UTME CBT Practice Test – Mathematics (Diagnostic Test) – Set 3

Hello and Welcome to UTME CBT Practice Test - Mathematics (Diagnostic Test) - Set 3

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Calculus

Find the maximum value of y in the equation y = 1 - 2x - 3x2

A. $\frac{5}{4}$    B. $\frac{5}{3}$    C. $\frac{3}{4}$    D. $\frac{4}{3}$

Geometry/Trigonometry

In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72°, find x.

A. 36°    B. 18°    C. 72°    D. 24°

Calculus

A circle with a radius 5 cm has its radius increasing at the rate at 0.2cms-1. What will be the corresponding increase in the area?

A. 2 π   B. 5 π   C. π   D. 4 π

Number and Numeration

A trader bought goats for N 4000 each. He sold them for N 1801000 at a loss of 25%. How many goats did he buy?

A. 60  B. 50   C. 45   D. 36

Number and Numeration

The Venn diagram above shows the number of students offering Music and History in a class of 80 students. If a student is picked at random from the class, what is the probability that he offers Music only?

A. 0.38    B. 0.13    C. 0.50    D. 0.25

Statistics

The acres for rice, pineapples, cassava cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What la the angle of the sector for cassava in a pie chart?

A. 108°    B. 180°    C. 36°    D. 60°

Geometry/Trigonometry

The triangle POR above is _______

A. an obtuse-angled triangle    B. a scalene triangle    C. an isosceles triangle    D. an equilateral triangle

Geometry/Trigonometry

If tan θ = $\frac{4}{3}$, calculate sin2θ - cos2θ

A. $\frac{16}{25}$    B. $\frac{24}{25}$    C. $\frac{7}{25}$    D. $\frac{9}{25}$

The range of the data k + 2, k - 3, k + 4, k - 2, k, k + 5, k + 3, k - 1 and k + 6 is ______

A. 10   B. 11    C. 6   D. 8

Number and Numeration

In a school 220 students offer Biology or Mathematics or both. 125 offer Biology and 110 Mathematics. How many offer Biology but, not Mathematics?

A. 95    B. 80    C. 125    D. 110

Algebra

The binary operation * is defined on the set of integers p and q by p*q = pq + p + q. Find 2*(3*4).

A. 59   B. 19    C. 67    D. 38

Calculus

The inverse of the function f(x) = 3x + 4 is _____

A. $\frac{1}{3}$ (x - 4)    B. $\frac{1}{5}$ (x — 5)    C. $\frac{1}{4}$ (x + 3)    D. $\frac{1}{3}$ (x + 4)

Geometry/Trigonometry

In the diagram above, a cylinder is surmounted by a hemispherical bowl. Calculate the volume of the solid.

A. 180 π cm3    B. 162 π cm3    C. 216 π cm3    D. 198 π cm3

Geometry/Trigonometry

Find the value of α if the line 2y - αx + 4 = 0 is perpendicular to the line y + $\frac{1}{4}$  -  7 = 0

A. -4    B. 4    C. 8     D. -8

If a function is defined by f(x + 1) = 3x2 - x + 4, find f(0)

A. 4 B. 6 C. 8 D. 10

Algebra

Solve for x in the equation x3 - 5x2 - x + 5 = 0

A. 1, -l or 5    B. 1, 1 or -5    C. -1, 1 or- 5    D. 1, 1 or 5

Calculus

If y = $x^{2}-\frac{1}{x}$  find  $\frac{dy}{dx}$

A. $2x-\frac{1}{x^{2}}$     B. 2x + x2     C. 2x - x2     D. $2x+\frac{1}{x^{2}}$

Simplify $\left&space;(&space;\sqrt{0.7}+\sqrt{70}&space;\right&space;)^{2}$

A. 84.7   B. 70.7    C. 217.7    D. 168.7

Calculus

lf  $\frac{dy}{dx}$  = 2x - 3 and y = 3 when x = 0, find y in terms of x.

A. 2x2 - 3x      B. x2 - 3x      C. x2 - 3x - 3       D. x2 - 3x + 3

Number and Numeration

Simplify 52.4 - 5.7 - 3.45 - 1.75

A. 41.4    B. 41.5   C. 42.1   D. 42.2

For the set of numbers 2, 3, 5, 6, 7, 7, 8

A. the median is greater than the mode ,
B. the mean is less than the median.
C. the mean is greater than the median
D. the median is equal to the mean

Geometry/Trigonometry

In the diagram above, XZ is the diameter of the circle XYZW, with centre O and radius $\frac{15}{2}$ cm. If XY = 12 cm, find the area of the triangle XYZ.

A. 54 cm2    B. 45cm2    C. 27cm2     D. 75cm2

Algebra

If x varies directly as $\sqrt{n}$ and x = 9 when n = 9, find x when n = $\frac{17}{9}$

A. 4    B. 27    C. $\sqrt{3}$    D. $\sqrt{17}$

Statistics

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. $\frac{1}{27}$

Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7 and 8

A. 2 $\frac{1}{6}$    B. 2 $\frac{1}{2}$    C. 1 $\frac{1}{6}$    D. 2 $\frac{1}{3}$

Algebra

Make r the subject of the formula $\frac{x}{r+a}&space;=\frac{a}{r}$

A. $\frac{a^{2}}{x-a}$    B. $\frac{a^{2}}{x+a}$    C. $\frac{a}{x-a}$    D. $\frac{a}{x+a}$

Calculus

The slope of the tangent to the curve y = 3x2 - 2x + 5 at the point (1, 6) is ______

A. 4     B. 1   C. 6    D. 5

Geometry/Trigonometry

The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?

A. 12     B. 20    C. 40    D. 10

Algebra

If The 9th term of an AP is five times the 5th term, find the relationship between a and d.

A. 2a + d = 0     B. 3a + 5d = 0     C. a + 3d = 0     D. a + 2d = 0

Calculus

Find the derivative of y = sin2(5x) with respect to x.

A. 10 sin 5x cos 5x     B. 5 sin 5x cos 5x     C. 2 sin 5x cos 5x    D. 15 sin 5x cos 5x

Geometry/Trigonometry

A bucket is 12 cm in diameter at the top, 8 cm in diameter at the bottom and 4cm deep. Calculate its volume.

A. $\frac{304}{3}$ π cm3    B. 144 π cm3      C. $\frac{128}{3}$ π cm3    D. 72 π cm3

Algebra

The sum to infinity of the series 1 + $\frac{1}{3}$ + $\frac{1}{9}$ + $\frac{1}{27}$ + ...... is ______

A. $\frac{11}{3}$     B. $\frac{10}{3}$     C. $\frac{5}{2}$     D. $\frac{3}{2}$

Find the mean of the data: 7, -3, 4, -2, 5, 9, 4, 8, -6, 12

A. 3   B. 4   C. 1   D. 2

Algebra

Find the range of values of x for which  <img title="\frac{x+2}{4}-\frac{2x-3}{3}< 4" src="https://latex.codecogs.com/gif.latex?\frac{x+2}{4}-\frac{2x-3}{3}

A. x > -6    B. x > -3     C. x < 8    D. x < 4

Statistics

How many three-digit numbers can be formed from 32564 without any digit being repeated?

A. 120    B. 10    C. 20    D. 60

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