# 2023 Further Mathematics objectives and paper 2 for WASSCE(WAEC)

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Hi Student, I commend your resilience towards searching for information that will set you at the top. Although
Further Mathematics is not a core subject, you can add it to your list of subject if you are a science student.
You need to have an open heart and a positive mindset if you want to write Further Mathematics in your Wassce
examination.
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In this article, I have Written down 40 questions and answers including pdf which contain the
paper 2 from WASSCE (WAEC) for Further Mathematics 2023.
This will guide you to understand the pattern WAEC follows when setting WASSCE questions for Further Mathematics. Help
yourself by going through each question and answer to prepare yourself for the real exam. I wish
you success ahead.
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**You can study the 40 (forty) WASSCE Further Mathematics past questions and answer for 2023 by checking the content below or using the table of content below to navigate to the number of your choice**

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###### Table of Contents

**WASSCE/WAEC Further Mathematics (2023) Questions and Answers 1 - 10****WASSCE/WAEC Further Mathematics (2023) Questions and Answers 11 - 20****WASSCE/WAEC Further Mathematics (2023) Questions and Answers 21 - 30****WASSCE/WAEC Further Mathematics (2023) Questions and Answers 31 - 40****Download WASSCE/WAEC Further Mathematics pdF (2023) Paper 2 (essay questions and answer 1 - 15)**

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## WASSCE/WAEC Further Mathematics (2023) Questions and Answers 1 - 10

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**1. Express $\frac {3}{3 - {\sqrt {6}}}$ in the form x + m $\sqrt {y}$**

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**(a) 3 + 3 $\sqrt {6}$**

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**(b) 3 + $\sqrt {6}$**

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**(c) 3 - $\sqrt {6}$**

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**(d) 3 - 3 $\sqrt {6}$**

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**The correct answer is:**(b) 3 + $\sqrt {6}$

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**2. If ${(\frac {1}{9})}^{2x-1}$ = ${(\frac {1}{81})}^{(2-3x)}$, find the value of x**

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**(a) $\frac {3}{8}$**

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**(b) $\frac {5}{8}$**

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**(c) $-\frac {5}{8}$**

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**(d) $-\frac {3}{4}$**

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**The correct answer is:**(b) $\frac {5}{8}$

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**3. If (x-5) is a factor of ${x}^{3} - {4x}^{2} - 11x + 30$, find the remaining factors**

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**(a) (x - 3) and (x + 2)**

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**(b) (x - 3) and (x - 2)**

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**(c) (x + 3) and (x + 2)**

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**(d) (x + 3) and (x + 2)**

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**The correct answer is:**(c) (x + 3) and (x + 2)

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###### 4. Consider the statements:

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**x: The school bus arrived late**

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**y: The students walked down to school**

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**Which of the following can be represented by $y {\Rightarrow} x$**

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**(a) Emmanuella did not go to school because the school bus arrived late**

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**(b) The school bus arrived early and Kate ran to school**

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**(c) Mary walked to school because the school bus arrived late**

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**(d) Either the school bus arrived late or Maryan walked to school**

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**The correct answer is:**(c) Mary walked to school because the school bus arrived late

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**5. Evaluate: $\int_{x=0}^1 x{({x}^{2} - 2)}^2\,dx$**

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**(a) $\frac {1}{7}$**

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**(b) $\frac {6}{7}$**

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**(c) $1\frac {1}{6}$**

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**(d) $3\frac {1}{6}$**

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**The correct answer is:**(c) $1\frac {1}{6}$

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###### 6. In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?

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**(a) 720**

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**(b) 500**

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**(c) 350**

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**(d) 210**

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**The correct answer is:**(d) 210

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###### 7. Given that:

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**$\frac{3x + 4}{(x-2)(x + 3)} {\equiv} {\frac {P}{x + 3}} + {\frac{Q}{x - 2}}$, find the value of Q**

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**(a) -2**

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**(b) -1**

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**(c) 1**

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**(d) 2**

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**The correct answer is:**(d) 2

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**8. If ${\alpha} and {\beta}$ are the roots of ${7x}^2 + 12x - 4 = 0$, find the value of $\frac{{\alpha}{\beta}}{{{\alpha} + {\beta}}^2}$**

