UTME CBT Practice Test – Mathematics (Diagnostic Test) – Set 8

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1. You are to attempt 40 Objectives Questions ONLY for Â 30 minutes.
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Algebra

For what range of values of x isÂ  $\frac{1}{2}$ x + $\frac{1}{4}$Â  >Â  $\frac{1}{3}$ x + $\frac{1}{2}$

A. x > $-\frac{3}{2}$ Â Â  B. x > $\frac{3}{2}$ Â Â  C. x < $\frac{3}{2}$ Â Â  D. x < $-\frac{3}{2}$

Algebra

IfÂ  $\begin{vmatrix}&space;x&space;&&space;3\\&space;2&space;&&space;7&space;\end{vmatrix}$, find the value of x.

A. 4Â Â Â  B. 5 Â Â  C. 2Â Â Â  D. 3

Algebra

If x * y = x + y2, find the value of (2 * 3) * 5

A. 25Â Â Â  B. 11Â Â Â  C. 55Â Â Â  D. 36

The table above shows the marks obtained in a given test. How many students took the test?

A. 16Â Â Â  B. 20Â Â Â  C. 13Â Â Â  D. 15

From the table above, if the pass mark is 5, how many students failed the test?

A. 6Â Â Â  B. 2Â Â Â  C. 9Â Â Â  D. 7

Algebra

Make Q the subject of the formula if $P&space;=&space;\frac{M}{5}\left&space;(&space;X&space;+&space;Q&space;\right&space;)+1$

A. $\frac{5P+MX-5}{M}$ Â Â Â  B. $\frac{5P-MX-5}{M}$ Â Â Â  C. $\frac{5P-MX+5}{M}$ Â Â Â  D. $\frac{5P+MX+5}{M}$

Calculus

If y = (2x + 1)3,Â  findÂ  $\frac{dy}{dx}$ .

A. 6(2x + 1)Â Â Â Â  B. 3(2x + 1)Â Â Â  C. 6(2x + 1)2 Â Â  D. 3(2x + 1)2

Number and Numeration

Which of the Venn diagrams below represents P' âˆ© Q âˆ© R'?

Number and Numeration

Express the product of 0.21 and 0.34 in standard form

A. 7.14 x 10-2 Â Â  B. 7.14 x 10-1 Â Â  C. 7.14 x 10-4 Â Â  D. 7.14 x 10-3

Calculus

At what value of x does the function y = -3 â€“ 2x + x2 attain minimum value?

A. -1Â Â Â  B. -4Â Â Â  C. 4Â Â Â  D. 1

Geometry/Trigonometry

Find the distance between the points $\left&space;(&space;\frac{1}{2},\frac{1}{2}&space;\right&space;)$ and $\left&space;(&space;-\frac{1}{2},-\frac{1}{2}&space;\right&space;)$

A. $\sqrt{2}$ Â Â  B. 0Â Â Â  C. 1Â Â Â  D. $\sqrt{3}$

Statistics

A bag contains 5 black, 4 white and x red marbles. If the probability of picking a red marble is $\frac{2}{5}$ find the value of x.

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

Calculus

If y = x cos x, findÂ  $\frac{dy}{dx}$Â

A. sin x - x cos xÂ Â Â Â  B. sin x + x cos xÂ Â Â Â  C. cos x + x sin xÂ Â Â Â  D. cos x - x sin x

Statistics

In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?

A. 100Â Â Â  B. 200Â Â Â  C. 30Â Â Â  D. 50

Geometry/Trigonometry

From the cyclic quadrilateral TUVW above, find the value of x.

A. 24Â°Â Â Â  B. 26Â°Â Â Â  C. 20Â°Â Â Â  D. 23Â°

Find the standard deviation of 2, 3, 5 and 6.

A. $\sqrt{\frac{5}{2}}$ Â Â Â  B. $\sqrt{10}$ Â Â Â  C. $\sqrt{6}$ Â Â Â  D. $\sqrt{\frac{2}{5}}$

Statistics

If three unbiased coins are tossed, find the probability that they are all heads.

A. $\frac{1}{8}$ Â Â  B. $\frac{1}{3}$ Â Â  C. $\frac{1}{6}$ Â Â  D. $\frac{1}{9}$

Rationalize $\frac{2\sqrt{3}+\sqrt{5}}{\sqrt{5}-\sqrt{3}}$

A. $\frac{3\sqrt{15}+11}{2}$ Â Â Â  B. $\frac{3\sqrt{15}-11}{2}$ Â Â Â  C. $3\sqrt{15}-11$ Â Â Â  D. $3\sqrt{15}+11$

Calculus

Find the value of x for which the function f(x) = 2x3 - x2 - 4x + 4 has a minimum value.

