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Unified Tertiary Matriculation Examination Mathematics 2010


1:

What mathematics Question Paper Type is given to you?

A:

Type A

B:

Type B

C:

Type C

D:

Type D

E:

No option

View Solution

2:

Find r, if 6r78 = 5119

A:

5

B:

2

C:

3

D:

6

E:

No option

View Solution

3:

Simplify   {left ( frac{3}{4} of frac{4}{9} div 9frac{1}{2} right )} div 1frac{5}{19}

A:

frac{1}{25}

B:

frac{1}{4}

C:

frac{1}{5}

D:

frac{1}{36}

E:

No option

View Solution

4:

A student measures a piece of rope and found that it was 1.26m long. If the actual length of the rope was 1.25m, what was the percentage error in the measurement?

A:

0.40%

B:

0.01%

C:

0.25%

D:

0.80%

E:

No option

View Solution

5:

At what rate will the interest on #400 increase to #24 in 3 years reckoning in simple interest?

A:

4%

B:

2%

C:

3%

D:

5%

E:

No option

View Solution

6:

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

A:

9:10:15

B:

12:15:16

C:

12:15:10

D:

10:15:24

E:

No option

View Solution

7:

Evaluate   left ( frac{81}{16} right )^{-frac{1}{4}} times 2^{-1}

A:

frac{1}{3}

B:

6

C:

3

D:

frac{1}{6}

E:

No option

View Solution

8:

Given that log 2 = 0.3010, log 7 = 0.8451. Evaluate log 112

A:

2.5441

B:

2.0491

C:

2.1461

D:

3.1461

E:

No option

View Solution

9:

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

A:

frac{3sqrt{15} + 11}{2}

B:

frac{3sqrt{15} - 11}{2}

C:

3sqrt{15} - 11

D:

3sqrt{15} + 11

E:

No option

View Solution

10:

Express the product of 0.21 and 0.34 in standard form 

A:

7.14times10^{-3}

B:

7.14times10^{-1}

C:

7.14times10^{-2}

D:

7.14times10^{-4}

E:

No option

View Solution

11:

Which of the venn diagrams below represents  P'cap Qcap R'

A:

A

36958-IMG_20171004_093720.jpg
B:

B

46627-IMG_20171004_093741.jpg
C:

C

70969-IMG_20171004_093751.jpg
D:

D

61299-IMG_20171004_093801.jpg
E:

No option

View Solution

12:

In a survey of 50 newspaper readers, 40 read Champion and 30 read Guardian, how many read both papers?

A:

15

B:

5

C:

10

D:

20

E:

No option

View Solution

13:

Make Q the subject of the formula if   P = frac{M}{5}(X + Q) + 1

A:

frac{5P + MX - 5}{M}

B:

frac{5P - MX - 5}{M}

C:

frac{5P - MX + 5}{M}

D:

frac{5P + MX + 5}{M}

E:

No option

View Solution

14:

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

A:

3x - 2y

B:

2y - 3x

C:

2y + 3x

D:

3x + 2y

E:

No option

View Solution

15:

Factorize completely  frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8}

A:

frac{x^{2} + 5}{2x + 4}

B:

frac{x(x + 5)}{2(x + 2)}

C:

frac{x(x - 5)}{2(x + 2)}

D:

frac{x(x - 5)}{2(x - 2)}

E:

No option

View Solution

16:

Solve for x and y if x - y = 2 and x2 - y2 = 8

A:

(1,3)

B:

(3,1)

C:

(-1,3)

D:

(-3,1)

E:

No option

View Solution

17:

If y varies directly as the square root of x and y = 3 when x = 16, Calculate y when x = 64

A:

5

B:

12

C:

6

D:

3

E:

No option

View Solution

18:

If x is inversely proportional to y and x = 2frac{1}{2}  when y = 2, find x if  y = 4

A:

2frac{1}{4}

B:

5

C:

4

D:

1frac{1}{4}

E:

No option

View Solution

19:

For what range of values of x is   frac{1}{2}x + frac{1}{4} > frac{1}{3}x + frac{1}{2}  ?

A:

x > -frac{3}{2}

B:

x> frac{3}{2}

C:

x< frac{3}{2}

D:

x< -frac{3}{2}

E:

No option

View Solution

20:

Solve the inequalities -6 leq 4-2x < 5-x

A:

-1leq x< 6

B:

-1 < x leq 5

C:

-1< x< 5

D:

-1leq xleq 6

E:

No option

View Solution

21:

Find the sum to infinity of the following series.

0.5 + 0.05 + 0.005 + 0.0005 ...

A:

frac{5}{9}

B:

frac{5}{7}

C:

frac{5}{8}

D:

frac{5}{11}

E:

No option

View Solution

22:

The 3rd term of an arithmetic progression is -9 and the 7th term is -29. Find the 10th term of the progression.

A:

44

B:

-165

C:

-44

D:

165

E:

No option

View Solution

23:

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

A:

36

B:

11

C:

25

D:

55

E:

No option

View Solution

24:

If p and q are two non zero numbers and 18(p+q) = (18+p)q, which of the following must be true?

