View Details

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

Correct A. $y = \frac{1}{2}x + 1$

B. $y = \frac{1}{2}x - 1$

C. $y = \frac{1}{2}x + 2$

D. $y = \frac{1}{2}x - 2$

Correct Answer: A

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Question 3 View Details

Solve the system of equations: $egin{cases} x + y = 4 \ xy = 5 \end{cases}$.

Correct A. $x = 1, y = 3$

B. $x = 3, y = 1$

C. $x = 2, y = 2$

D. $x = 4, y = 0$

Correct Answer: A

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Question 4 View Details

Find the equation of the circle with center ( (2,3) ) and radius ( 4 ).

Correct 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 + $y - 3$^$2 = 25$ )

Correct Answer: A

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Question 5 View Details

Find the mean and standard deviation of the data set: ( { 2, 4, 6, 8, 10 } ).

Correct A. Mean: 6, Standard Deviation: 2

B. Mean: 6, Standard Deviation: 4

C. Mean: 6, Standard Deviation: 6

D. Mean: 6, Standard Deviation: 8

Correct Answer: A

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Question 6 View Details

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

Correct A. $10^4$

B. $10^2$

C. 10

D. $10^8$

Correct Answer: A

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Question 7 View Details

A particle moves in a straight line with its position given by ( s(t) = $(2t^3 - 5t^2 + 3t + 1$\) ). Find the velocity at time $t = 2\\((2t^3 - 5t^2 + 3t + 1) ). Find the velocity at time$ seconds.

Correct A. $4t^2 - 10t + 3$

B. $6t^2 - 10t + 2$

C. $2t^2 - 5t + 1$

D. $t^2 - 5t + 2$

Correct Answer: A

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Question 8 View Details

A quadratic equation has roots at $x = 2$ and x = -3. Write the equation in factored form.

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

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

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

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

Correct Answer: A

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Question 9 View Details

A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that both balls are blue?

Correct A. $1/8$

B. $1/7$

C. $1/6$

D. $1/5$

Correct Answer: A

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Question 10 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 4$.

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 11 View Details

Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value between 0.5 and 1.

A. $\frac{1}{2}$\)

Correct B. $\frac{3}{4}$\)

C. $\frac{7}{8}$\)

D. $\frac{5}{6}$\)

Correct Answer: B

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Question 12 View Details

Solve the inequality $2x^2 + 5x - 3 \geq 0$.

Correct A. \left$- \infty, - \frac{3}{2} \right$ \cup \left$\frac{3}{2}, \infty \right$

B. \left$- \infty, - \frac{3}{2} \right$ \cap \left$\frac{3}{2}, \infty \right$

C. \left$- \infty, \frac{3}{2} \right$ \cup \left$\frac{3}{2}, \infty \right$

D. \left$- \infty, \frac{3}{2} \right$ \cap \left$\frac{3}{2}, \infty \right$

Correct Answer: A

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Question 13 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 2x$ about the x-axis.

A. $\frac{32 \pi}{3}$\)

B. $\frac{64 \pi}{3}$\)

Correct C. $\frac{128 \pi}{3}$\)

D. $\frac{256 \pi}{3}$\)

Correct Answer: C

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Question 14 View Details

A vector ( mathbf{a} ) has magnitude 5 and direction $30 \degree$ counterclockwise from the positive x-axis. Find the vector ( mathbf{a} ).

Correct A. \begin{pmatrix} 4.33 \ 2.50 \end{pmatrix}

B. \begin{pmatrix} 2.50 \ 4.33 \end{pmatrix}

C. \begin{pmatrix} 3.54 \ 3.54 \end{pmatrix}

D. \begin{pmatrix} 5.00 \ 0.00 \end{pmatrix}

Correct Answer: A

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Question 15 View Details

Find the sum of the first 5 terms of the geometric series $2x^2 + 3x + 1$.

Correct A. $2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1$

B. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

C. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

D. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

Correct Answer: A

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Question 16 View Details

Find the value of x in the equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) if $$1x \$ = $\frac{3}{4}$\) ).

Correct A. $\frac{\pi}{4}$

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

C. $\frac{5\pi}{4}$

D. $\frac{7\pi}{4}$

Correct Answer: A

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Question 17 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$ using the quadratic formula.

Correct A. $x < -\frac{5}{2}$ or $x > \frac{3}{2}$

B. $x < -\frac{3}{2}$ or $x > \frac{5}{2}$

C. $x < -\frac{5}{2}$ or $x < \frac{3}{2}$

D. $x > -\frac{5}{2}$ or $x < \frac{3}{2}$

Correct Answer: A

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Question 18 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^2 + 1}$\)\) ) using the chain rule.

Correct A. ( f'$(x) =$$\frac{-2x}{x^2 + 1$ ^2}\)\) )

B. ( f'$(x) =$$\frac{2x}{x^2 + 1$ ^2}\)\) )

C. ( f'$(x) =$$\frac{2}{x^2 + 1$ ^2}\)\) )

D. ( f'$(x) =$$\frac{-2}{x^2 + 1$ ^2}\)\) )

Correct Answer: A

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Question 19 View Details

Determine the sum of the infinite geometric series $sum_{n = 1}^{\infty} \frac{1}{2^n}$.

A. $\frac{1}{2}$

Correct B. $\frac{2}{3}$

C. $\frac{3}{4}$

D. $\frac{4}{5}$

Correct Answer: B

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Question 20 View Details

Solve the system of equations $egin{cases} x + y = 2 \ x - y = 1 \end{cases}$ using substitution.

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

B. $x = 1, y = 3$

C. $x = 3, y = 1$

D. $x = 3, y = 3$

Correct Answer: A

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Question 21 View Details

Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.

Correct A. $\frac{\pi}{2}$

B. $\frac{\pi}{4}$

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

D. $\frac{\pi}{6}$

Correct Answer: A

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Question 22 View Details

Solve for ( x ) in the equation $2^x + 3^x = 5^x$.

A. $x = 1$

Correct B. $x = 2$

C. $x = 3$

D. $x = 4$

Correct Answer: B

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Question 23 View Details

Find the value of $\log_{10} 1000 \$ ).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 24 View Details

Solve the inequality $x^2 - 4x + 3 > 0$.

Correct A. $x < -1$ or $x > 3$

B. $x < 1$ or $x > 3$

C. $x < -1$ or $x < 3$

D. $x > 1$ or $x > 3$

Correct Answer: A

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Question 25 View Details

Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ldots ).

Correct A. ( 62 )

B. ( 64 )

C. ( 66 )

D. ( 68 )

Correct Answer: A

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