### 2021-2022 WAEC PAST QUESTIONS on Further Mathematics: Objectives and Essay with ANSWERS with easy study

2021-2022 WAEC PAST QUESTIONS on Further Mathematics: Objectives and Essay with ANSWERS with easy study – Are you interested in WAEC Further Mathematics. Here are WAEC Further Mathematics questions and answers, WAEC Further Mathematics syllabus 2022, past questions on mathematics, WAEC further mathematics expo 2022.

As a matter of fact, WAEC Further Mathematics questions and answers for 2022/2023 are here. Are you a WAEC candidate? If your answer is yes, this post will show you the WAEC Further Mathematics answers and the tricks you need to excel in your WAEC exam.

WAEC questions are set and compiled by the West African Senior School Certificate Examination Board (WASSCE). Make sure you follow the instructions as provided by WAEC.

## The Focuses:

0.1 2021/2022 WAEC Further Mathematics Questions and Answers

1 WAEC Further Maths Questions

2 WAEC Further Maths Essay and Objective 2021 (EXPO)

2021/2022 WAEC Further Mathematics Questions and Answers

Symbols used:

^ means raise to power

/ division

The Further Mathematics examination paper is going to comprise of two papers

Paper 1: Essay

Paper 2: Objectives

And, PAPER 1: will consist of forty multiple-choice objective questions, covering the entire Futher Mathematics syllabus. Candidates will be required to answer all questions in 1 hour for 40 marks. The questions will be set from the sections of the syllabus as sated here under:

Pure Mathematics – 30 questions

Statistics and probability – 4 questions

Vectors and Mechanics – 6 questions

### 2021-2022 WAEC PAST QUESTIONS on Further Mathematics

PAPER 2: will consist of two sections, Sections A and B, to be answered in 2 hours for 100 marks.

Section A will consist of eight compulsory questions that areelementary in type for 48 marks. The questions shall be distributed as follows:

Pure Mathematics – 4 questions

Statistics and Probability – 2 questions

Vectors and Mechanics – 2 questions

Section B will consist of seven questions of greater length and difficulty put into three parts thus;

Part I: Pure Mathematics – 3 questions

Part II: Statistics and Probability – 2 questions

And, Part III: Vectors and Mechanics – 2 questions

WAEC Further Maths Questions

- Integrate 3x^2 + 4x – 8 with respect to x

A. x^3 + 2x^2 + 8x + k

B. 6x + 4 + k

C. x^3 – 2x^2 + 8x + k

D. x^3 + x^2 – 8x + k

E. x^3 + 2x^2 – 8x + k

ANSWER: A

- Given that y = 3x^3 + 4x^2 + 7. Find dy/dx at x = 1

A. 14

B. 15

C. 17

D. 30

E. 35

ANSWER: C

- The gradient of a curve is 8x+2 and it passes through (1,3). Find the equation of the curve

A. y = 4x^2 + 2x + 3

B. y = -4x^2 + 2x -3

C. y = 4x^2 – 2x + 3

D. y = 4x^2 + 2x + 3

E. y= 4x^2 – 2x – 3

ANSWER: A

- Given the matrix M=

2 -4 -4

1 8 2

1 1 -2

find |M|

A. -24

B. -8

C. 8

D. 24

E. 48

ANSWER: A

- If logy18 = 3, find the value of y.

A. -2

B. -12

C. 12

D. 2

- A binary operation Δ is defined on the set of real numbers, R, by aΔb=a+bab√, where a≠ 0, b≠ 0. Evaluate −3Δ−1.

A. −43–√

B. −43√3

C. −33√4

D. −33√4

### 2021-2022 WAEC PAST QUESTIONS on Further Mathematics

- Simplify 1(1−3√)2

A. 1−123–√

B. 1+123–√

C. 3–√

D. 1+3–√ - If x2−kx+9=0 has equal roots, find the values of k.

A. 3, 4

B. ±3

C. ±5

D. ±6

- Find the coordinates of the centre of the circle 3×2+3y2−4x+8y−2=0

A. (-2,4)

B. (−23,43)

C. (23,−43)

D. (2, -4)

10.The function f: x →4−2x−−−−−√ is defined on the set of real numbers R. Find the domain of f.

A. x<2 B. x≤2 C. x=2 D. x>−2

- Given that f(x)=x+12, find f1(−2).

A. -5

B. -3

C. −12

D. 5

- Given that 6x+m2x2+7x−15≡4x+5−22x−3, find the value of m.

A. 20

B. 12

C. -10

D. -22

- Find the coefficient of x4 in the expansion of (1−2x)6.

A. -320

B. -240

C. 240

D. 320

- Find the 21st term of the Arithmetic Progression (A.P.): -4, -1.5, 1, 3.5,…

A. 43.5

B. 46

C. 48.5

D. 51

- How many ways can 6 students be seated around a circular table?

A. 36

B. 48

C. 120

D. 720

### 2021-2022 WAEC PAST QUESTIONS on Further Mathematics

- If (2413)(54) = k(17.540.0), find the value of k.

A. 1.2

B. 3.6

C. 0.8

D. 0.5

- Express cos150° in surd form.

A. −3–√

B. −3√2

C. −12

D. 2√2

- A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.

A. 2x-3y=2

B. 2x-3y=-2

C. 2x+3y=-4

D. 2x+3y=4

- α and β are the roots of the equation 2×2−3x+4=0. Find α+β.

