Are you writing the National Examination Council also know as NECO, if yes, you need the NECO Further Mathematics Past Questions and Answer which include Paper II (Essay) and Paper III (Objective).

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**General Instruction for NECO Past Questions in Further Mathematics**

- Use HB pencil throughout.
- Use of mobile phone is not allowed.
- Use of scientific calculator is allowed.
- Complete the top section of your answer sheet as follows:

(a) In the space marked Candidate’s Name, write your surname in capital letters followed by your other names.

(b) In the space marked School Name, write the name of your centre, and in the space marked Subject Name, write FURTHER MATHEMATICS III.

(c) In the box marked Subject Code, write the digits 1023 in the spaces. There are numbered spaces in line with each digit. Shade carefully the space with the same number as each digit.

(d) In the box marked Examination Number, write your examination number in the spaces at the top of the box. Shade the corresponding numbered spaces in the same way as for Subject Code.

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## Further Mathematics NECO Objective Question

**Further Mathematics**

Paper III (Objective)

- Find the quotient when x
^{3}+ 1 is divided by x+1.

A. x^{2}-1

B. x^{2}-x-1

C. x^{2}+x+1

D. x^{2}-x+1

E. x^{2}+x-1

- The operation * on die set R of real numbers is defined by:

x*y = 3x + 2y-l; x, y R. Determine -4*5.

A. 5

B. 4

C. 3

D. -3

E. -4

- If n = log 0.00058, find the value of n.

A. 4.7634

B. 4.5800

C. 0.7634

D. 4.5800

E. 4.7634

- Find the coefficient of the 6
^{th}term in the expression of (p + q)^{9}

A. 160

B. 157

C. 146

D. 144

E. 126

- Two places on the same latitude 20°S lie respectively on longitudes 12°E and 82°E. Find their distance apart measured along the line of latitude.

(Take ? = 22/7, R = 6400Km)

A. 7822 km

B. 7350 km

C. 5250 km

D. 3911 km

E. 3675 km

- Given that T = 3P
^{2}, find the increase in T when P increases from 4 to-4.02.

A. 0.02

B. 0.28

C. 0.48

D. 0.68

- If A and B are the only subsets of U and they are not disjoint, then (AnB)
^{1}is a set of all elements of U that are in

A. A but not in B.

B. B but not in A.

C. either A or B but not both.

D. either A or B or both.

E. neither A nor B.

- Divide the polynomial 25x
^{4}— 9x^{2}by 5x^{2}— 3x

A. 5x^{2}+ 3x

B. 5x^{2}– 3x

C. 5x + 3

D. 5x – 3

E. 5x^{3}– 3x^{2}

- Which of the following values of satisfies the equation

sin + sin^{2}= 0?

I 0°

II 90°

III 180°

A. I only

B. I and II only

C. I and III only

D. I, II and III only

E. II and III only

- Differentiate (3x + 2)
^{2}with respect to x.

A. 9x + 4

B. 12x + 9

C. 14x – 6

D. 16x + 12

E. 18x + 12

- Find the magnitude of the resultant of two vectors x and y having the same magnitude of 15 units and inclined at an angle of 120° to each other.

A. 5 units

B. 7.5 units

C. 10 units

D. 12 units

E. 15 units

- A bus leaves Minna at 6:20am and arrives Anambra at 3:45pm. What is the average velocity to the nearest whole number if the journey is 900 km?

A. 69 kmh^{-1}

B. 87 kmh^{-1}

C. 96 kmh^{-1}

D. 100kmh^{-1}

E. 150 kmh^{-1}

- Forces of magnitudes 3 N, 5 N and 7 N acting on a particle are in equilibrium. Find the angle between the forces with magnitudes 3 N and 7 N to the nearest degree.

A. 22°

B. 38°

C. 120°

D. 142°

E. 158°

- A body is projected with an initial velocity of 30ms
^{-1}at an angle of 26° to the horizontal. Calculate the vertical component of the velocity after one second.

A. 2.51ms^{-1}

B. 3.05ms^{-1}

C. 3.15ms^{-1}

D. 4.15ms^{-1}

E. 4.51ms^{-1}

- A force of 150 N is the resultant R of the two forces x and y. If x = 60 N and makes an angle of 50° to R, find the magnitude of y.

A. 110.5 N

B. 120.5 N

C. 130.7 N

D. 140.8 N

E. 150.9 N

- A constant force F of magnitude 88.2N is applied to a body of mass 9.8 kg. If die body starts from rest, what velocity does it attain after 4 seconds?

A. 9ms^{-1}

B. 13ms^{-1}

C. 18ms^{-1}

D. 27ms^{-1}

E. 36ms^{-1}

- If the probability that Musa will score a goal in a match is 0.8 and the probability that Ighalo will score in the same match is 0.4, what is the probability that both of them will score?

A. 0.12

B. 0.16

C. 0.20

D. 0.24

E. 0.32

- Find the area between Z = 0.37 and Z = 1.92.

A. 32.83%

B. 43.94%

C. 48.90%

D. 58.92%

E. 61.69%

- Three hunters shoot at a target. The probabilities that the three of them hit the target are 2/3 1/4 and 1/5 respectively. Find the probability that only one hits the target.

A. 17/36

B. 19/44

C. 1/3

D. 13/44

E. 1/10

Use the information below to answer questions 49 and 50.

A fabricator discovers that the cost of operating his welding machine whose initial cost is N120,000.00 for 6 consecutive years are as given below:

Year | 1 | 2 | 3 | 4 | 5 | 6 |

Running cost | 1,700 | 2,500 | 3,200 | 4,700 | 5,600 | 6,500 |

Resale value | 110,000 | 90,000 | 85,000 | 72,000 | 65,000 | 52,000 |

- Find the capital cost at the end of the 4
^{th}year.

A. N32,000.00

B. N35,000.00

C. N42,000.00

D. N48,000.00

E. N55,000.00 - What is the total cost at the end of the 2
^{nd}year?

A. N11,700.00

B. N32,000.00

C. N32,500.00

D. N35,300.00

E. N38,200.00

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