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**(a) $\frac{36}{7}$**

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**(b) $\frac{7}{36}$**

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**(c) $-\frac{7}{36}$**

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**(d) $-\frac{36}{7}$**

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**The correct answer is:**(c) $-\frac{7}{36}$

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**9. If $f:x{\rightarrow}2$ tan x and $g:x{\rightarrow} {\sqrt{{x}^2 + 8}}$, find $(gof){(45^0)}$.**

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**(a) 6**

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**(b) $3{\sqrt{2}}$**

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**(c) 4**

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**(d) $2{\sqrt{3}}$**

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**The correct answer is:**(d) $2{\sqrt{3}}$

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**10. An exponential sequence (G.P.) is given by ${\frac{9}{2}}, {\frac{3}{4}}, {\frac{1}{8}},...$ find its sum to infinity**

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**(a) $4{\frac{1}{5}}$**

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**(b) $5{\frac{2}{5}}$**

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**(c) $6{\frac{3}{4}}$**

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**(d) $13{\frac{1}{2}}$**

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**The correct answer is:**(b) $5{\frac{2}{5}}$

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## WASSCE/WAEC Further Mathematics (2023) Questions and Answers 11 - 20

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**11. A function f is defined by $f:x {\rightarrow} {\frac{x + 2}{x - 3}}, x {\neq} 3$. Find the inverse of f**

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**(a) ${\frac{3x - 2}{x + 1}}, x{\neq}-1$**

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**(b) ${\frac{3x + 2}{x + 1}}, x{\neq}-1$**

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**(c) ${\frac{x + 3}{x - 2}}, x{\neq}2$**

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**(d) ${\frac{x - 3}{x + 2}}, x{\neq}-2$**

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**The correct answer is:**(b) ${\frac{3x + 2}{x + 1}}, x{\neq}-1$

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###### 12. Given that M is the midpoint of T(2,4) and Q(-8,6), find the length MQ

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**(a) $\sqrt{24}$ units**

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**(b) $\sqrt{26}$ units**

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**(c) $\sqrt{28}$ units**

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**(d) $\sqrt{30}$ units**

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**The correct answer is:**(b) $\sqrt{26}$ units

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**13. Given that ${y}^{2} + xy = 5$, find $\frac{dy}{dx}$**

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**(a) $\frac{-y}{2y - y}$**

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**(b) $\frac{-y}{2y + x}$**

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**(c) $\frac{y}{2y - x}$**

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**(d) $\frac{y}{2y + x}$**

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**The correct answer is:**(b) $\frac{-y}{2y + x}$

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**14. Given that P = x : 2 $\leq$ x $\leq$ 8 and Q = x : 4 < x $\leq$ 12 are subsets of the universal sets $\mu$ = x : x $\in$ R, find P $\cap$ Q'.**

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**(a) $x: 4 \leq x \leq 8$**

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**(b) $x: 2 \leq x 4$**

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**(c) $x: 4 < x < 8$**

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**(d) $x: 2 < x \leq$4**

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**The correct answer is:**(b) $x: 2 \leq x 4$

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**15. The probabilities that Atta and Tunde will hit a target in a shooting contest are $\frac{1}{6}$ and $\frac{1}{9}$ respectively. Find the probability that only one of them will hit target**

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**(a) $\frac{1}{54}$**

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**(b) $\frac{13}{54}$**

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**(c) $\frac{20}{27}$**

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**(d) $\frac{41}{54}$**

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**The correct answer is:**(b) $\frac{13}{54}$

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###### 16. The table below shows the marks obtained by students in a Test

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**If the mean mark is 3, find the value of k**

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**(a) 1**

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**(b) 2**

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**(c) 3**

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**(d) 4**

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**The correct answer is:**(a) 1

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**17. If ${3x}^{2} + px + 12 = 0$ has equal roots, find the values of p**

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**(a) $\pm$3**

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**(b) $\pm$4**

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**(c) $\pm$6**

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**(d) $\pm$12**

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**The correct answer is:**(d) $\pm$12

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**18. Simplify: $\frac{log{\sqrt{27}} - log{{\sqrt{8}}}}{log3 - log2}$**

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**(a) $-\frac{1}{4}$**

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**(b) $-\frac{3}{2}$**

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**(c) $\frac{1}{4}$**

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**(d) $\frac{3}{2}$**

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**The correct answer is:**(d) $\frac{3}{2}$

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** 19. A particle began to move at ${27ms}^{-2}$ along a straight line with constant retardation of ${9ms}^{-2}$. Calculate the time it took the particle to come to a stop**
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**(a) 4 sec**

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**(b) 3 sec**

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**(c) 2 sec**

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**(d) 1 sec**

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**The correct answer is:**(b) 3 sec

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###### 20. In how many ways can four mathematicians be selected from six?

