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Unified Tertiary Matriculation Examination Mathematics 2011


1:

Which Mathematics Question Paper Type is given to you?

A:

Type A

B:

Type B

C:

Type C

D:

Type D

E:

No option

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2:

If 2q35 = 778, Find q

A:

2

B:

1

C:

4

D:

0

E:

No option

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3:

Simplify      frac{3frac{2}{3}timesfrac{5}{6}timesfrac{2}{3}}{frac{11}{15}timesfrac{3}{4}timesfrac{2}{27}}

A:

5frac{2}{3}

B:

30

C:

4frac{1}{3}

D:

50

E:

No option

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4:

A man invested #5,000 for 9 months at 4%. What is the simple interest?

A:

#150

B:

#220

C:

#130

D:

#250

E:

No option

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5:

If the numbers M,N,Q are in the ratio 5:4:3, find the value of frac{2N - Q}{M}

A:

2

B:

3

C:

1

D:

4

E:

No option

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6:

Simplify left ( frac{16}{81} right )^{frac{1}{4}} div left ( frac{9}{16} right )^{-frac{1}{2}}

A:

frac{2}{3}

B:

frac{1}{2}

C:

frac{8}{9}

D:

frac{1}{3}

E:

No option

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7:

If log318 + log33 - log3x = 3, find x

A:

1

B:

2

C:

0

D:

3

E:

No option

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8:

Rationalize frac{2 - sqrt{5}}{3 - sqrt{5}}

A:

frac{1 - sqrt{5}}{2}

B:

frac{1 - sqrt{5}}{4}

C:

frac{sqrt{5} - 1}{2}

D:

frac{1 + sqrt{5}}{4}

E:

No option

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9:

Simplify   left [ sqrt{2} + frac{1}{sqrt{3}} right ]left [ sqrt{2} - frac{1}{sqrt{3}} right ]

A:

frac{7}{3}

B:

frac{5}{3}

C:

frac{5}{2}

D:

frac{3}{2}

E:

No option

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10:

From the venn diagram below, the complement of the set P cap Q is given by

21861-ques.jpg
A:

{a, b, d, e}

B:

{b, d}

C:

{a, e}

D:

{c}

E:

No option

View Solution

11:

Ralia has 7 different posters to be hung in her bedroom, living room and kitchen. Assuming she has plans to place, at least, a poster in each of the 3 rooms, how many choices does she have?

A:

49

B:

170

C:

21

D:

210

E:

No option

View Solution

12:

Make R the subject of the formula if    T = frac{KR^{2} + M}{3}

A:

frac{sqrt{3T - K}}{M}

B:

frac{sqrt{3T + M}}{K}

C:

frac{sqrt{3T + K}}{M}

D:

frac{sqrt{3T - M}}{K}

E:

No option

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13:

Find the remainder when x3 - 2x2 + 3x - 3 is divided by x2 + 1

A:

2x - 1

B:

x + 3

C:

2x + 1

D:

x - 3

E:

No option

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14:

Factorize completely 9y2 - 16x2

A:

(3y - 2x)(3y - 4x)

B:

(3y + 4x)(3y + 4x)

C:

(3y + 2x)(3y - 4x)

D:

(3y + 4x)(3y - 4x)

E:

No option

View Solution

15:

Solve for x and y respectively in the simultaneous equations -2x - 5y = 3, x + 3y = 0

A:

-3, -9

B:

9, -3

C:

-9, 3

D:

3, -9

E:

No option

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16:

If x varies directly as square root of y and x = 81 when y = 9, find x when y = 1frac{7}{9}

A:

20frac{1}{4}

B:

27

C:

2frac{1}{4}

D:

36

E:

No option

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17:

T varies inversely as the cube of R. When R = 3, T = frac{2}{81}, find T when R = 2

A:

frac{1}{18}

B:

frac{1}{12}

C:

frac{1}{24}

D:

frac{1}{6}

E:

No option

View Solution

18:

Which of the following diagrams represents the solution of the inequalities yleq x - 2 and ygeqslant x^{2} - 4

A:

A

63542-option a.jpg
B:

B

37371-option b.jpg
C:

C

62968-option c.jpg
D:

D

80563-option d.jpg
E:

No option

View Solution

19:

Solve the inequalities -6(x + 3)leq 4(x - 2)

A:

xleq 2

B:

xgeq -1

C:

xgeq -2

D:

xleq -1

E:

No option

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20:

Solve the inequalities x^{2} + 2x > 15

 

A:

x < -3 or x > 5

B:

-5 < x < 3

C:

x < 3 or x > 5

D:

x > 3 or x < -5

E:

No option

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21:

Find the sum of the first 18 terms of the series 3, 6, 9, ......, 36

A:

505

B:

513

C:

433

D:

635

E:

No option

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22:

The second term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms.

A:

60

B:

62

C:

54

D:

64

E:

No option

View Solution

23:

A binary operation oplus on real numbers is defined by x oplus y = xy + x + y for two real numbers x and y. Find the value of 3 oplus -frac{2}{3}

A:

-frac{1}{2}

B:

frac{1}{3}

C:

-1

D:

2

E:

No option

View Solution

24:

If    begin{vmatrix} 2 & 3 5 & 3x end{vmatrix} = begin{vmatrix} 4 & 1 3 & 2x end{vmatrix}, find the value of x

A:

-6

B:

6

C:

-12

D:

12

E:

No option

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25:

Evaluate     begin{vmatrix} 4 & 2 & -1 2 & 3 & -1  -1 & 1 & 3 end{vmatrix}

A:

25

B:

45

C:

15

D:

55

E:

No option

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26:

The inverse of matrix N = begin{bmatrix} 2 & 3 1 & 4 end{bmatrix}

A:

frac{1}{5}begin{bmatrix} 2 & 1 3 & 4 end{bmatrix}

B:

frac{1}{5}begin{bmatrix} 4 & -3 -1 & 2 end{bmatrix}

C:

frac{1}{5}begin{bmatrix} 2 & -1 -3 & 4 end{bmatrix}

D:

frac{1}{5}begin{bmatrix} 4 & 1 3 & 2 end{bmatrix}

E:

No option

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27:

What is the size of each interior angle of a 12-sided regular polygon?

