# NECO Mathematics Questions And Answers For 2023 | Theories And Objectives

NECO Mathematics Questions and Answers for 2023 Theories and Objectives.

It has become very obvious that a lot of NECO candidates have been anxious to know the NECO mathematics questions and answers for 2023 before entering the examination so as to perform pass the examination as they desire.

For this reason, I have decided to go a very long way to get the 2023 NECO Mathematics Questions and their respective answers to help the general public who will be sitting for this examination. This is an article that not NECO candidate would want to miss.

Note: The following are not for the 2023 examination. It is for 2022

1 – 20: CBBCDCCBDCBDABDDCDDB

21 – 40: BBDCDBADBACCABCEDAC (NO correct Ans for 33)

## NECO Mathematics Theory Questions for 2023

The following are the theory questions for 2022 NECO mathematics examination:

1(a) Without using mathematical tables,

find the value of log10 6 + log1045 – log10 27.

(b) Solve the equation 8x=  32.

(c) Simplify 811/6/27-1/9

(8marks)

2(a) A straight line passes through the points A(3, 0) and B(2,-1). Find the:

• (ii) Equation of the line

(b) ABCD is a parallelogram with /AD/=8 cm, /AB/ =6 cm and ABC = 60°. Calculate, correct to 3 significant figures, the area of

(i) Triangle ABC

(ii) Parallelogram ABCD

(8marks)

3(a) A village P is 12 km from village Q. It takes 3 hours 20 minutes to travel from Q to P and back to Q by a boat. If the boat travels at a speed of 6 km/h from P to Q and (6+x) km/h back to P, find the value of x.

(b) Find the quadratic equation whose roots are 2/3 and 3/4

(8marks)

4(a) Differentiate y = x2/1 + x2 with respect to x.

(b) Solve the equation 2/3(3x+2)=2/4(2x-3).

(8marks)

5(a) The table below shows the mass of logs of wood to the nearest kilogramme.

Calculate the:

• Mean
• Mode

(8marks)

#### PART II

Attempt five questions only in this part.

6(a) If the 2nd term of a Geometric Progression (G.P.) is 6 and the 4th term is 54, find the:

• 1st term
• (ii) 5th term

(b) In a school of 160 pupils, 75 have pencils, 87 have pens and 93 have rulers. 25 have both pencils and pens, 30 have both pencils and rulers while 47 have both pens and rulers. Each pupil has at least one of the three items.

(i) Draw a venn diagram to illustrate this information.

(ii) How many pupils have pencils only?

(12marks)

7(a) Use the information in the figure below to find the value of x.

(b) A boat sails 6 km on a bearing of 040° and then 8 km on a bearing of 100o.

(i) How far is the boat from its starting point?

(ii) Calculate the bearing of the boat from its starting point.

(12marks)

8(a) Find the area enclosed by the curve y = 2x² +3, the x-axis and the ordinates x=2, x=1.

(b) In a community, men contribute Np each and women Nq each towards the Community Development Fund. In a week, 3 men and 5 women contributed a total of N9,500.00. In another week, 5 men and 10 women contributed a total of N17,500.00. Find the:

(i) Value of p and q

(ii) Total amount that will be contributed by 8 men and 12 women

(12marks)

9. An aircraft flies from P(12°N, 11°W) to Q(12°N, 11°E) in 2 hours and then changes its course and arrives at S(44°N, 11°E) in 6 hours after leaving Q. Calculate, correct to 3 significant figures, the:

(a) Total distance covered

(b) Average speed of the aircraft

(c) Time difference between Q and S

(Use π = 3.142 and R=6,400 km)

10(a) Copy and complete the table below for the relation y = x2 -2x-3.

(b) Draw the graph of the relation in (a) above using a scale of 2 cm to 1 unit on x-axis and 1cm to l unit on y-axis. Hence, determine the roots of x2 -2x-3=0.

(c) Using the same axis, draw the graph of y=2-2x.

(d) Deduce the roots of the equation x2 -2x-3=2-2x.

(e) Find the minimum value of y= x²-2x-3.

(12marks)

11 (b) The first and last terms of an Arithmetic Progression (A. P.) are 5 and 89 respectively.

If the sum of the A. P. is 611, find the:

(i) Number of terms in the A. P.

(ii) Common difference

(12marks)

12. The score of 30 students in a Biology test are given below;

40      74      12      27      34      26

32      77      14      20      11      31

51      52      19      65      35      30

19      50      21      38      43      24

52      64      10      27      90      32

(a) (i) Construct a frequency table with class interval 1 – 20, 21 – 40…

(ii) Using an assumed mean of 30.5, calculate the standard deviation of the distribution.

(b) Find the probability that a student selected at random scored above 60 marks.

