# Sulvme!

### Senior School Certificate Exams Neco Mathematics 2017 (Nov/Dec) Objectives View Theory

1:

Simplify $1\frac{1}{2} + 2\frac{2}{3} \times \frac{3}{4} - \frac{1}{2}$

A:

$3\frac{3}{4}$

B:

$3\frac{1}{4}$

C:

$2\frac{3}{4}$

D:

$1\frac{3}{4}$

E:

$1\frac{1}{4}$

2:

Evaluate $\frac{16.54}{0.0536 \times 18.25}$ and leave your answer to three significant figures

A:

16.697

B:

16.820

C:

16.900

D:

16.909

E:

16.910

3:

Simplify $\frac{8^{2} \times 4^{0} \times 8^{-3}}{7^{3} \div 7^{6}}$

A:

$\frac{343}{8}$

B:

$\frac{343}{7}$

C:

$\frac{343}{5}$

D:

$\frac{243}{8}$

E:

$\frac{243}{5}$

4:

Simplify $\frac{1}{3}log_{2}64$

A:

2

B:

3

C:

4

D:

6

E:

12

5:

If $log_{10}2 = 0.3010$ and $log_{10}3 = 0.4771$, find $log_{10}54$ correct to the nearest whole number

A:

6

B:

5

C:

3

D:

2

E:

1

6:

Express $0.6721 \times 0.0261$ and express your answer in standard form

A:

df

B:

$1754 \times 10^{3}$

C:

$1.754 \times 10^{-3}$

D:

$1.754 \times 10^{-2}$

E:

$1.754 \times 10^{-1}$

7:

The first term of a Geometric Progression is 6. If its common ratio is $\frac{2}{3}$, find the 5th term

A:

$\frac{128}{243}$

B:

$\frac{61}{81}$

C:

$\frac{8}{3}$

D:

$\frac{16}{9}$

E:

$\frac{32}{27}$

8:

The first and last terms of an Arithmetic Progression are 6 and 153 respectively. If there are 50 terms in the sequence, find its common difference

A:

9

B:

7

C:

6

D:

4

E:

3

9:

Given that 244x = 10224, what is the positive value of x?

A:

3

B:

4

C:

5

D:

6

E:

7

10:

If 30145 = 21125 + y5, find the value of y

A:

10131

B:

5131

C:

5126

D:

902

E:

402

11:

Simplify $\frac{2 + \sqrt{5}}{2 \sqrt{5} - 1}$

A:

ds

B:

$\frac{1}{19}(12 - 4 \sqrt{5})$

C:

$\frac{1}{19}(12 + 4 \sqrt{5})$

D:

$\frac{1}{19}(12 - 5 \sqrt{5})$

E:

$\frac{1}{19}(12 + 5 \sqrt{5})$

12:

A shareholder bought shares worth #100,000.00 on ordinary share at #2.00 each. If a dividend of 15 kobo per share is declared, how much dividend was received?

A:

#13,333.33

B:

#12,000.00

C:

#10,000.00

D:

#9,500.00

E:

#7,500.00

13:

Find the future value of an ordinary annuity of #500.00 paid yearly for 4 years at 10% per annum.

A:

#700.00

B:

#732.05

C:

#923.50

D:

#1,232.05

E:

#2,320.50

14:

Find the determinant of the matrix

$K = \begin{pmatrix} 3 & 0 & -1\\ 1 & 2 & -3\\ -2 & -1 & 1 \end{pmatrix}$

A:

-6

B:

-3

C:

0

D:

3

E:

6

15:

Find the sum of the first 40 even positive integers.

A:

1,600

B:

1,640

C:

1,680

D:

3,200

E:

3,280

16:

The first term of an Arithmetic Progression is -3. If the sixth term is 22, find the mean of the common difference and the first term

A:

1

B:

4

C:

5

D:

7

E:

8

17:

Find the perimeter of a sector of a circle with radius 7cm which subtends an angle of 1800 at the centre of the circle

A:

36cm

B:

44cm

C:

58cm

D:

74cm

E:

108cm

18:

Victoria went for a doctor's appointment on Monday. If her next appointment is 45 days after, which day of the week will it be?

A:

Friday

B:

Monday

C:

Saturday

D:

Thursday

E:

Wednesday

19:

Solve the inequality

$3x - 5 \geq 20 - 2x$

A:

$x >4$

B:

$x \geq 4$

C:

$x \geq 5$

D:

$x < 5$

E:

$x \leq 6$

20:

Expand (2a + b)2 - (b - 2a)2.

A:

-8ab

B:

4ab

C:

8ab

D:

-4ab

E:

16ab

21:

If 4x2 - 12x + c is a perfect square, find the value of c.