A:

120o

B:

150o

C:

30o

D:

180o

E:

No option

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28:

A circle of perimeter 28cm is opened to form a square. What is the maximum possible area of the square?

A:

56cm2

B:

49cm2

C:

98cm2

D:

28cm2

E:

No option

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29:

A chord of a circle of radius 7cm is 5cm from the center of the circle. What is the length of the chord?

A:

4sqrt{6}cm

B:

3sqrt{6} cm

C:

6sqrt{6}cm

D:

2sqrt{6}cm

E:

No option

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30:

A solid metal cube of side 3cm is placed in a rectangular tank of dimensions 3, 4 and 5cm. What volume of water can the tank now hold?

A:

48cm3

B:

33cm3

C:

60cm3

D:

27cm3

E:

No option

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31:

The perpendicular bisector of a line XY is the locus of a point 

A:

whose distance from X is always twice its distance from Y

B:

whose distance from Y is always twice its distance from X

C:

which moves on the line XY

D:

which is equidistant from the points X and Y

E:

No option

View Solution

32:

The midpoint of P(x,y) and Q(8,6) is (5,8). Find x and y

A:

(2,10)

B:

(2,8)

C:

(2,12)

D:

(2,6)

E:

No option

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33:

Find the equation of a line perpendicular to line 2y = 5x + 4 which passes through (4,2)

A:

5y - 2x - 18 = 0

B:

5y + 2x - 18 = 0

C:

5y - 2x + 18 = 0

D:

5y + 2x - 2 = 0

E:

No option

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34:

In a right angled triangle, if   tanTheta = frac{3}{4} . What is cosTheta - sinTheta?

A:

frac{2}{5}

B:

frac{3}{5}

C:

frac{1}{5}

D:

frac{4}{5}

E:

No option

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35:

A man walks 100m due West from a point X to Y, he then walks 100m due North to a point Z. Find the bearing of X to Z

A:

195o

B:

135o

C:

225o

D:

045o

E:

No option

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36:

The derivative of (2x + 1)(3x + 1) is

A:

12x + 1

B:

6x + 5

C:

6x + 1

D:

12x + 5

E:

No option

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37:

Find the derivative of   frac{sinTheta }{cosTheta }

A:

sec^{2}Theta

B:

tanTheta cosecTheta

C:

cosecTheta secTheta

D:

cosec^{2}Theta

E:

No option

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38:

Find the value of x at the minimum point of the curve y = x3 + x2 - x + 1

A:

frac{1}{3}

B:

-frac{1}{3}

C:

1

D:

-1

E:

No option

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39:

Evaluate   int_{0}^{1}(3 - 2x)dx

A:

3

B:

5

C:

2

D:

6

E:

No option

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40:

Find    int cos 4x dx

A:

frac{3}{4}sin4x + k

B:

-frac{1}{4}sin4x + k

C:

-frac{3}{4}sin4x + k

D:

frac{1}{4}sin4x + k

E:

No option

View Solution

41:

The pie chart shows the distribution of courses offered by students. What percentage of the students offer English?

81853-circle.jpg
A:

30%

B:

25%

C:

35%

D:

20%

E:

No option

View Solution

42:

The bar chart below shows the distribution of SS2 students in a school. Find the total number of students

74444-main 42.jpg
A:

180

B:

135

C:

210

D:

105

E:

No option

View Solution

43:

The sum of four consecutive integers is 34. Find the least of these numbers

A:

7

B:

6

C:

8

D:

5

E:

No option

View Solution

44:

From the table below, find the median and range of the data respectively

1226-number44.PNG
A:

(8,5)

B:

(3,5)

C:

(5,8)

D:

(5,3)

E:

No option

View Solution

45:

Find the mode of the distribution below

7093-number45.PNG
A:

9

B:

8

C:

10

D:

7

E:

No option

View Solution

46:

Find the standard deviation of the distribution below

A:

sqrt{5}

B:

sqrt{3}

C:

sqrt{7}

D:

sqrt{2}

E:

No option

View Solution

47:

In how many ways can the letters of the word FLATION be arranged?

A:

6!

B:

7!

C:

5!

D:

8!

E:

No option

View Solution

48:

In how many ways can five people sit round a circular table?

A:

24

B:

60

C:

12

D:

120

E:

No option

View Solution

49:

Find the probability that a number picked at random from the set {43, 44, 45,...... 60} is a prime number.

A:

frac{2}{3}

B:

frac{1}{3}

C:

frac{2}{9}

D:

frac{7}{9}

E:

No option

View Solution

50:

In a class of 60 students, 30 offer physics and 40 offer chemistry. If a student is picked at random from the class, what is the probability that the students offers both physics and chemistry?

A:

frac{1}{3}

B:

frac{1}{4}

C:

frac{1}{2}

D:

frac{1}{6}

E:

No option

View Solution