A. -2

B. -32

C. 32

D. 2

- α and β are the roots of the equation 2×2−3x+4=0. Find αβ+βα

A. −98

B. −78

C. 78

D. 98 - If B=(2153), find B−1.

A. A=(−31−52)

B. A=(31−52)

C. A=(3−1−52)

D. A=(−315−2)

### 2021-2022 WAEC PAST QUESTIONS on Further Mathematics

- Given that sinx=513 and siny=817, where x and y are acute, find cos(x+y).

A. 130221

B. 140221

C. 140204

D. 22023

- A circle with centre (4,5) passes through the y-intercept of the line 5x – 2y + 6 = 0. Find its equation.

A. x2+y2+8x−10y+21=0

B. x2+y2+8x−10y−21=0

C. x2+y2−8x−10y−21=0

D. x2+y2−8x−10y+21=0

- If y=1+x1−x, find dydx.

A. 2(1−x)2

B. −2(1−x)2

C. −11−x√

D. 11−x√

- Evaluate ∫0−1(x+1)(x−2)dx

A. 76

B. 56

C. −56

D. −76 - Simplify 128√32√−22√

A. 22–√

B. 32–√

C. 3

D. 4 - There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys

A. 1638

B. 2730

C. 6006

D. 7520

- The 3rd and 7th term of a Geometric Progression (GP) are 81 and 16. Find the 5th term.

A. 4729

B. 8116

C. 27

D. 36

- Differentiate 5×3+x2x,x≠0 with respect to x.

A. 10x+1

B. 10x+2

C. x(15x+1)

D. x(15x+2)

- A curve is given by y=5−x−2×2. Find the equation of its line of symmetry.

A. x=−418

B. x=−14

C. x=14

D. x=418

- In a class of 10 boys and 15 girls, the average score in a Biology test is 90. If the average score for the girls is x, find the average score for the boys in terms of x.

A. 200−2×3

B. 225−3×2

C. 250−2x

D. 250−3x

- A fair die is tossed twice. What is its smple size?

A. 6

B. 12

C. 36

D. 48

- Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a – 8b).

A. 9i + 44j

B. -9i + 44j

C. -9i – 44j

D. 9i – 44j

- Solve 32x−3x+2=3x+1−27

A. 1 or 0

B. 1 or 2

C. 1 or -2

D. -1 or 2 - Find the magnitude and direction of the vector p=(5i−12j)

A. (13, 113.38°)

B. (13, 067.38°)

C. (13, 025.38°)

D. (13, 157.38°)

### 2021-2022 WAEC PAST QUESTIONS on Further Mathematics

### 36 The velocity, V, of a particle after t seconds, is V=3t2+2t−1. Find the acceleration of the particle after 2 seconds.

A. 10ms−2

B. 12ms−2

C. 14ms−2

D. 17ms−2

- Given that f(x)=2×2−3 and g(x)=x+1 where x∈R. Find g o f(x).

A. 2(x2−1)

B. 2×2+4x−1

C. 2×2+6x−1

D. 3(x2−1)

- If P = n2+1:n=0,2,3 and Q = n+1:n=2,3,5, find P∩ Q.

A. {5, 10}

B. {4, 6}

C. {1, 3}

D. { }

- If (2×2−x−3) is a factor of f(x)=2×3−5×2−x+6, find the other factor

A. (x – 2)

B. (x – 1)

C. (x + 1)

D. (x + 32)

- Simplify 3√3√−1+3√3√+1

A. 12

B. 3

C. 23–√

D. 6 - Find the domain of g(x)=4×2−19×2+1√

A. x:x∈R,x=12

B. x:x∈R,x≠13

C. x:x∈R,x=13

D. x:x∈R - Given that f(x)=3×2−12x+12 and f(x)=3, find the values of x.

A. 1, 3

B. -1, -3

C. 1, -3

D. -1, 3

- A binary operation * is defined on the set of real numbers, by a∗b=ab+ba. If (x−−√+1)∗(x−−√−1)=4, find the value of x.

A. 6

B. 5

C. 4

D. 3

- If 4×2+5kx+10 is a perfect square, find the value of k.

A. 510√4

B. 410−−√

C. 510−−√

D. 410√5

- if the polynomial f(x)=3×3−2×2+7x+5 is divided by (x – 1), find the remainder.

A. -17

B. -7

C. 5

D. 13

- P=1,3,5,7,9,Q=2,4,6,8,10,12,R=2,3,5,7,11 are subsets of U=1,2,3,…,12. Which of the following statements is true?

A. Q∩R=∅

B. R⊂P

C. (R∩P)⊂(R∩U)

D. n(P′∩R)=2

### 2021-2022 WAEC PAST QUESTIONS on Further Mathematics

- If log3a−2=3log3b, express a in terms of b.

A. a=b3−3

B. a=b3−9

C. a=9b3

D. a=b39

- If α and β are the roots of 2×2−5x+6=0, find the equation whose roots are (α+1) and (β+1).

A. 2×2−9x+15=0

B. 2×2−9x+13=0

C. 2×2−9x−13=0

D. 2×2−9x−15=0

- Resolve 3x−1(x−2)2,x≠2 into partial fractions.

A. x2(x−2)−5(x−2)2

B. 5(x−2)+x2(x−2)2

C. 12(x−2)+5×2(x−2)2

D. −12(x−2)+8×2(x−2)2

- If α and β are the roots of the equation 2×2+5x+n=0, such that αβ=2, find the value of n.

A. -4

B. -2

C. 2

D. 4

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