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Unified Tertiary Matriculation Examination Mathematics 2007


1:

If 5, 8, 6 and 2 occur with frequencies 3, 2, 4 and 1 respectively, find the product of the modal and the median number.

A:

36

B:

48

C:

30

D:

40

E:

No option

View Solution

2:

In a basket, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?

A:

frac{6}{30}

B:

frac{5}{30}

C:

frac{17}{30}

D:

frac{11}{30}

E:

No option

View Solution

3:

The histogam below represents the weights of students who travelled out of their school for an examination. How many people made the trip?

 

81477-mainno3.jpg
A:

78

B:

38

C:

29

D:

69

E:

No option

View Solution

4:

A senatorial candidate has planned to visit seven cities prior to a primary election. However, he could only visit four of the cities. How many different itineraries could be considered?

A:

640

B:

840

C:

520

D:

720

E:

No option

View Solution

5:

The pie chart below illustrates the amount of private time a student spends in a week studying various subjects. Find the value of k

56401-mainno5.jpg
A:

90o

B:

60o

C:

30o

D:

15o

E:

No option

View Solution

6:

The table below shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?

12365-mainno6.PNG
A:

frac{27}{40}

B:

frac{17}{20}

C:

frac{3}{30}

D:

frac{33}{40}

E:

No option

View Solution

7:

What is the mean deviation of 3, 5, 8, 11, 12 and 21 ?

A:

4.7

B:

60

C:

3.7

D:

10

E:

No option

View Solution

8:

The table below gives the frequency distribution of marks obtained by a group of students in a test. If the total mark scored is 200, caclulate the value of y

68082-mainno8.PNG
A:

15

B:

13

C:

11

D:

9

E:

No option

View Solution

9:

In how many ways can 6 subjects be selected from 10 subjects for an examination

A:

218

B:

216

C:

215

D:

210

E:

No option

View Solution

10:

The cummulative frequency for 5leq xleq12 from the distribution above is

 

82440-mainno10.jpg
A:

40

B:

72

C:

22

D:

46

E:

No option

View Solution

11:

Integrate frac{x^{2} - sqrt{x}}{x} with respect to x

A:

frac{x^{2}}{2} - 2 sqrt{x} + k

B:

frac{2(x^{2} - x)}{3x}+k

C:

frac{x^{2}}{2}-sqrt{x} + k

D:

frac{x^{2} - sqrt{x}}{x^{2}} + k

E:

No option

View Solution

12:

If y = x cos x, find dy/dx

A:

sin x - x cos x

B:

sin x + x cos x

C:

cos x + x sin x

D:

cos x - x sin x

E:

No option

View Solution

13:

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

A:

frac{2}{3}

B:

1

C:

-frac{2}{3}

D:

-1

E:

No option

View Solution

14:

Determine the value of  int_{0}^{frac{pi}{2}}(-2cosx)dx

A:

-2

B:

-frac{1}{2}

C:

-3

D:

-frac{3}{2}

E:

No option

View Solution

15:

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

A:

2x - 1

B:

x - 1

C:

2 + 2x

D:

1 + 2x

E:

No option

View Solution

16:

A binary operation oplus on real numbers is defined by xoplus y = xy + x + y for any two real numbers x and y. The value of left ( -frac{3}{4} right ) oplus 6 is?

A:

frac{3}{4}

B:

-frac{9}{2}

C:

frac{45}{4}

D:

-frac{3}{4}

E:

No option

View Solution

17:

The graph below is represented by?

 

59319-mainno17.jpg
A:

y = x3 - 3x - 2

B:

y = x3 + 2x2 - x - 2

C:

y = x3 - 4x2 + 5x - 2

D:

y = x3 - 4x + 2

E:

No option

View Solution

18:

Make L the subject of the formula if d = sqrt{frac{42W}{5L}}

A:

sqrt{frac{42W}{5d}}

B:

frac{42W}{5d^{2}}

C:

frac{42}{5dW}

D:

frac{1}{d}sqrt{frac{42W}{5}}

E:

No option

View Solution

19:

The solution of the quadratic inequality (x^{2} + x - 12) geq 0 is

A:

x geq-3 or x leq4

B:

x geq3 or x geq-4

C:

x leq3 or x leq-4

D:

x geq3 or x leq-4

E:

No option

View Solution

20:

Factorize 2t2 + t - 15

A:

(2t - 3)(t + 5)

B:

(t + 3)(2t - 5)

C:

(t + 3)(t - 5)

D:

(2t + 3)(t - 5)

E:

No option

View Solution

21:

Solve the inequality -3(x - 2) < -2(x + 3)

A:

x > 12

B:

x < 12

C:

x > -12

D:

x < -12

E:

No option

View Solution

22:

W aa L^{2} and W = 6 when L = 4. If L = sqrt{17}, find W.

A:

6frac{7}{8}

B:

6frac{5}{8}

C:

6frac{3}{8}

D:

6frac{1}{8}

E:

No option

View Solution

23:

A binary operation Delta is defined by aDelta b = a + b + 1 for any real numbers a and b. Find the inverse of the real number 7 under the operation Delta, if the identity element is -1

A:

-7

B:

-9

C:

5

D:

9

E:

No option

View Solution

24:

The nth term of the sequence frac{3}{2},3,7,16,35,74,..... is

A:

5.2n - 2 - n

B:

5.2^{n - 2} - frac{n+1}{2}

C:

3.2n - 2

D:

frac{3}{2}n

E:

No option

View Solution

25:

If f(x) = 3x - 2, P = begin{pmatrix} 2 & 1 -1 & 0 end{pmatrix} and I is 2 times 2 identity matrix, evaluate f(P)

A:

h

B:

begin{pmatrix} 2 & 0\ 0 & 2 end{pmatrix}

C:

dd

D:

d

E:

dsf

View Solution

26:

Find the sum to infinity of the series 2 + frac{3}{2} + frac{9}{8} + frac{27}{32} + ....

