Hello and Welcome to UTME CBT Practice Test - Mathematics (Diagnostic Test) - Set 8

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Geometry/Trigonometry

If cot θ = , where θ is acute, find sin θ.

A.    B.    C.    D.

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

A. 28     B. 30     C. 32     D. 34

Calculus

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

A. -1    B. -4    C. 4    D. 1

Geometry/Trigonometry

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

A. y + 4x + 11 = 0
B. y – 4x – 11 = 0
C. y + 4x – 11 = 0
D. y – 4x + 11 = 0

Statistics

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

A. 100    B. 200    C. 30    D. 50

Number and Numeration

Find r, if 6r78 = 5119.

A. 5    B. 2    C. 3    D. 6

Algebra

If  , find the value of x.

A. 4    B. 5    C. 2    D. 3

Statistics

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

A.    B.    C.    D.

Algebra

Make Q the subject of the formula if

A.     B.     C.     D.

Geometry/Trigonometry

Find the distance between the points and

A.    B. 0    C. 1    D.

Number and Numeration

Which of the Venn diagrams below represents P' ∩ Q ∩ R'? Number and Numeration

Simplify

A.     B.     C.     D.

Calculus

If y = x cos x, find

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

Geometry/Trigonometry

An arc subtends an angle 50° at the centre of circle of radius 6 cm. Calculate the area of the sector formed. [π = ]

A. cm2    B. cm2    C. cm2    D. cm2

Rationalize

A.     B.     C.     D.

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

A. 24°    B. 26°    C. 20°    D. 23°

Algebra

If x is inversely proportional to y and x = 2½ when y =2, find x if y = 4.

A.     B. 5     C. 4     D.

Number and Numeration

If p : q = : and q : r = : , find p : q : r.

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

Geometry/Trigonometry

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

A. y = -x – 6    B. y = x + 6     C. y = x – 6     D. y = -x + 6

Calculus

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

A.     B. 1     C.     D. -1

Geometry/Trigonometry From the diagram above, find x.

A. 65°    B. 50°    C. 55°    D. 75°

Algebra

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

A. 2y + 3x     B. 2y – 3x     C. 3x + 2y     D. 3x – 2y From the table above, if the pass mark is 5, how many students failed the test?

A. 6    B. 2    C. 9    D. 7

Number and Numeration

Express the product of 0.21 and 0.34 in standard form

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

Calculus

If y = (2x + 1)3,  find  .

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

Statistics

A bag contains 5 black, 4 white and x red marbles. If the probability of picking a red marble is find the value of x.

A.     B. 2     C.     D. 6

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

A.     B.     C.     D.

Algebra

For what range of values of x is  x +   >  x +

A. x >    B. x >    C. x <    D. x <

Algebra

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

A. 25    B. 11    C. 55    D. 36

Calculus If y = x sinx, find .

A. sinx - xcosx     B. sinx + xcosx    C. sinx – cosx    D. sinx + cosx The table above shows the marks obtained in a given test. How many students took the test?

A. 16    B. 20    C. 13    D. 15

Algebra

Find the sum of infinity of the following series 0.5 + 0.05 + 0.005 + 0.0005 + …

A.    B.    C.    D.

Calculus

Find (sin x + 2) dx.

A. -cosx + 2x + k
B. cosx + 2x + k
C. -cosx + x2 + k
D. cosx + x2 + k The table above shows the marks obtained in a given test. Find the mean mark.

A. 3.1    B. 3.0    C. 3.3    D. 3.2

Geometry/Trigonometry

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

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

Algebra

Factorize completely

A.      B.      C.      D.

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