A:

36

B:

9

C:

$\frac{9}{4}$

D:

$-\frac{9}{4}$

E:

-9

22:

If (a - 3) is one of the factors of a2 + 14a - 51, find the other factor

A:

(a - 11)

B:

(a + 17)

C:

(a - 17)

D:

(a + 48)

E:

(a - 48)

23:

Find the gradient of a straight line joining the points (-3, 0) and (0, 5).

A:

20

B:

10

C:

$1\frac{2}{3}$

D:

$-\frac{3}{2}$

E:

$-\frac{5}{3}$

24:

A quadratic equation whose roots are $-\frac{5}{4}$ and $-\frac{3}{4}$ is

A:

16x2 + 2x - 15 = 0

B:

16x2 - 2x + 15 = 0

C:

16x2 - 4x - 15 = 0

D:

16x2 - 8x + 15 = 0

E:

16x2 + 8x - 15 = 0

25:

If P varies directly as $\sqrt{Q}$ and P = 6 when Q = 81, find the value of P when $Q = \frac{1}{4}$

A:

3

B:

$\frac{1}{2}$

C:

$\frac{1}{3}$

D:

$-\frac{1}{2}$

E:

-3

26:

What is the maximum value of y?

A:

6.05

B:

4.05

C:

-4.05

D:

-5.05

E:

-10.05

27:

What is the value of y when x = 0 ?

A:

9

B:

6

C:

5

D:

-9

E:

-15

28:

Let p: I study hard

q: I pass physics

r:  I am happy

Translate $p \Rightarrow (q \vee r)$ into statement

A:

I am unhappy but I pass physics

B:

I pass physics and I am happy

C:

If i do not study hard, then I pass physics and I am happy

D:

If I study hard, then I pass physics and I am happy

E:

If I study hard, then I pass physics or I am happy

29:

Let p : I like bread with egg.

q :  I like ginger in tea

Translate "I like ginger in tea but not bread with egg" into symbol.

A:

$q \vee p$

B:

$q \wedge p$

C:

dsff

D:

dsf

E:

sdf

30:

Given that

(2x - 1) (x + 5) = 2x2 - mx - 5, find the value of m.

A:

11

B:

5

C:

-5

D:

-9

E:

-10

31:

Find the midpoint of a line joining the points M(4, 0) and N(3, p)

A:

$\left ( \frac{p}{2}, \frac{7}{2} \right )$

B:

$\left ( \frac{7}{2}, \frac{p}{2} \right )$

C:

$\left ( \frac{1}{2}, \frac{p}{2} \right )$

D:

$\left ( \frac{p}{2}, \frac{1}{2} \right )$

E:

$\left ( 0, \frac{7}{2} \right )$

32:

Find the equation of a line with gradient 3, passing through (1, 4)

A:

3x - y = 1

B:

3x - y = -2

C:

y - 3x = 1

D:

y - 3x = -4

E:

y - 3x = 3

33:

Solve the simultaneous equations:

$y = \frac{1}{3}x - 1, 3x - 2y = 4$

A:

$\frac{12}{7}, \frac{5}{7}$

B:

$\frac{7}{6}, -\frac{5}{7}$

C:

$\frac{6}{7}, -\frac{5}{7}$

D:

$-\frac{5}{7}, \frac{6}{7}$

E:

$\frac{3}{5}, \frac{2}{7}$

34:

Given that sin $\theta$ = $\frac{7}{9}$, find the value of $9cos \theta$

A:

$\frac{7}{81}$

B:

$\frac{4 \sqrt{2}}{9}$

C:

$4 \sqrt{2}$

D:

$9 \sqrt{2}$

E:

$36 \sqrt{2}$

35:

Find the value of x in the figure below

A:

$2 \sqrt{2}cm$

B:

$3\sqrt{2}cm$

C:

$3 \sqrt{3}cm$

D:

$\sqrt{3}cm$

E:

$\frac{\sqrt{3}}{2}cm$

36:

In the figure below, $\Delta ABC$ is isosceles. Calculate $\angle BED$

A:

1050

B:

1000

C:

950

D:

850

E:

750

37:

In the figure above, if the area of the square is 162cm2, calculate the radius of the circle.

A:

12cm

B:

10cm

C:

9cm

D:

8cm

E:

7cm

38:

Calculate the area of the shaded region in the figure below.

A:

16.73cm2

B:

27.75cm2

C:

48.05cm2

D:

93.20cm2

E:

110.00cm2

39:

In the figure above, AOB is a diameter. Find the angle marked x

A:

600

B:

550

C:

500

D:

450

E:

300

40:

In the figure below, AD is a chord of a circle centred at O. Find $\angle ACD$

A:

900

B:

800

C:

700

D:

500

E:

400

41:

In the figure below, ABCD is a cyclic quadrilateral and O is the centre of the circle. Find $\angle ACB$

A:

200

B:

400

C:

600

D:

800

E:

1000

42:

Calculate nearest to the nearest degree, the parallel of latitude in the southern hemisphere along which a journey of 320km makes a change of 210 in longitude.