A:

1

B:

2

C:

8

D:

4

E:

No option

View Solution

27:

Evaluate begin{pmatrix} 3 & -2\ -7 & 5 end{pmatrix} + 2begin{pmatrix} -2 & 4\ 3 & -1 end{pmatrix}

A:

sdf

B:

df

C:

sdfs

D:

dfs

E:

dfs

View Solution

28:

Find y, if  sqrt{12} - sqrt{147} + ysqrt{3} = 0

A:

5

B:

1

C:

7

D:

3

E:

No option

View Solution

29:

If x10 = 12145 find x.

A:

124

B:

121

C:

184

D:

180

E:

No option

View Solution

30:

Evaluate frac{(0.5625)^{2} - (0.4375)^{2}}{0.04} correct to 3 significant figures

A:

3.11

B:

3.13

C:

0.313

D:

3.12

E:

No option

View Solution

31:

Find the value of x for which 2(32x-1) = 162

A:

frac{5}{2}

B:

frac{3}{2}

C:

frac{2}{5}

D:

frac{1}{2}

E:

No option

View Solution

32:

Simplify frac{3}{5}+(frac{2}{7} times frac{4}{3} + frac{4}{9})

A:

frac{4}{5}

B:

frac{7}{10}

C:

frac{2}{5}

D:

frac{1}{2}

E:

No option

View Solution

33:

If log102 = x, express log1012.5 in terms of x.

A:

2(1 + x)

B:

2 + 3x

C:

2(1 - x)

D:

2 - 3x

E:

No option

View Solution

34:

A man made a profit of 5% when he sold an article for #60,000.00. How much would he have to sell the article to make a profit of 26%?

A:

#68 000

B:

#72 000

C:

#65 000

D:

#70 000

E:

No option

View Solution

35:

Given:

P = {1, 3, 5, 7, 9, 11} and Q = {2, 4, 6, 8, 10, 12}.

Determine the relationship between P and Q

 

A:

P cap Q = phi

B:

coming

C:

coming

D:

coming

E:

No option

View Solution

36:

Evaluate 101122 - 10122

A:

1100002

B:

1102

C:

11000002

D:

110002

E:

No option

View Solution

37:

The sum of the ages of Musa and Lawal is 28 years. After sharing a certain sum of money in the ratio of their ages, Musa gets #600 and Lawal #800. How old is Lawal?

A:

20 years

B:

16 years

C:

14 years

D:

12 years

E:

No option

View Solution

38:

If X = {all perfect squares less than 40} and

  Y = {all odd numbers from 1 to 15}

Find mathbf{X} cap mathbf{Y}

A:

{3, 9}

B:

{9}

C:

{9, 25}

D:

{1, 9}

E:

No option

View Solution

39:

Calculate the length of an arc of a circle of diameter 14cm, which subtends an angle of 900 at the centre of the circle

A:

frac{7 pi}{2}cm

B:

7 pi cm

C:

14 pi cm

D:

frac{7 pi}{4}cm

E:

No option

View Solution

40:

If the lines 3y = 4x - 1 and qy = x + 3 are parallel to each other, the value of q is

A:

-frac{4}{3}

B:

-frac{3}{4}

C:

frac{4}{3}

D:

frac{3}{4}

E:

No option

View Solution

41:

In the parallelogram PQRS above, find angle SQR

A:

1000

B:

800

C:

500

D:

300

E:

No option

View Solution

42:

The volume of a hemispherical bowl is 718frac{2}{3}cm^{3}. Find its radius

(pi = frac{22}{7})

A:

4.0cm

B:

5.6cm

C:

7.0cm

D:

3.8cm

E:

No option

View Solution

43:

A particle P moves between points S and T such that angle SPT is always constant. Find the locus of P.

A:

It is a semi-circle with ST as diameter

B:

It is a perpendicular bisector of ST

C:

It is a quadrant of a circle with ST as diameter

D:

It is a straight line perpendicular to ST

E:

No option

View Solution

44:

If the lines 2y - kx + 2 = 0 and y + x - frac{k}{2} = 0. Intersect at (1, -2), find the value of k

A:

-4

B:

-3

C:

-2

D:

-1

E:

No option

View Solution

45:

A man 40m from the foot of a tower observes the angle of elevation of the tower to be 300. Determine the height of the tower.

A:

frac{40 sqrt{3}}{3}m

B:

20m

C:

40 sqrt{3}m

D:

40m

E:

No option

View Solution

46:

Find the locus of points equidistant from two straight lines y - 5 = 0 and y - 3 = 0

A:

y - 2 = 0

B:

y - 4 = 0

C:

y - 1  = 0

D:

y - 3 = 0

E:

No option

View Solution

47:

What is the value of k if the mid-point of the line joining (1-k, -4) and (2, k+1) is (-k, k)?

A:

-3

B:

-1

C:

-4

D:

-2

E:

No option

View Solution

48:

Find the size of each exterior angle of a regular octagon.

A:

510

B:

450

C:

400

D:

360

E:

No option

View Solution

49:

Find the value of frac{tan 60^{0} - tan 30^{0}}{tan 60^{0} + tan 30^{0}}

A:

frac{4}{sqrt{3}}

B:

frac{2}{sqrt{3}}

C:

1

D:

frac{1}{2}

E:

No option

View Solution

50:

The area of a square is 144 sq cm. Find the length of the diagonal

A:

13cm

B:

12 sqrt{2}cm

C:

12cm

D:

11 sqrt{3}cm

E:

No option

View Solution