Sulvme!

Unified Tertiary Matriculation Examination Mathematics 2005

1:

Find the value of m if 13m + 24m = 41m

A:

8

B:

6

C:

5

D:

2

E:

No option

2:

If 3214 is divided by 234 and leaves a remainder r, what is the value of r?

A:

0

B:

1

C:

2

D:

3

E:

No option

3:

Simplify

A:

B:

C:

D:

E:

No option

4:

A father decided to give 20% of his monthly income to his three children as their monthly allowance. The eldest child got 45% of the allowance and the youngest got 25%. How much was the father's monthly income if the second child got #3,000 ?

A:

#33,000

B:

#45,000

C:

#50,000

D:

#60,000

E:

No option

5:

If the interest on #150.00 for  years is #4.50, find the interest on #250.00 for 6 months at the same rate.

A:

#1.50

B:

#7.50

C:

#15.00

D:

#18.00

E:

No option

6:

Three boys shared some oranges, the first received  of the oranges and the second received  of the remainder. If the third boy received the remaining 12 oranges, how many oranges did they share?

A:

60

B:

54

C:

48

D:

42

E:

No option

7:

Evaluate

A:

3

B:

1

C:

D:

E:

No option

8:

If log102 = 0.3010 and log103 = 0.4771, evaluate log104.5

A:

0.9542

B:

0.6532

C:

0.4771

D:

0.3010

E:

No option

9:

Simplify

A:

0

B:

C:

D:

1

E:

No option

10:

If U = {x/x is a positive integer less than 10} and P = {x/ x is a prime factor of 30}, find the complement of P

A:

{1, 2, 4. 7. 8. 9}

B:

{1, 2, 4. 6, 7. 8. 9}

C:

{1, 4. 6, 7. 8. 9}

D:

{1, 4. 7. 8. 9}

E:

No option

11:

The venn diagram below shows a class of 40 students with the games they play. How many of the students play two games only?

A:

19

B:

16

C:

15

D:

4

E:

No option

12:

If m = 3, p = -3, q = 7 and , evaluate m(p + q + r)

A:

19.50

B:

19.15

C:

18.95

D:

18.05

E:

No option

13:

Divide 6x2 - 13x + 5 by 2x - 1

A:

3x + 5

B:

3x - 5

C:

5x - 3

D:

5x + 3

E:

No option

14:

A polynomial in x whose zeros are -2, -1 and 3 is

A:

x3 - 7x + 6

B:

x3 + 7x - 6

C:

x3 + 7x + 6

D:

x3 - 7x - 6

E:

No option

15:

The time taken to do a piece of work is inversely proportional to the number of men employed. If it takes 30 men to do a piece of work in 6 days, how many men are required to do the work in 4 days?

A:

20

B:

35

C:

45

D:

60

E:

No option

16:

The weight W kg of a metal bar varies jointly as its length L metres and the square of its diameter d metres. If W = 140 and d =  and L = 54, find d in terms of W and L

A:

B:

C:

D:

E:

No option

17:

Find the range of values of x for which 7x - 3 > 25 + 3x

A:

x > 7

B:

x < 7

C:

x > -7

D:

x < -7

E:

No option

18:

The diagram below is the graph of the function f(x). Determine the range of values of x for which

A:

B:

C:

D:

E:

No option

19:

If the 7th term of an AP is twice the third term and the sum of the first four terms is 42, find the common difference

A:

6

B:

3

C:

2

D:

1

E:

No option

20:

Find the sum of the first 20 terms of the series 8, 12, 16, ........., 96

A:

1400

B:

1040

C:

960

D:

920

E:

No option

21:

An operation * is defined on the set of real numbers by a * b = ab + 2 (a + b + 1). Find the identity element.

A:

2

B:

1

C:

-1

D:

-2

E:

No option

22:

If M and N are two matrices defined by

and

Evaluate 2M - 3N

A:

B:

C:

D:

E:

No option

23:

If , find the determinant of matrix P

A:

75

B:

57

C:

-57

D:

-75

E:

No option

24:

In the diagram below, calculate the value of x.

