2005 NECO Mathematics Past Questions & Answers

Question 1

If A(I,2,3,...,10) ; B = (-5,-4,.....,-1) ; C = (-1, 0, 1, 2,....5) List all the elements in (B ∪ C) ∩ A

Accepted Answer

C. (1,2,..5)

Answer

A. (-1,2,...5)

Answer

B. (-1,1,....5)

Answer

D. (2,3,...10)

Answer

E. (1,2,...10)

Question 2

T varies directly as D and inversely as A. Given that T = 6, D = 3, and A = 2, find A when T = 3 and D = 6.

Accepted Answer

C. 8

Answer

A. 4

Answer

B. 6

Answer

D. 12

Answer

E. 24

Question 3

In Δ ABC, A = 60°, C = 90° and AC = 12m. Find the Length of the hypotenuse.

Accepted Answer

A. 24m

Answer

B. 14m

Answer

C. 12m

Answer

D. 7m

Answer

E. 6m

Question 4

If 2x : ( x + 1) = 3 : 2, what is the value of x?

Accepted Answer

D. 3

Answer

A. $\frac{1}{2}$

Answer

B. 1

Answer

C. 1$\frac{1}{2}$

Answer

E. 3$\frac{1}{2}$

Question 5

Mohammed is 8 years older than Joy now. In five years’ time he will be twice as old as Joy. How old is Joy now?

Accepted Answer

B. 3years

Answer

A. 1$\frac{1}{2}$years

Answer

C. 4$\frac{1}{2}$years

Answer

D. 6 years

Answer

E. 8 years

Question 6

Simplify P-6 × P3 × P2 ÷ P4 × P0

Accepted Answer

E. p-5

Answer

A. p5

Answer

B. p4

Answer

C. p3

Answer

D. p-3

Question 7

A bag contains 4 blue and 8 red identical balls. If two balls are picked at random with replacement, what is the probability of picking two balls of different colours?

Accepted Answer

D. $\frac{4}{9}$

Answer

A. 1

Answer

B. $\frac{13}{26}$

Answer

C. $\frac{5}{18}$

Answer

E. $\frac{2}{9}$

Question 8

A flagpole is placed at the top of a tower. The angles of elevation of the bottom and top of the flagpole from a point on the ground 10m away are 40° and 50° respectively. Find the length of the flagpole.

Accepted Answer

B. 3.5m

Answer

A. 1.8m

Answer

C. 8.4m

Answer

D. 11.9m

Answer

E. 17.3m

Question 9

Two fair dice are tossed together once. What is the probability of getting a total of at least 9 from the outcome?

Accepted Answer

C. $\frac{5}{18}$

Answer

A. $\frac{1}{9}$

Answer

B. $\frac{1}{6}$

Answer

D. $\frac{1}{3}$

Answer

E. $\frac{13}{18}$

Question 10

Find the standard deviation of the numbers 6, 9, 10, 8 and 7

Accepted Answer

A. 1.4

Answer

B. 2

Answer

C. 2.4

Answer

D. 5

Answer

E. 8

Question 11

What is the Value of 11101$_{two}$+ 10011$_{two}$ - 10001$_{two}$?

Accepted Answer

D. 11111$_{two}$

Answer

A. 10001$_{two}$

Answer

B. 10011$_{two}$

Answer

C. 10111$_{two}$

Answer

E. 111111$_{two}$

Question 12

A car dealer sells a car and makes a profit of 15%. If the car costs N320,000.00, how much did he sell the car?

Accepted Answer

D. N368,000.00

Answer

A. N272,000.00

Answer

B. N296,000.00

Answer

C. N300,000.00

Answer

E. N400,000.00

Question 13

What is the positive difference between the squares of 2.5 and 2.1 to 1 significant figures?

Accepted Answer

D. 2

Answer

A. – 2.0

Answer

B. – 184

Answer

C. -1.84

Answer

E. 18.4

Question 14

A ship sails 6km from a port on a bearing 070° and then 8km on a bearing of 040°. Find the distance from the port.

Accepted Answer

B. 13.53km

Answer

A. 7.21km

Answer

C. 16.86km

Answer

D. 44.57km

Answer

E. 67.17km

Question 15

A surveyor measured the length of a obtained 42.55 metres. If his measurement was more than the actual length and the percentage error of his measurement was 8%, calculate the actual length of the land

Accepted Answer

A. 39.40 metres

Answer

B. 46.20 metres

Answer

C. 46.25 metres

Answer

D. 46.50 metres

Answer

E. 48.25 metres

Question 16

The parallel sides of a trapezium are 13cm and 7cm. If the area of the trapezium is 50cm2, find the perpendicular distance between the parallel sides.

Accepted Answer

A. 5cm

Answer

B. 6cm

Answer

C. 7cm

Answer

D. 10cm

Answer

E. 12cm

Question 17

If 7 is subtracted from twice a certain number x, the result is at most 5. What is the range of the number?