(12marks)

## NECO Mathematics Objective Questions

The following are the kinds questions that you are likely going to see in your 2023 NECO Mathematics Examination. Do yourself a favour by studying them very if you really want to make good grade in your result.

1. Express 0.001025 in standard form

A. 1.025X10-5

B. 1.025X10-4

C. 1.025X10-3

D. 1.025X10-2

E. 1.025X10-1

2. Find the positive difference between rounding off of 3,847,934,000 to the nearest billion and million

A. 150,000,000

B. 152,000,000

C. 200,000,000

D. 250,000,000

E. 252,000,000

3. Evaluate (1/81)-1/2/0.3 x (0.09)1/2

A. 81

B. 9

C. 3

D. 1/3

E. 1/9

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4. Simplify (0.027)1/3 x (0.09)-3/2

A. [3/10]-2

B. [9/10]-2

C. [3/10]1/2

D. [3/10]2

E. [3/10]4

5. A particular bank 50k dividend per share. What would be the percentage yield for a customer who invested N5.00 per share?

A. 1

B. 2

C. 5

D. 10

E. 50

A. 2.8X10-2

B. 2.8X10-1

C. 2.8X100

D. 2.8X101

E. 2.8×102

7. The cost of a motorbike is N110,000.00. If the value depreciates by 10% yearly, what will be its value at the beginning of the following year?

A. N11,000.00

B. 88,000.00

C. N99,000.00

D. N108,900.00

E. N121,000.00

8. A and B are sets such that n(A) = 26, n(B) = 19 and n(AՈB)=11. Find n(AUB).

A. 30

B. 34

C. 37

D. 45

E. 56

9. 2y1/4 – 5 = -1, find the value of y

A. 1/16

B. 1/8

C. ½

D. 16

E. 81

10. Solve the equation (23x)1/2 = 1/0.25

A. 2/3

B. ¾

C. 1 1/3

D. 2

E. 3

11. How many years will N100,000.00 amount to #180,000.00 at 5% simple interest per annum?

A. 4

B. 16

C. 20

D. 36

E. 50

12. If y is a whole number such that 3y+4=7 mod 8, find the value of y.

A. 1

B. 2

C. 3

D. 4

E. 5

13. The 3rd and 7th terms of a Geometric Progression (G.P.) are 72 8

and 8/9 respectively.

Find the 1st term.

.A. 720

B. 648

C. 567

D. 288

E. 216

14. In a class of 30 students, every student has at least a ruler. If 25 students have white rulers and 20 students yellow rulers, how many students have rulers of both colours?

A. 55

B. 50

C. 45

D. 15

E. 10

15. Five numbers form a Geometric Progression (G.P.). If the 2nd and 5th numbers are 9 and 243 respectively, find the common ratio.

A. -9

B. -3

C. 2

D. 15

E. 10

16. The first and last terms of an Arithmetic Progression (A.P.) are -2a and 38a respectively. Determine the number of terms if its common difference is 5a.

A. 7

B. 8

C. 9

D. 8a

E. 9a

17. On Clara’s tenth birthday, she began to save N2,000.00 every year in a kidsave account with an annual interest rate of 20% compounded annually. What will be the worth of the account when she turns 18?

A. N8,599.63

B. N20,799.00

C. N32,998.17

D. N41,597.80

E. N46,000.00

18. The cost (C) of a car service is partly constant and partly varies with the time (T) it takes to do the work. If it costs N500.00 for a 2-hour service and N300.00 for an hour service, find the cost of a 3-hour service.

A. N600.00

B. N650.00

C. N680.00

D. N700.00

E. N800.00

20. Find the gradient of a line joining the points (-5, -6) and (5, -2).

A. 1/4

B. 2/5

C. 1/2

D. 1  1/3

E. 1 ½

20. Given that    e: ABCD is a rhombus.

f: ABCD is a rectangle.

h: ABCD is a square.

Which of the following statements represents e ˄ f↔h?

A. ABCD is a rectangle if it is a square and rhombus.

B. ABCD is a square and only if it is a rhombus and rectangle.

C. ABCD is a square if and only if it is not a rhombus and rectangle.

D. ABCD is a rectangle if and only if it is not a square and rectangle.

E. ABCD is a rhombus if it is not a rectangle and square.

21. Solve the simultaneous equation, 2a + 3b = 5, 2a + b = 1

A. a = -1/2, b = -2

B. a = ½, b = 2

C. a = ½, b = -2

D. a = -1, b = 2

E. a = 2, b = ½

22. Solve the equation, (2x-1)/2 – (3x-2)/3 = x/2

A. -3

B. -7/3

C. -1/3

D. 1/3

E. 3

23. Determine the equation whose product and sum of the roots are -4.5 and -3.2 respectively.

A. 10x2 – 32x – 45 =0

B. 10x2 + 32x + 45 = 0

C. 10x2 + 32x – 45 = 0

D. 10x2 + 16x – 9 = 0

E. 10x2 – 16x – 9 = 0

24. If p: x is an even number. q: x is a multiple of 3.

What does ~(p˄q) stand for?

