UTME 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
If # 225.00 yields # 27.00 in x years simple interest at the rate of 4% per annum, find x.
A. 3
B. 4
C. 12
D. 17
Question 2
If \( \sin \theta=\cos \theta \), find \( \theta \) between \( 0^{\circ} \) and \( 360^{\circ} \).
A. 45,\( 225^{0} \)
B. \( 135^{0} , 315^{0} \)
C. \( 45^{0} \),\( 315^{0} \)
D. \( 135^{0} \),\( 225^{0} \)
Question 3
Evaluate \( \frac{3 5 2 4}{0.05} \) correct to 3 significant figures.
A. 705
B. 70,000
C. 70,480
D. 70,500
Question 4
The probability of a student passing any examination is \( \frac{2}{3} \). If the student takes three examinations, what is the probability that he will not pass any of them?
A. \frac{2}{3}
B. \frac{4}{9}
C. \frac{8}{27}
D. \frac{1}{27}
Question 5
Ice forms on a refrigerator ice-box at the rate of (4 - 0.6t)g per minute after minutes. If initially there are of ice in the box, find the mass of ice formed in 5 minutes.
A. 19.5
B. 170
C. 14.5
D. 12.5
Question 6
The pie chart above represents 400 fruits on display in a grocery store. How many apples are in the store?
A. 45
B. 50
C. 60
D. 75
Question 7
Obtain a maximum value of the function \( f(x) = x^3 - 12x + 11 \).
A. -5
B. -2
C. 2
D. 27
Question 8
If the hypotenuse of a right-angled isosceles triangles is 2 cm, what is the area of the triangle?
A. 1 / 2 cm²
B. 1 cm²
C. \( \sqrt{2} \) cm²
D. 2 \( \sqrt{2} \) cm²
Question 9
Solve the pair of equations for \( x \) and \( y \) respectively \( 2 x^{-1}-3 y^{-1}=4 \) and \( 4 x^{-1}+y^{-1}=1 \).
A. 1,2
B. 1,-2
C. 2,1
D. 2,-1
Question 10
Solve the equation: \( y-11\sqrt{y}+24=0 \).
A. 8,3
B. 64,9
C. 6,4
D. 9,-8
Question 11
If 5,8,6 and k occur with frequencies 3,2,4 and 1 respectively and have a mean of 5.7. Find the value of k.
A. 4
B. 3
C. 2
D. 1
Question 12
The minimum value of \( y \) in the equation \( y=x^{2}-6 x+8 \) is
A. 8
B. 3
C. 0
D. -1
Question 13
In the figure, \( \mathrm{YXZ}=30^{\circ} \), \( X Y Z=105^{\circ} \) and \( X Y=8 \mathrm{~cm} \). Calculate YZ.
A. 16 \( \sqrt{2} \) cm
B. 8\( \sqrt{2} \) cm
C. 4\( \sqrt{2} \) cm
D. 22 cm
Question 14
\[ \begin{array}{|l|c|c|c|c|c|c|} \hline Marks & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\ \hline \text{No of Students} & 3 & 4 & 1 & 0 & 4 & 5 & 2 & 1 \\ \hline \end{array} \] The table above shows the distribution of marks of students in a test. Find the probability of passing the test if the pass mark is 5.
A. \( \frac{3}{5} \)
B. \( \frac{2}{5} \)
C. \( \frac{7}{20} \)
D. \( \frac{1}{5} \)
Question 15
Find the probability of selecting a figure which is a parallelogram from a square, a rectangle, a rhombus, a kite and a trapezium.
A. \frac{3}{5}
B. \frac{2}{5}
C. \frac{4}{5}
D. \frac{1}{5}

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