Accepted Answer

E. x < 6

Answer

A. x < 2

Answer

B. x < 3

Answer

C. x < 4

Answer

D. x < 5

Question 18

For what value(s) of x is the expression (x2 + 15x + 50) ÷ (x - 5) not defined

Accepted Answer

D. 5

Answer

A. -5, -10

Answer

B. -10

Answer

C. -5

Answer

E. 10, 5

Question 19

Find the value of 2a - b if a + b = 8 and 4a - b = 22

Accepted Answer

E. 10

Answer

A. 2

Answer

B. 4

Answer

C. 6

Answer

D. 8

Question 20

If a = {x : 1 < x < 9} ; b = {x : 0 < x < 9} ; C = {x : 2 x < 9} and a, b, c U, what are the elements in U?

Accepted Answer

B. U = {0 < x < 9}

Answer

A. U = {-1 < x < 9}

Answer

C. U = {1 < x < 9}

Answer

D. U = {1 < x < 10}

Answer

E. {2 < x < 10}

Question 21

A chord 20cm long subtends an angle of 60° at the circumference of a circle, what is the diameter of the circle the nearest cm?

Accepted Answer

C. 23cm

Answer

A. 12cm

Answer

B. 20cm

Answer

D. 60cm

Answer

E. 80cm

Question 22

Find the Iength of a diagonal of a square whose area is 288cm2.

Accepted Answer

A. 24cm

Answer

B. 48cm

Answer

C. 95cm

Answer

D. 100cm

Answer

E. 124cm

Question 23

Calculate without using tables Tan 45° + Cos 60°

Accepted Answer

C. 1$\frac{1}{2}$

Answer

A. $\sqrt{\frac{3}{2}}$ - 1

Answer

B. $\frac{1}{2}$

Answer

D. $\sqrt{\frac{3}{2}}$ + 1

Answer

E. 2

Question 24

A is at 50°N and B is at 10°N, If A and B are on the same longitude, find the distance AS. Correct your answer to Four significant figures. (Earth radius = 6400km)

Accepted Answer

C. 4470km

Answer

A. 6468km

Answer

B. 5469km

Answer

D. 3470km

Answer

E. 2488km

Question 25

Find the absolute mean deviation of the sample 10, 12, 14, 11, 13.

Accepted Answer

E. 1.2

Answer

A. 14.6

Answer

B. 14

Answer

C. 12

Answer

D. 6.2

Question 26

If 25a2 = 5-1 × 125. Find the value of a?

Accepted Answer

C. a = ±1

Answer

A. a = -1

Answer

B. a = 1

Answer

D. a = ±5

Answer

E. a = 25

Question 27

If (x - a) is a factor of bx - ax + x2 - ab, what is the other factor?

Accepted Answer

A. (x + b)

Answer

B. (b - a)

Answer

C. (x - a)

Answer

D. (a + b)

Answer

E. (a - b)

Question 28

Evaluate 0.0025 × 2.5 × 102 to 2 significant figures.

Accepted Answer

E. 6.3 × 10-1

Answer

A. 0.625 × 10-3

Answer

B. 0.63 × 10-2

Answer

C. 6.25 × 10-3

Answer

D. 6.3 × 10-2

Question 29

If log 3 = 0.4771 and log 2 = 0.3010, what is the value of log 12?

Accepted Answer

C. 1.0791

Answer

A. 0.0432

Answer

B. 0.4322

Answer

D. 1.2552

Answer

E. 1.5225

Question 30

3 - 7, 8 - 12, 13 - 17, 18 - 22. Which of the following is/are true? I. The class Interval is 4 II. The class boundaries are 2.5, 7.5, 12.5, 18.5, 22.5 III. The mid-marks are 5, 10, 15, and 20

Accepted Answer

C. III only

Answer

A. I only

Answer

B. II only

Answer

D. I and II only

Answer

E. I and III only

Question 31

Solve for x in the quadratic equation. 2x2 + 12x + 10 = 0

Accepted Answer

A. x = -5, -1

Answer

B. x = -5,1

Answer

C. x = -3, -2

Answer

D. x = 3, 2

Answer

E. x = 6, 5

Question 32

If y2+ 14y + k is a perfect square, then k =

Accepted Answer

D. 49

Answer

A. 4

Answer

B. 7

Answer

C. 28

Answer

E. 196

Question 33

Simplify (6 - x - x2) ÷ (x2 - 4)

Accepted Answer

D. (3 - x) ÷ (x + 2)

Answer

A. (3 + x) ÷ (x + 2)

Answer

B. (x - 3) ÷ (x - 2)

Answer

C. (x - 3) ÷ (x + 3)

Answer

E. (3 - x) ÷ (x - 2)

Question 34

If x + $\frac{1}{x}$ = 8, find x$^2$ + $\frac{1}{x^2}$

Accepted Answer

B. 62

Answer

A. 64

Answer

C. 32

Answer

D. 16

Answer

E. 4

Question 35

Evaluate log 18 + log6 - log16$^{\frac{1}{2}}$

Accepted Answer

E. 3 log 3

Answer

A. log 3

Answer

B. log 9

Answer

C. log 20

Answer

D. 3 log 2

Question 36

The diagonals of a rhombus are 6cm and 8cm. Find the area of the rhombus.

Accepted Answer

C. 24cm2

Answer

A. 96cm2

Answer

B. 48cm2

Answer

D. 0.14cm2

Answer

E. 12cm2

2005 NECO Mathematics Past Questions

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