**NECO Further Mathematics Past Questions and Answers PDF Download**| This is to inform those who are going to write the National Examination Council Examination in 2021 that the past questions is available in PDF format and those who are writing Further Mathematics are urged to read this article till the end.

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.

##### 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

1.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 te other end of the plank, the plank is on the point of turning

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