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

Algebra

Factorize completelyÂ Â  $\frac{x^{3}+3x^{2}-10x}{2x^{2}-8}$

A. $\frac{x^{2}+5}{2x+4}$ Â Â Â Â  B. $\frac{x(x+5)}{2(x+2)}$ Â Â Â Â  C. $\frac{x(x-5)}{2(x+2)}$ Â Â Â Â  D. $\frac{x(x-5)}{2(x-2)}$

Geometry/Trigonometry

What is the locus of points equidistant from points P(1, 3) and Q(3, 5)?

A. y = -x â€“ 6Â Â Â  B. y = x + 6Â Â Â Â  C. y = x â€“ 6Â Â Â Â  D. y = -x + 6

The table above shows the marks obtained in a given test. Find the mean mark.

A. 3.1Â Â Â  B. 3.0 Â Â  C. 3.3Â Â Â  D. 3.2

Calculus

Find $\int$(sin x + 2) dx.

A. -cosx + 2x + kÂ Â Â
B. cosx + 2x + k
C. -cosx + x2 + k
D. cosx + x2 + k

Algebra

If x is inversely proportional to y and x = 2Â½ when y =2, find x if y = 4.

A. $2\frac{1}{4}$ Â Â Â  B. 5Â Â Â Â  C. 4Â Â Â Â  D. $1\frac{1}{4}$

Number and Numeration

Simplify $\left&space;(&space;\frac{3}{4}\:&space;of&space;\frac{4}{9}\div&space;9\frac{1}{2}&space;\right&space;)\div&space;1\frac{5}{19}$

A. $\frac{1}{25}$ Â Â Â  B. $\frac{1}{4}$ Â Â Â  C. $\frac{1}{5}$ Â Â Â  D. $\frac{1}{36}$

If the mean of five consecutive integers is 30, find the largest of the numbers

A. 28Â Â Â Â  B. 30Â Â Â Â  C. 32Â Â Â Â  D. 34

Number and Numeration

Find r, if 6r78 = 5119.

A. 5Â Â Â  B. 2Â Â Â  C. 3Â Â Â  D. 6

Geometry/Trigonometry

If cot Î¸ = $\frac{8}{15}$, where Î¸ is acute, find sin Î¸.

A. $\frac{13}{15}$ Â Â  B. $\frac{15}{17}$ Â Â  C. $\frac{8}{17}$ Â Â  D. $\frac{16}{17}$

Geometry/Trigonometry

Find the equation of a line parallel to y = -4x + 2 passing through (2, 3).

A. y + 4x + 11 = 0Â Â Â
B. y â€“ 4x â€“ 11 = 0 Â Â
C. y + 4x â€“ 11 = 0Â Â Â
D. y â€“ 4x + 11 = 0

Geometry/Trigonometry

From the diagram above, find x.

A. 65Â°Â Â Â  B. 50Â°Â Â Â  C. 55Â°Â Â Â  D. 75Â°

Geometry/Trigonometry

The interior angles of a quadrilateral are (x + 15)Â°, (2x â€“ 45)Â°, (x â€“ 30)Â° and (x + 10)Â°. Find the value of the least interior angle.

A. 82Â°Â Â Â  B. 52Â° Â Â  C. 112Â°Â Â Â  D. 102Â°

Algebra

Find the sum of infinity of the following series 0.5 + 0.05 + 0.005 + 0.0005 + â€¦

A. $\frac{5}{9}$ Â Â  B. $\frac{5}{7}$ Â Â  C. $\frac{5}{8}$ Â Â  D. $\frac{5}{11}$

Calculus If y = x sinx, find $\frac{dy}{dx}$.

A. sinx - xcosxÂ Â Â Â  B. sinx + xcosxÂ Â Â  C. sinx â€“ cosxÂ Â Â  D. sinx + cosx

Number and Numeration

If p : q = $\frac{2}{3}$ : $\frac{5}{6}$ and q : r = $\frac{3}{4}$ : $\frac{1}{2}$ , find p : q : r.

A. 12 : 15 : 10Â Â Â Â  B. 12 : 15 : 16Â Â Â Â  C. 10 : 15 : 24Â Â Â Â  D. 9 : 10 : 15

Algebra

If 9x2 + 6xy + 4y2 is a factor of 27x3 â€“ 8y3, find the other factor.

A. 2y + 3xÂ Â Â Â  B. 2y â€“ 3xÂ Â Â Â  C. 3x + 2yÂ Â Â Â  D. 3x â€“ 2y

Geometry/Trigonometry

An arc subtends an angle 50Â° at the centre of circle of radius 6 cm. Calculate the area of the sector formed. [Ï€ = $\frac{22}{7}$]

A. $\frac{90}{7}$ cm2 Â Â  B. $\frac{110}{7}$ cm2 Â Â  C. $\frac{100}{7}$ cm2 Â Â  D. $\frac{80}{7}$ cm2

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