UTME 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
If x = 1 is the root of the equation \( x^3 \) - \( 2x^2 \) - \( 5x + 6 \), find the other roots.
A. -3 and 2
B. -2 and 2
C. 3 and -2
D. 1 and 3
Question 2
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 3
\( \begin{array}{r@{\quad}cccc} & 4 & 2 & 4 & 3 \\ - & 1 & 3 & x & 4 \\ \hline & y & 3 & 4 & 4 \\ \hline \end{array} \) Find x and y respectively in the subtraction above.
A. 2,4
B. 3,2
C. 4,2
D. 4,3
Question 4
Express the product of 0.00043 and 2000 in standard form.
A. \(8.6 \times 10\)
B. \(8.6 \times 10^{-3}\)
C. \(8.3 \times 10^{-2}\)
D. \(8.6 \times 10^{-1}\)
Question 5
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 6
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 7
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 8
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 9
In the figure above what is the equation of the line that passes the \( y \)-axis at (0,5) and passes the \( x \)-axis at \( (5,0) \) .
A. y=-x-5
B. -y=x+5
C. y=-x+5
D. y=x-5
Question 10
If \( \mathrm{gt}^{2}-4-\mathrm{w}=0 \) make g the subject of the formula.
A. \frac{u-w}{t}
B. \frac{u+w}{t^{2}}
C. \frac{u-w}{t^{2}}
D. \frac{u+w}{t}
Question 11
If the lines \( 3y = 4x - 1 \) and \( qy = x + 3 \) are parallel to each other, the value of \( q \) is
A. \( -\frac{4}{3} \)
B. \( -\frac{5}{4} \)
C. \( \frac{4}{5} \)
D. \( \frac{3}{4} \)
Question 12
Find the value of x for which the function f(x) = \( 2x^{2} - x^{2} - 4x + 4 \) has a maximum value.
A. \(\frac{2}{3}\)
B. 1
C. \(-\frac{2}{3}\)
D. -1
Question 13
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 14
Calculate the simple interest on N 1,500 for 8 years at 5% per annum.
A. N5,000
B. N600
C. N500
D. N150
Question 15
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. \( 19^\circ \)

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