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**(a) 15**

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**(b) 60**

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**(c) 90**

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**(d) 360**

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**The correct answer is:**(a) 15

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## WASSCE/WAEC Further Mathematics (2023) Questions and Answers 21 - 30

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**21. A linear transformation on the oxy plane is defined by P : (x,y) $\rightarrow$ (2x + y, -2y). Find $p^2$**

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**The correct answer is:**(c)

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**22. The velocity of a body of mass 4.56kg increases from ${({10ms}^-1, {060}^o)}$ to ${({50ms}^-1, {060}^o)}$ in 16 seconds. Calculate the magnitude of the force acting on it**

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**(a) 36.5N**

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**(b) 17.1N**

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**(c) 11.4N**

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**(d) 5.7N**

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**The correct answer is:**(c) 11.4N

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23. Find the fifth term in the binomial expansion of ${(q + x)}^7$
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**(a) ${21q}^{4}{x}^{3}$**

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**(b) ${35q}^{5}{x}^{2}$**

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**(c) ${35q}^{3}{x}^{4}$**

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**(d) ${21q}^{2}{x}^{5}$**

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**The correct answer is:**(b) Contribution

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###### 24. Given that:

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**and the determinant of Q is three more than that of P, find the values of x**

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**(a) -2, $-\frac{3}{2}$**

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**(b) -2, $\frac{3}{2}$**

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**(c) 2, $-\frac{3}{2}$**

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**(d)2, $\frac{3}{2}$**

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**The correct answer is:**(c) 2, $-\frac{3}{2}$

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**25. Solve $6sin2{\theta}tan{\theta}$ = 4, where $0^o < {\theta} < {90}^o$**

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**(a) ${35.26}^o$**

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**(b) ${30.00}^o$**

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**(c) ${19.47}^o$**

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**(d) ${18.43}^o$**

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**The correct answer is:**(a) ${35.26}^o$

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26. Calculate, correct to one decimal place, the angle between 5**i**+ 12

**j**and -2

**i**+ 3

**j**

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**(a) ${54.8}^o$**

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**(b) ${56.3}^o$**

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**(c) ${66.4}^o$**

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**(d) ${76.3}^o$**

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**The correct answer is:**(b) ${56.3}^o$

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**27. The distance S metres moved by a body in t seconds is given by $S = {5t}^{3} - {\frac{19}{2}t}^{2} + 6t - 4$. Calculate the acceleration of the body after 2 seconds?**

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**(a) ${19ms}^{-2}$**

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**(b) ${21ms}^{-2}$**

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**(c) ${31ms}^{-2}$**

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**(d) ${41ms}^{-2}$**

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**The correct answer is:**(d) ${41ms}^{-2}$

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**28. Find the equation of the normal to the curve $y = {3x}^{2} + 2$ at point (1,5).**

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**(a) 6y - x - 29 = 0**

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**(b) 6y + x -31 = 0**

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**(c) y - 6x + 1 = 0**

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**(d) y - 6x - 1 = 0**

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**The correct answer is:**(b) 6y + x -31 = 0

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###### 29. Adu's scores in five subjects in an examination are 85, 84, 83, 86, and 87. Calculate the standard deviation

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**(a) 1.4**

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**(b) 1.6**

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**(c) 1.8**

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**(d) 2.0**

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**The correct answer is:**(a) 1.4

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**30. Differentiate f(x) = $\frac{1}{{(1 - x^2)}^5}$ with respect to x**

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**(a) $\frac{10x}{{(1 - x^2)}^6}$**

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**(b) $\frac{5x}{{(1 - x^2)}^6}$**

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**(c) $\frac{-5x}{{(1 - x^2)}^6}$**

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**(d) $\frac{10x}{{(1 - x^2)}^6}$**

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**The correct answer is:**(a) $\frac{10x}{{(1 - x^2)}^6}$

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## WASSCE/WAEC Further Mathematics (2023) Questions and Answers 31 - 40

