UTME 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A baking recipe calls for 2.5 kg of sugar and 4.5 kg of flour. With this recipe some cakes were baked using 24.5 kg of a mixture of sugar and flour. How much sugar were used?
A. 12.25 kg
B. 6.75 kg
C. 8.75 kg
D. 15.75 kg
Question 2
If x + 2 and x - 1 are factors of the expression \( lx^3 \) + \( 2kx^2 \) + 24, find the value of l and k.
A. l=-6, k=-2
B. l=-2, k=1
C. l=-2, k=-1
D. l=0, k=1
Question 3
If f(x) = \(\frac{1}{x-1} + \frac{x-1}{x^{2}-1}\), find f(1-x).
A. \(\frac{1}{x} + \frac{1}{x-2}\)
B. x + \(\frac{1}{2x-1}\)
C. \(\frac{-1}{x} + \frac{1}{x-2}\)
D. \(\frac{-1}{x} + \frac{1}{x-1}\)
Question 4
Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them giving your answer to three significant figures.
A. 4.46
B. 4.48
C. 4.47
D. 4.49
Question 5
Convert \(241_{\text{5}} \) to base 8.
A. \( 71_{\text{8}} \)
B. \( 107_{\text{8}} \)
C. \( 176_{\text{8}} \)
D. \( 241_{\text{8}} \)
Question 6
In the figure above, KL//NM, LN bisects < KNM. If angles KLN is \( 54^\circ \) and angle MKN is \( 35^\circ \), calculate the size of angle KMN
A. \( 91^\circ \)
B. \( 89^\circ \)
C. \( 37^\circ \)
D. \( 19^\circ \)
Question 7
Make y the subject of the formula: Z = x^2 + \(\frac{1}{y^{3}}\)?
A. y = \(\frac{1}{(z-y^{2})^{3}}\)
B. y = \(\frac{1}{(z+x^{2})^{3}}\)
C. y = \(\frac{1}{(Z-x^{2})^{1/3}}\)
D. y = \(\frac{1}{\sqrt[3]{Z}-\sqrt{3x^{2}}}\)
Question 8
Find the gradient of a line which is perpendicular to the line with equation \( 3x + 2y + 1 = 1 \)
A. \( \frac{3}{2} \)
B. \( -\frac{2}{3} \)
C. \( -\frac{2}{5} \)
D. \( -\frac{3}{2} \)
Question 9
The first term of an Arithmetic Progression is 3 and the fifth term is q. Find the number of terms in the progression if the sum of the terms is 81?
A. 12
B. 27
C. 9
D. 7
Question 10
\( \begin{array}{r@{\quad}cccc} & 4 & 2 & 4 & 3 \\ - & 1 & 3 & x & 4 \\ \hline & y & 3 & 4 & 4 \\ \hline \end{array} \) Find x and y respectively in the subtraction above.
A. 2,4
B. 3,2
C. 4,2
D. 4,3
Question 11
In the diagram above \( PQ \parallel RS \). The size of the angle marked x is
A. \( 100^{\circ} \)
B. \( 80^{\circ} \)
C. \( 50^{\circ} \)
D. \( 30^{\circ} \)
Question 12
A train moves from P to Q at an average speed of 40 km/hr and immediately returns from Q to P at 45 km/hr. Find the average speed for the entire journey.
A. 55 km/hr
B. 50 km/hr
C. 67.50 km/hr
D. 75 km/hr
Question 13
Simplify without using tables. \(\frac{2 \sqrt{14} \times 3 \sqrt{21}}{7 \sqrt{24} \times 2 \sqrt{98}}\)
A. \(\frac{3 \sqrt{14}}{4}\)
B. \(\frac{3 \sqrt{2}}{4}\)
C. \(\frac{3 \sqrt{14}}{28}\)
D. \(\frac{3 \sqrt{2}}{28}\)
Question 14
A cubic function f(x) is specified by the graph shown above. The values of the independent variable for which the function vanishes are:
A. \( -1,0,1 \)
B. \( -1 \leq x \leq 1 \)
C. \( x < -1 \)
D. \( x > 1 \)
Question 15
Solve the quadratic inequality \( x^2 - 5x + 6 \geq 0 \)
A. \( x \geq 2, x \leq 7 \)
B. \( x \leq 3, x \geq 2 \)
C. \( x \leq -2, x \geq -3 \)
D. \( x \leq -3, x \geq 2 \)

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