A:

600

B:

1000

C:

1200

D:

1400

E:

No option

25:

Three straight lines EF, GH and LK intersect at O as shown below. If  and , calculate the size of

A:

260

B:

430

C:

520

D:

850

E:

No option

26:

The sum of the interior angles of a regular polygon is 18000. Calculate the size of one exterior angle of the polygon

A:

300

B:

240

C:

180

D:

120

E:

No option

27:

In the diagram below, O is the centre of the circle,  and , Calculate

A:

200

B:

250

C:

500

D:

800

E:

No option

28:

A chord of a circle subtends an angle of 600 at the centre of a circle of radius 14cm. Find the length of the chord

A:

7cm

B:

14cm

C:

21cm

D:

28cm

E:

No option

29:

A sector of a circle has an area of 55cm2. If the radius of the circle is 10cm, calculate the angle of the sector.

()

A:

450

B:

630

C:

750

D:

900

E:

No option

30:

Find the curved surface area of a cone with circular base diameter 10cm and height 12cm

A:

B:

C:

D:

E:

No option

31:

Two lines PQ and ST intersect at 750. The locus of points equidistant from PQ and ST lies on the

A:

perpendicular bisector of PQ

B:

perpendicular bisector of ST

C:

bisector of the angles between lines PQ and ST

D:

bisector of the angles between lines PT and QS

E:

No option

32:

Find the equation of the perpendicular at point (4, 3) to the line y + 2x = 5

A:

2y - x = 4

B:

y + 2x = 3

C:

y + 2x = 5

D:

2y - x = 2

E:

No option

33:

Find the coordinates of the midpoint of the line joining (3, -4) and (-1, 10)

A:

(1, 3)

B:

(1, 2)

C:

(2, 3)

D:

(3, 2)

E:

No option

34:

If sin  =  for 0 <  < 3600, the value of  is

A:

300 and 1500

B:

1500 and 2100

C:

2100 and 3300

D:

1500 and 3300

E:

No option

35:

From the diagram below, find the bearing of R from S

A:

2260

B:

2240

C:

1360

D:

1340

E:

No option

36:

If y = (1 - 2x)3, find the value of  at x = -1

A:

57

B:

27

C:

-6

D:

-54

E:

No option

37:

Find the derivative of y = sin (2x3 + 3x - 4)

A:

cos (2x3 + 3x - 4)

B:

-cos (2x3 + 3x - 4)

C:

(6x2 + 3) cos (2x3 + 3x - 4)

D:

- (6x2 + 3) cos (2x3 + 3x - 4)

E:

No option

38:

The radius r of a circular disc is increasing at the rate of 0.5cm/sec. At what rate is the area of the disc increasing when its radius is 6cm?

A:

36  cm2 /sec

B:

18  cm2 /sec

C:

cm2 /sec

D:

cm2 /sec

E:

No option

39:

The maximum value of the function

f(x) = 2 + x - x2 is

A:

B:

C:

D:

E:

No option

40:

Find the area of the figure bounded by the given pair of curves y = x2 - x + 3 and y = 3

A:

units (sq)

B:

units (sq)

C:

units (sq)

D:

units (sq)

E:

No option

41:

Evaluate

A:

1

B:

0

C:

D:

-1

E:

No option

42:

The histogram below shows the distribution of the monthly incomes of the workers in a company. How many workers earn more than #700.00?

A:

16

B:

12

C:

8

D:

6

E:

No option

43:

The grades of 36 students in a test are shown in the pie chart above. How many students had excellent?

A:

7

B:

8

C:

9

D:

12

E:

No option

44:

The table below shows the scores of a group of students in a test. If the average score is 3.5, find the value of x

A:

1

B:

2

C:

3

D:

4

E:

No option

45:

The modal height and range of heights 1.35, 1.25, 1.35, 1.40, 1.35, 1.45, 1.50, 1.35, 1.50 and 1.20 are m and r respectively. Find m + 2r

A:

1.35

B:

1.65

C:

1.95

D:

3.00

E:

No option

46:

Find the value of t if the standard deviation of 2t, 3t, 4t, 5t and 6t is

A:

1

B:

2

C:

3

D:

4

E:

No option

47:

In how many ways can 6 coloured chalks be arranged if 2 are of the same colour?

A:

60

B:

120

C:

240

D:

360

E:

No option

48:

How many possible ways are there of seating seven people P, Q, R, S, T, U and V at a circular table?

A:

360

B:

720

C:

2520

D:

5040

E:

No option

49:

A box contains 5 blue balls, 3 red balls and 2 white balls. Two balls are selected from the box with replacement. Find the probability of obtaining two blue or two red balls

A:

B:

C:

D:

E:

No option

50:

What is the probability that an integer x,  chosen at random is divisible by both 2 and 3

A:

B:

C:

D:

E:

No option