(Take $\pi = \frac{22}{7}$ and R = 6400km)

A:

80

B:

160

C:

660

D:

820

E:

920

43:

The positions of two cities M and N are (140N, 300E) and (720N, 300E) respectively. How far is city N from M ?

(Take $\pi = \frac{22}{7}$ and R = 6400km)

A:

9610.16km

B:

8610.16km

C:

6481.27km

D:

6400.27km

E:

5364.18km

44:

Calculate the volume of a sphere with radius 6cm (Take $\pi$ = 3.14)

A:

2716.96cm3

B:

904.32cm3

C:

902.88cm3

D:

452.16cm3

E:

216.00cm3

45:

What is the value of x if the gradient of the line joining (-2, x) and (x, 3) is 1/4

A:

-3

B:

-2

C:

1

D:

2

E:

3

46:

An arc of a circle of radius 6cm subtends an angle of 450 at the centre of the circle. Find the length of the arc in terms of $\pi$

A:

$7 \pi cm$

B:

$2 \pi cm$

C:

$\frac{3}{2} \pi cm$

D:

$\frac{\pi}{2} cm$

E:

$\frac{\pi}{6} cm$

47:

Find the distance between the points C(3,3) and D(-1,5)

A:

$4 \sqrt{17}$

B:

$3 \sqrt{17}$

C:

$4 \sqrt{5}$

D:

$2 \sqrt{5}$

E:

$\sqrt{3}$

48:

The bearing of a town Q from a town P is 0450. Find the bearing of P from Q

A:

0450

B:

0900

C:

1350

D:

1800

E:

2250

49:

Find the mean of $4\frac{1}{2},$, $7$, $6.5$, $8$, $5\frac{1}{2}$, $3.25$, $5\frac{1}{2}$, $1\frac{1}{4}$ and $3\frac{1}{2}$

A:

sdfsdf

B:

sdfd

C:

5

D:

dsfds

E:

9

50:

Find the mode of the data below.

A:

6.7

B:

6.3

C:

5.8

D:

5.2

E:

4.4

51:

A farmland of 160 acres was used in planting various fruits as shown below

Use the information above to answer questions 51 to 53

Find the angle subtended by the sector for pineapples

A:

660

B:

630

C:

530

D:

430

E:

330

52:

What is the percentage of farmland used for planting oranges?

A:

40%

B:

35%

C:

30%

D:

25%

E:

20%

53:

How many acres of land is used in planting guava?

A:

14

B:

16

C:

18

D:

24

E:

34

54:

Find the mean of the data below.

A:

20.5

B:

21.0

C:

21.5

D:

22.0

E:

22.5

55:

The probabilities of two independent events P and Q occurring are $\frac{3}{8}$ and $\frac{2}{5}$ respectively. Find the probability that none of the events will occur.

A:

$\frac{3}{20}$

B:

$\frac{3}{8}$

C:

$\frac{2}{5}$

D:

$\frac{3}{5}$

E:

$\frac{5}{8}$

56:

The table below shows the age distribution of students in a college. Use the information to answer questions 56 and 57

Find the probability that a student selected at random is at least 17 years old.

A:

$\frac{1}{10}$

B:

$\frac{1}{5}$

C:

$\frac{3}{10}$

D:

$\frac{2}{5}$

E:

$\frac{3}{5}$

57:

Find the probability that a student selected at random is either 17 or 18 years old.

A:

$\frac{3}{50}$

B:

$\frac{1}{5}$

C:

$\frac{3}{10}$

D:

$\frac{1}{2}$

E:

$\frac{7}{10}$

58:

Evaluate $\int(9x^{2} - 4x + 2)dx$

A:

x3 - x2 + x + c

B:

x3 + x2 + x + c

C:

3x3 - 2x2 + 2x + c

D:

3x3 + 2x2 + 2x + c

E:

18x3 - 4x2 + 2x + c

59:

Find the derivative of ***

A:

$\frac{x - 2}{(x + 1)^{2}}$

B:

$\frac{2 - x}{(x + 1)^{2}}$

C:

$\frac{-3}{(x + 1)^{2}}$

D:

$\frac{3}{(x + 1)^{2}}$

E:

$\frac{3}{(2x - 1)^{2}}$

60:

Evaluate $\int \frac{dx}{3x + 2}$

A:

In(4x + 2) + c

B:

$\frac{1}{6}In(3x + 2) + c$

C:

$\frac{1}{4}In(3x + 2) + c$

D:

$\frac{1}{3}In(3x + 2) + c$

E:

$\frac{1}{2}In(3x + 2) + c$