**NECO Mathematics Questions and Answers – Objective and Theory 2021/2022.**

**NECO Mathematics Questions and Answers: Below is the National Examination Council (NECO) Mathematics questions 2021 and the complete NECO 2021 Mathematics answers 2021 free expo runs for candidates.**

**This is an expo material for NECO Mathematics questions 2021 for both theory and OBJ answers 2021. The material covers NECO 2021 Mathematics answers for paper 1 (objectives) and paper 2 (essay).**

**NECO Math Expo**

NECO candidates are to use this material to pass their *NECO Mathematics exam* for free. With this, you will know the possible 2021 NECO questions that you will see in this Mathematics 2021 exam.

The *National Examination Council* is an examination body in Nigeria that conducts the Senior Secondary Certificate Examination and the General Certificate in Education in June/July and November/December respectively.

**NECO Mathematics Objective (OBJ) Answers to questions for 2021**

The NECO Mathematics OBJ questions are those set of questions that are usually accompanied by 4 or 5 different options like (A, B, C, D, or E), and each of these questions has just one correct option. They are called multiple-choice questions.

Below are some of the NECO Mathematics objective questions and answers. They are sample questions gotten from NECO Mathematics past questions and answers.

Please, these questions are not the actual questions for this year’s exam but there are NECO 2021 possible questions and answers for Mathematics.

**1. Evaluate log _{9}27**

- x =1
^{1}/3 - x = 1½
- x =2½
- x =2
^{1}/_{3} - x =1
^{2}/_{3}

**The correct answer is B. x =1½; **scroll to bottom to see working…

**2. Solve log _{5}0.04**

- r =-1
- r =+1
- r =-2
- r= +2
- r =-
^{1}/_{25}

**Correct answer is C. r =-2; **scroll to bottom to see working…

**3. Solve 2x ^{2 }+ 9x =5.**

- x = ½ or x = -5
- x = -½ or x = -5
- x = -½ or x = 5
- x = ½ or x = 5
- x = 1 or x = 5

**The correct answer is A. x = ½ or x = -5; **scroll to bottom to see working…

**4. Solve 3x ^{2} –xy = 0 and 2y – 5x = 1 simultaneously**

- (0, ½) and (1, 2).
- (2, ½) and (2, 3).
- (1, ½) and (1, 2).
- (0, ½) and (1, 3).
- (0, ½) and (2, 4).

**The correct answer is D. (0, ½) and (1, 3); **scroll to the bottom to see working…

5. An item is marked ‘cost N7000 VAT inclusive’. If the rate of VAT is 5%, how much VAT does the Government receive?

- N333
^{1}/_{3} - N323
^{1}/_{2} - N331
^{1}/_{3} - N332
^{1}/_{2} - N313
^{1}/_{3}

**The correct answer is A. N333 ^{1}/_{3}**; scroll to the bottom to see working…

**6. Use the chain rule to differentiate (3x + 8) ^{6}**

- 18 (3x + 8)
^{5} - 8 (3x + 8)
^{5} - 18 (3x + 8)
^{6} - 16 (3x + 5)
^{8} - 18 (3x + 8)
^{5}

**The correct answer is = B. 8 (3x + 8) ^{5}**; scroll to bottom to see working…

**7. Find the equation of the tangent to the curve y = x ^{2} – 4x + 3 at the point (3, 1).**

- y = 5x – 2
- y = 2x + 5
- y = 3x + 4
- y = 4x – 3
- y = 2x – 5

**The correct is E. y = 2x – 5; **scroll to bottom to see working…

**8. Factorize this 5y2 + 2y – 3a2?**

- (y + a) (5y – 3a)
- (5y + a) (y – 3a)
- 5y2 + a (2y – 3a)
- (y – a) (5y + 3a)
- (5y – a) (y + 3a)

**Solution Solving: **5y 2 + 5ay – 3ay – 3a 2

5y(y + a) – 3a(y + a)

(y + a) (5y – 3a)

**Therefore the Correct Answer is A**

9. The radius of a circle of latitude is 6370km and Abidjan is 40 west of Accra but on the same circle of latitude. Calculate how far Abidjan is west of Accra.

The answer should be corrected to the nearest kilometer. [π = 22/7]?

- 222km
- 5005km
- 890km
- 445km
- 10010km

**Solution Solving to question 9:** θ/360 * 2πr = Rcos4o = 4/360 * 40041/1 = 445km

**Therefore, the answer is D**

10. Find the area of the curved surface of the cone if the cone is made from a sector of a circle that has a radius of 14cm and an angle of 90. (x = 22/7)?

- 308cm
^{2} - 22cm
^{2} - 154cm
^{2} - 38.5cm
^{2} - 77cm
^{2}

**Solution Solving: **Length of arc = θ/360 * 2πr => r = 90/360 * 14/4 = 3.5

slant height t = 14cm

curved surface area of cone = πrl

=> 3.142 x 3.5 x 14 = 153.95

**Therefore, the answer is C**

11. Find the size of the angle of the sector if a rope of length 18m is used to form a sector of a circle of radius 3.5m on a school playing field.

Correct your answer to the nearest degree.