A:

q = 18

B:

p = 18

C:

p<1

D:

q<1

E:

No option

View Solution

25:

If   begin{vmatrix} x & 3 2 & 7 end{vmatrix} = 15 , find the value of x

A:

3

B:

5

C:

4

D:

2

E:

No option

View Solution

26:

Evaluate   begin{vmatrix} 2 & 0 & 5 4 & 6 & 3 8 & 9 & 1 end{vmatrix} 

A:

-42

B:

102

C:

18

D:

-102

E:

No option

View Solution

27:

If   P = begin{pmatrix} 2 & -3 1 & 1 end{pmatrix} , what is P-1 

A:

begin{pmatrix} frac{1}{5} & frac{3}{5}\ frac{1}{5} & frac{2}{5} end{pmatrix}

B:

begin{pmatrix} frac{1}{5} & frac{3}{5}\ -frac{1}{5} & frac{2}{5} end{pmatrix}

C:

begin{pmatrix} -frac{1}{5} & frac{3}{5}\ -frac{1}{5} & frac{2}{5} end{pmatrix}

D:

begin{pmatrix} -frac{1}{5} & -frac{3}{5}\ -frac{1}{5} & -frac{2}{5} end{pmatrix}

E:

No option

View Solution

28:

From the diagram below, find x

 

63787-angles2.jpg
A:

65o

B:

50o

C:

55o

D:

75o

E:

No option

View Solution

29:

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

A:

102o

B:

52o

C:

82o

D:

112o

E:

No option

View Solution

30:

From the cyclic quadrilateral TUVW below, find the value of x

 

77678-cyclic2.jpg
A:

23o

B:

26o

C:

24o

D:

20o

E:

No option

View Solution

31:

If the two smaller sides of a right angled triangle are 4cm and 5cm, find its area

A:

10cm2

B:

6cm2

C:

8cm2

D:

24cm2

E:

No option

View Solution

32:

An arc subtends an angle of 50o at the center of circle of radius 6cm. Calculate the area of the sector formed.

(pi = frac{22}{7})

A:

frac{90}{7}cm^{2}

B:

frac{110}{7}cm^{2}

C:

frac{100}{7}cm^{2}

D:

frac{80}{7}cm^{2}

E:

No option

View Solution

33:

A cylindrical pipe 50m long with radius 7m has one end open. What is the total surface area of the pipe?

A:

700pi m^{2}

B:

98pi m^{2}

C:

350pi m^{2}

D:

749 pi m^{2}

E:

No option

View Solution

34:

What is the locus of point that is 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

E:

No option

View Solution

35:

Find the distance between the points  left ( frac{1}{2}, frac{1}{2} right ) and  left ( -frac{1}{2}, -frac{1}{2} right )

A:

sqrt{2}

B:

0

C:

1

D:

sqrt{3}

E:

No option

View Solution

36:

Find the gradient of the line passing through the points P(1,1) and Q(2,5)

A:

4

B:

2

C:

3

D:

5

E:

No option

View Solution

37:

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

E:

No option

View Solution

38:

If   cot theta = frac{8}{15} , where theta is acute, find sin theta 

A:

frac{13}{15}

B:

frac{15}{17}

C:

frac{8}{17}

D:

frac{16}{17}

E:

No option

View Solution

39:

If the area of triangle PQR below is 12sqrt{3} cm^{2}, find the value of q?

96553-tri2.jpg
A:

6 cm

B:

8 cm

C:

7 cm

D:

5 cm

E:

No option

View Solution

40:

If y = (2x + 1)3, find dy/dx

A:

3(2x + 1)2

B:

3(2x + 1)

C:

6(2x + 1)

D:

6(2x + 1)

E:

No option

View Solution

41:

If y = xsinx, find dy/dx

A:

sinx + cosx

B:

sinx + xcosx

C:

sinx - xcosx

D:

sinx - cosx

E:

No option

View Solution

42:

At what value of x does the function y = -3 - 2x + xattain a minimum value?

A:

1

B:

-4

C:

-1

D:

4

E:

No option

View Solution

43:

Evaluate   int_{0}^{2}(x^{3} + x^{2})dx 

A:

2frac{5}{6}

B:

6frac{2}{3}

C:

4frac{5}{6}

D:

1frac{5}{6}

E:

No option

View Solution

44:

Find  int (sin x + 2)dx

A:

cosx + x2 + k

B:

cosx + 2x + k

C:

-cosx + 2x + k

D:

-cosx + x2 + k

E:

No option

View Solution

45:

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

31443-snipped1.PNG
A:

7

B:

2

C:

6

D:

9

E:

No option

View Solution

46:

Use the table below to answer question 46 and 47

The table below shows the marks obtained in a given test

How many students took the test?

72966-snipped2.PNG
A:

15

B:

20

C:

16

D:

13

E:

No option

View Solution

47:

Find the mean mark

A:

3.2

B:

3.0

C:

3.1

D:

3.3

E:

No option

View Solution

48:

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

A:

sqrt{frac{5}{2}}

B:

sqrt{10}

C:

sqrt{6}

D:

sqrt{frac{2}{5}}

E:

No option

View Solution

49:

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

A:

50

B:

200

C:

100

D:

30

E:

No option

View Solution

50:

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

A:

frac{1}{8}

B:

frac{1}{3}

C:

frac{1}{6}

D:

frac{1}{9}

E:

No option

View Solution