Further Mathematics can be passed in one sitting though a lot of people tend to be afraid of it. We would outline some questions that you can use to prepare for your Further Mathematics examination and ensure that you practice more questions after going through the questions here.

The NECO further mathematics examination is divided into different sections and paper two is made up of 50 objective questions and paper II is made up of two parts(**Part A and Part B**) and candidates would be made to answer a specific amount of questions from each section. This past question can also be used by those who are participating in the NECO GCE examination.

The timetable has been released and those who would write Mathematics as one of their subjects should ensure that they practice ahead with the questions below. We did not outline the instructions below however, note that the first step to passing your NECO Further Mathematics examination is to ensure that you read instructions carefully before you start answering your examination.

**NECO Further Mathematics Past Questions and Answers**

The following are some NECO further mathematics objective questions:

1.The operations * on the set Q of rational numbers is defined by a*b = (a^2 + b – 2ab)/3 a.b ∈ θ

Determine 2⁄13 * -1⁄3

a.-1(11⁄18)b.-11⁄18

c.11⁄54

d.1(11⁄18)

e.2

2. Simplify 2⁄√7 – 2 + 1⁄√7 + 2

a.3√7frasl;4

b.3+√7⁄4

c.6-√7⁄3

d.3√7+√2⁄3

e.3√7+2⁄3

3. Find the product of the roots of the quadratic equation 2⁄3(x^{2}) – 6x-2 = 0

a. -6

b. -3

c. -2

d. 2⁄3

e.(1)1⁄2

4. Given the statements:

p: He is good in Mathematics

q: He is good in Chemistry

Which of the following describes the statement”He is good either in Mathematics or in Chemistry”?

a.~p ∨ q

b.p ∨~q

c. ~p ∧ q

d. p ∨ q

e.p ∧ q

5.Given that f: x→ 2^{x} and g = x→3x-2, find fg(2)

a. 4

b.16

c. 36

d. 49

e. 81

6. Resolve 5x + 14⁄(x + 2)(x + 4) into partial fractions

a.2⁄(x+2) + 3⁄(x+4)

b. 5x⁄(x+2) + 3⁄(x + 4)

c. 5x⁄(x + 4) + 14⁄(x + 2)

d. 3x⁄(x + 2) + 14⁄(x + 4)

e. 2x⁄(x + 2) + 3⁄(x + 4)

7. Find the remainder when f(x) = 4x^{3} + 3x^{2} – 2x + 1 is divided by x + 2

a. -17

b. -15

c. 15

d. 17

e. 19

8. Given that tan θ = x/y where θ is an acute angle, find the value of xcosθ – ysinθ/xcosθ + ysinθ

a. 0

b. 1

c. 2

d. 3

e. 4

9. Given the equation y(x^{2} + 1) = 7x, find the first derivative in terms of x and y

a. 7 + 2xy/x^{2} + 1

2xy-7/x^{2} + 1

c. 7 -2xy/x^{2} + 1

d. x^{2} + 1/7-2xy

e. x^{2}-y/7 + 2xy

10. What is the probability of obtaining 3 heads when a fair coin is tossed 7 times?

a. 0.12

b.0.16

c.0.20

d.0.27

e.0.31

**PART A**

Answer all the questions in this section

- Simplify 3√2 – 3√5⁄5√2 + 2√5

b. Prove that tan(x + y) = tan x + tan y/1- tanxtany. Hence, evaluate tan(x + y)if x and y are acute angles such that cos x = 12/13 and sin y = 3/5

2. Three candidates sat for a Mathematics examination and their probabilities of passing were 4/5,3/5 and 2/5. Find the probability that:

a. at least one passed;

b. at least one failed;

3. Use the expansion of (3 + 2y)^{5} to find the value of (3.04)^{5} correct to 5 decimal places

4a. Find the area of the triangle whose vertices are X(4,2), Y(4,5), and Z(-2,2)

b. Obtain an equation of the line through the points (4,1) and (-2,3)

**PART B**

This part is divided into three sections with section I being Pure Mathematics, Part II mechanics, and Part II being Statistical and operation research

**PURE MATHEMATICS**

1.If the 5th term of a Geometric Progression (G.P) is 162 and the 8th term is 4373, find the

i. 1st three terms of the sequence

ii. Sum of the first 10 terms

**SECTION II- MECHANICS**

1.A Uniform plank PQ, length 5m is balanced horizontally on two pivots A and B, such that PA = 0.8m and BQ = 1m. It is discovered that, if an object of mass 30kg is attached to one end or the other end of the plank, the plank is on the point of turning.

If you can answer these questions without failing anyone, then that means you are well prepared for the NECO examinations we combined questions from a lot of topics there. We would update these questions regularly so ensure that you visit this page regularly to know when we update this article.

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