.A. x is an even number and a

multiple of 3

B. x is an even number or a multiple of 3

C. x is not a multiple of 3 and is even

D. It is false that x is even and a multiple of 3

E. x is not an even number and not a multiple of 3

25. Solve the inequality x <x/3 + 4.

A. x < 12

B. x<6

C. x<4

D. x < 3

E. x<-12

26. Simplify a²-4a+3/a2-a-6

A. a-1/a+2

B. a+1/a-2

C. 1-a/a+2

D. a-1/a-2

E. a+1/a+2

27. The roots of a quadratic equation are -2 and¹. 3 Find the equation.

A. 3x²+5x+2=0

B. 3x²-5x+3=0

C. 3x²-5x-2=0

D. 3x²+5x-2=0

E. 3x²-5x-3=0

28. If x α 1/y2 and x = 4 when y = 3, find the value of x when y = 2.

A. 18

B. 9

C. 4

D. 3

E. 1

29. Make b the subject of the formula d = √ab/c –c2b.

A. b = cd2/a-c3

B. b = d2 /a-c3

C. b = d2/ c² -a

D. b = cd /a – c3

E. b= a –c3 /cd2

30. If u: I like bread with butter.

v: I like lemon for tea.

Translate “I like lemon for tea, but not bread with butter” into symbol.

A. u ˄ v

B. v ˅ u

C. v ˄~u

D. ~u ˅ v

E. u˅ ~ v

Use the graph below to answer questions 32 and 33.

31. Determine the solutions of the curve.

A. x=-1.2 or 3.2

B. x=-1.3 or 3.4

C. x=-1.4 or 3.5

D. x=-1.5 or 4.0

E. x=-1.5 or 5.0

32. Find the least value of y.

A. -5.2

B. -5.1

C. -4.5

D. -1.4

E. 3.5

33. If cosα= 3/5 and 0″ < a < 90°, evaluate 3 cosα – 2 sinα

A. 1/5

B. 2/5

C. ½

D. 3/5

E. 4/5

35. The bearing of Y and Z from X are 061° and 110° respectively. Calculate YZ if |YX = 3 cm and XZ = 5 cm, correct your answer to 2 significant figures.

A. 3.7 cm

B. 3.8 cm

C. 4.0 cm

D. 4.1 cm

E. 5.0 cm

36. The curved surface area of a hemisphere is 7,700 cm². Find its diameter.

(Take л=22/7)

A. 17.5 cm

B. 35.0 cm

C. 70.0 cm

D. 70.5 cm

E. 87.7 cm

37. In the figure below, PQ is a diameter of the circle PSQR with centre O. If PQS = 65°, find QRS.

.A. 115°

B. 90°

C. 65°

D. 40°

E. 25o

38. In the diagram below, MKLN is a cyclic quadrilateral and the diagonals ML and KN intersect at X. If NML = 40° and MXK = 80°, calculate MLK.

A. 100°

B. 80°

C. 60°

D. 40°

E. 20°

39. Find the y-intercept of the line 4y+3x-2= 0.

A. -2

B. -3/4

C. – ½

D. ½

E. 2

40. The angle of a sector of a circle is 295°. If the area of the sector is 35.2 cm², calculate its radius to 2 decimal places.

22 (Take π= 22/7)

A. 2.10 cm

B. 3.45 cm

C. 3.70 cm

D. 4.31 cm

E. 5.71 cm

41. Find the angle between two straight lines whose slopes are 4 and 5, correct to 1 d.p.

A. 2.5°

B. 2.6°

C. 2.7°

D. 2.8°

E. 2.9°

42. If the radius of a parallel of latitude is 4,500 km, find the latitude correct to the nearest degree. (Take R = 6,400 km)

A. 45° East or West

B. 45° North or East

C. 45° North or South

D. 50° East or West

E. 50° North or South

43. In the diagram below MNO is a tangent to the circle. Calculate PÑO.

A. 135°

B. 128°

C. 97°

D. 83°

E. 77°

44. A sphere has a radius of 7 cm. Find its surface area.

A. 616 cm²

B. 206 cm²

C. 205 cm²

D. 154 cm²

E. 88 cm²

45. Calculate the perimeter of a sector whose radius is 21 cm and its angle at the centre is 150°.

A. 2310 cm

B. 1310 cm

C. 210 cm

D. 105 cm

E. 97 cm

46. Find the equation of a line that passes through the point (1, 2) whose gradient is 1/3

A. 3y+x=7

B. 3y-x=-5

C. 3y-x=7

D. 3y-x=5

E. y-3x=7

47. Calculate the area of a circle of radius 3.69 cm, leaving your answer in 2 significant figures.

(л = 22/7)