- 33
^{0} - 180
^{0} - 90
^{0} - 40
^{0} - 270
^{0}

**Solution Solving: **Circumference = 2πr

2 x 22/7 x 3.5 ≅ 22m, 22m = 360

11m = 360/22 x 11 = 180^{0}

**The correct answer is B.**

**12. Find Q ∩ P if P = (all odd numbers from 1 to 10) and Q = (all perfect squares less than 30)?**

- (1, 9)
- (1, 4, 9, 16, 25)
- (1, 3, 4, 5, 7, 9, 16, 25)
- (1, 3, 5, 7, 9)
- E. Φ

**Solution Solving: **The only numbers that intersect between all odd numbers from 1 to 10 and all perfect squares that are less than 30 are [1 & 9]

**Therefore, the answer = A **

**See Also:** NECO Time Table

**Sample NECO Mathematics Theory Questions 2021 (Paper 2)**

Below are the sample NECO Mathematics theory questions 2021. They are essay questions gotten from last year’s exam. Study them effectively because they might be repeated in this year’s NECO Mathematics exam.

**1. Evaluate log _{9}27**

**Solution; let’s assume ^{x} = log_{9}27**

Then 9^{x }= 27

Therefore, (3^{2})^{x} = 3^{3}

3^{2x }= 3^{3}

Divide it through by the coefficient of 2^{x}

i.e. 3^{2x }/3 = 3^{3}/3

= 2x = 3 (equating indices) and x =1½

**2. Solve log _{5}0.04**

**Solution: **Let ^{r} be = log_{5}0.04, then 5^{r = }0.04 = ^{1}/_{25} = 5^{-2 }(equating indices)

Hence r = -2 Ans.

**3. Solve 2x ^{2 }+ 9x =5.**

**Solving solution: **2x^{2 }+ 9x =5

2x^{2 }+ 9x -5 =0

(2x – 1) (x + 5) = 0

Either 2x – 1 = 0 or x + 5 = 0

Therefore 2x = 1 or x = -5 so, x = ½ or x = -5 Ans.

**4. Solve 3x ^{2} –xy = 0 and 2y – 5x = 1 simultaneously**

**Solution solving**

3x^{2} – xy = 0 ———————- equation 1

2y – 5x = 1 ———————-equation 2

From equation 2, we have 2y = 1 + 5x

Y = ½ (1 + 5x) ——————-equation 3

Substitute ½(1 + 5x) for y in equation 1

3x^{2} – x [½(1 + 5x)] = 0

3x^{2} – ½x – 2½x^{2} = 0

½x^{2} – ½x = 0

½x (x – 1) = 0

Therefore, x =0 or x =1

**Substituting for x in equation 3**

When x =0, y = ½(1 + 5 X 0) = ½

And, when x =1, y = ½(1 + 5 X 0) =3

**Therefore, the solutions are x =0 and y =½**

x =1 and y =3

Or, in ordered pairs (0, ½) and (1, 3) Ans.

**5. An item is marked ‘cost N7000 VAT inclusive’. If the rate of VAT is 5%, how much VAT does the Government receive?**

**Solution: **The price tag means that a 5% VAT surcharge is included in the total price. Thus N7000 represents 105% of the actual cost of the item.

105% of the cost price =N7000

1% of the cost of the item = N7000/105

5% of the cost (i.e. the VAT) =N7000/105 X 5

=N333 ^{1}/_{3 }Ans.

**6. Use the chain rule to differentiate (3x + 8) ^{6}**

**Solution:** Let y = (3x + 8)^{6 }and t = 3x + 8 then,

y = t^{6}, dt/dx =3 and dy/dt =6t^{5}

By the chain rule, we have; dy/dx = dy/dt X dt/dx

= 6t^{5} X 3

= 6 (3x + 8)^{5} X 3

= 18 (3x + 8)^{5 }Ans.

**7. Find the equation of the tangent to the curve y = x ^{2} – 4x + 3 at the point (3, 1).**

**Solution:** y = x^{2} – 4x + 3

= dy/dx = 2x – 4, the gradient function.

If x = 3, the gradient of the curve at this point is 2 X 3 – 4 =2

Hence, the gradient of the tangent at x=3 is 2, i.e. the same as the gradient of the curve. The equation of the tangent is, y-1/x-3 = 2

- → y – 1 = 2(x-3)
- → y = 2x – 5 Ans.

**2021 NECO Exam Scheme and Format for Mathematics.**

The NECO Mathematics exam will be in two papers (paper 1 and paper 2).

- PAPER 1: Consist of compulsory questions which would last for fifty (50) minutes and carry fifty (50) marks. Each question has multiple-choice options ranging from A to D or E and only one of the options is to be selected for each question.
- PAPER 2: Paper 2 known as theory paper is a “show working paper”. Candidates are to answer the questions by solving them on the essay solving sheet. All solving steps are to be properly shown on the working sheet.

**Success hints:**

Check out the NECO 2021 Mathematics syllabus and area of concentration and make sure you cover all the topics listed there because they are the topics NECO will set Mathematics questions 2021 from.

- Go to the exam hall early.
- Use only HB pencil to shade your OBJ answers.
- Show working in all the theory questions.
- Go with your Math set.
- Remember to fill in your details (Name, Exam/Center Number) before you start.
- Do not cheat.
- Pray before and after your exam.

**If you have any questions concerning NECO Mathematics Questions and Answers , please feel free to use the comment box below and ask us your question. We will be very pleased to answer you.**

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