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**31. If X and Y are two independent events such that P(X) = $\frac{1}{8}$ and $P(X{\cup}Y)$ = $\frac{5}{8}$. Find P(Y)**

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**(a) $\frac{4}{7}$**

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**(b) $\frac{3}{7}$**

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**(c) $\frac{4}{21}$**

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**(d) $\frac{1}{6}$**

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**The correct answer is:**(a) $\frac{4}{7}$

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**The table shows the operation * on the set x,y,z,w**

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###### 32. Find the identity element

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**(a) x**

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**(b) y**

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**(c) z**

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**(d) w**

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**The correct answer is:**(c) z

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**33. Find the radius of the circle ${2x}^{2} + {2y}^{2} - 4x + 5y + 1 = 0$**

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**(a) $\frac{\sqrt{5}}{6}$**

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**(b) $\frac{5}{6}$**

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**(c) $\frac{33}{4}$**

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**(d) $\frac{\sqrt{33}}{4}$**

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**The correct answer is:**(d) $\frac{\sqrt{33}}{4}$

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**34. Evaluate: ${\int}{(2x + 1)}^{3}dx$**

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**(a) $8{(2x+1)}^2 + k$**

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**(b) $6{(2x+1)}^2 + k$**

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**(c) ${\frac{1}{6}}{(2x+1)}^{4} + k$**

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**(d) ${\frac{1}{8}}{(2x+1)}^{4} + k$**

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**The correct answer is:**(d) ${\frac{1}{8}}{(2x+1)}^{4} + k$

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###### 35. A uniform beam Pq of length 80cm and weight 60N rests on a support at X where |PX| = 30cm. If the body is kept in equilibrium by a mass m kg which is placed at P, calculate the value of m [Take g = 10m/s]

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**(a) 2.0**

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**(b) 2.5**

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**(c) 3.0**

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**(d) 4.0**

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**The correct answer is:**(a) 2.0

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**36. If m and (m + 4) are the roots of ${4x}^{2} -4x - 15 = 0$, find the equation whose roots are 2m and (2m + 8)**

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**(a) $x^2 + 8x - 15 = 0$**

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**(b) $x^2 - 8x - 15 = 0$**

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**(c)$x^2 + 2x - 15 = 0$**

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**(d) $x^2 - 2x - 15 = 0$**

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**The correct answer is:**(d) $x^2 - 2x - 15 = 0$

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**37. Find the coefficient of the 6th term in the binomial expansion of ${1 - {\frac{2x}{3}}}^10$ in ascending power of x**

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**(a) $-\frac{{896x}^6}{9}$**

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**(b) $-\frac{{896x}^6}{27}$**

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**(c) $-\frac{{896x}^5}{9}$**

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**(d) $-\frac{{896x}^5}{27}$**

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**The correct answer is:**(d) $-\frac{{896x}^5}{27}$

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**38. An exponential sequence (G.P) is given by $8\sqrt{2}$, $16\sqrt{2}$, $32\sqrt{2}$,... Find the nth term of the sequence**

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**(a) $8n\sqrt{2}$**

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**(b) $8\sqrt{2^n}$**

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**(c) $\sqrt{{2}^{(n+3)}}$**

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**(d) ${2}^{(n+2)}\sqrt{2}$**

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**The correct answer is:**(d) ${2}^{(n+2)}\sqrt{2}$

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**39. Given that r = (10N, ${200}^o$) and n = (16N, ${020}^o$), find (3r - 2n)**

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**(a) (16N, ${200}^o$)**

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**(b) (62N, ${020}^o$)**

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**(c) (62N, ${240}^o$)**

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**(d) (62N, ${280}^o$)**

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**The correct answer is:**(b) (62N, ${020}^o$)

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**40. Given that sin x = $\frac{4}{5}$ and cos y = $\frac{12}{13}$,**

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**(a) $\frac{16}{65}$**

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**(b) $\frac{48}{65}$**

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**(c) $\frac{56}{65}$**

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**(d) $\frac{63}{65}$**

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**The correct answer is:**No answer

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## Download WASSCE/WAEC Further Mathematics pdF (2023) Paper 2 (essay questions and answer 1 - 15)

**We have provided a pdf where you can practice wassce Paper 2 for Further Mathematics 2023. To download the pdf right away,**

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