.A. 11 cm²

B. 12 cm²

C. 23 cm²

D. 42 cm²

E. 43 cm²

48. Calculate the circumference of the parallel of latitude 60°S correct to 3 significant figures.

(Take R = 6,400 km and л = 22/7)

A. 20,000 km

B. 20,100 km

C. 20,110 km

D. 20,114 km

E. 40,200 km

49. Find the mean score of ten students if the variance of their scores is 8 and ∑x2 = 2040.

A. 2.82

B. 11.83

C. 14.00

D. 45.14

D. 64.00

50. The mean of five numbers is 6. If the numbers are 1, 6, x, 8, 7, what is the mode?

A. 1

B. 5

C. 6

D. 7

E. 8

51. Which of the following is not a measure of dispersion?

A. mean deviation

B. median

C. percentile

D. standard deviation

E. variance

52. The standard deviation of the ages of 10 students is 1.2. What is the variance?

A. 3.46

B. 3.16

C. 2.80

D. 1.86

E. 1.44

Use the cumulative frequency curve below to answer questions 53 to 55.

53. Find the median value.

A. 50.0

B. 34.5

C. 30.5

D. 25.0

E. 10.0

54. Calculate the 6th decile.

A. 50.0

B 40.0

C. 45.5

D. 36.0

E. 20.0

55. Determine the 80th percentile.

A. 60.5

B. 55.5

C. 45.5

D. 40.5

E. 35.5

Use the information below to answer questions 56 and 57.

The table below shows the age distribution of students in a school

choir.

56. How many students are in the school choir?

A. 10

B. 15

C. 20

D. 25

E. 30

57. What is the modal age?

A. 6

B. 8

C. 10

D. 15

E. 17

58. Differentiate 3x² -7x-4 with respect to x.

A. 3x³-7x²-4

B. x3 – 7x2/3 – 4x

C. 6x2-7

D. 6x-7

E. 7x-4

59. If y=x(x³ −x+1), evaluate ʃ1-1  ydx.

A. -4/15

B. 0

C. 11/15

D. 1

E. 3

60. What is the value of ʃ’0 (1–2x)2 dx?

A. -1/8

B. -1/4

C. 0

D. 1/3

E. 4

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### Tips on How to Pass NECO Mathematics Examination

I have heard many times as some students complain about how tough NECO mathematics used to be. But coming to check this very well, NECO mathematics examination is not usually hard as most candidates do conclude.

They are feeling that the subject is too hard because they have not gotten the right guides on how to answer NECO mathematics and get their desired scores.

In this section of this article, I will be giving you a bonus which is the tips on how to pass NECO mathematics examination. Once you can apply the principles that I am going to reveal to you in this article, your ‘A’ grade is guaranteed.

See the tips as follow;

A lot of candidates do overlook the given instructions and always delve into answering the main questions. Of course, this is not a good practice.

Once you have entered the NECO Mathematics examination hall and you have been provided with the question paper and answer booklet, it is very important that you first of all go through the given instructions.

Not only reading the instructions, you are mandatorily required to follow the given instructions strictly till the end of the examination so as to avoid any mistake that will cost you your score.

2. Start from the Easiest

In every examination, it is always noticed that all the questions are usually not the same in terms of the simplicity/complexity. In a condition where you have noticed that some of the NECO mathematics questions are easy while some are complex, what you have to do is to start from the easiest to the most complex ones.

What are the benefits of doing this?

By answering the easy ones as fast as possible, you are going to create enough time for yourself to think very well before you will start to answer the complex ones.

Also, you will be able to develop confidence to answer the assumed complex questions. This is because sometimes when the questions seem to be too hard for the candidate, fear will set in, thereby resulting to examination tension which is an hindrance to candidate’s excellent performance.

In NECO mathematics examination, this is another important aspect that every candidate has to take very serious. You must ensure that you finish all the required questions before submitting your answer booklet.

While you are about to submit, you have to cross check and review your answers to be sure that they complete and that you have supplied the right answers to every questions respectively.

Get more tips: How to Pass your NECO Examination at One Sitting

With these tips applied correctly during you NECO mathematics examination, you will be sure of making an ‘A’ at the end of the examination.

I hope that you have enjoyed reading this article. If you need any other assistance on NECO Mathematics Questions and Answers 2023 | Theories and Objectives, kindly drop your questions using the comment section below.