ordinary level 2026 littoral regional mock additional mathematics 2 replaced

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General Instructions

• Section A: Compulsory to all candidates.

• Requirement: Answer all questions.

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Question 1

• (i) Given that $(x – 1)$ is a factor of $f(x)$, where $f(x) = x^3 + ax^2 + x + b$. Find the value of $a$ and $b$. (4 marks)

• (ii) Given that $\alpha$ and $\beta$ are the roots of the quadratic equation $2x^2 + 6x – 2 = 0$. Find a quadratic equation with integral coefficients whose roots are $\alpha – 1$ and $\beta + 1$. (4 marks)

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Question 2

• (i) A class consists of 12 boys and 16 girls. A team of 3 students are to be chosen at random from the class as prefect, vice prefect and class delegate. In how many ways can this be done if the team must be mixed? (3 marks)

• (ii) Find the term in $x$ to the power 4 in the expansion of $(x – \frac{2}{x})^{10}$. (4 marks)

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Question 3

Tantoh is a young graduate who intends to establish his own business and needs to gather as much money as possible. A certain company offers him a job with a 5-year contract containing two types of salary payment grills:

• First Grill: He will be paid the sum of 100,000 FCFA every month for 5 years.

• Second Grill: He will be paid 50,000 FCFA on his first month and will receive an addition with value equivalent to 5% of the first salary every month for the 5 years contract.

Tasks:

• a) Calculate the additional amount involved in the second payment grill. (2 marks)

• b) How much will be earned in each proposal after 5 years? (5 marks)

• c) Which salary grill would you advise Tantoh to sign for? (1 mark)

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Question 4

• (i) The operation $*$ defined on the set $S = \{0, 1, 2, 3, 4\}$ by $a * b = (a + b + 1) \pmod 4$.

  • a) Copy and complete the following table: (3 marks)

*	0	1	2	3
0	1		3
1	2	3
2			1	2
3		1		3

• b) State the identity element for the operation. (1 mark)

• c) Show that the operation is associative over the set $S$. (1 mark)

• (ii) Given the matrix $M = \begin{pmatrix} 3 & 2 \\ 7 & 5 \end{pmatrix}$:

  • a) Find the inverse of $M$. (2 marks)

  • b) Hence solve the pair of equations $3x + 2y = 4$ and $7x + 5y = 9$. (2 marks)

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Question 5 (Problem Solving)

Mr. Mathias decided to organize a welcome party for his daughter. He decided to buy $x$ bottles of alcoholic drinks and $y$ bottles of non-alcoholic drinks and has only 24,000 frs for the drinks. Given that:

• A bottle of alcoholic drink costs 600 frs and a bottle of non-alcoholic drink costs 300 frs.

• The number of bottles of non-alcoholic drinks must be at least half those of alcoholic drinks. (Note: The text says “half those of non-alcoholic”, which appears to be a typo for “alcoholic”).

Tasks:

• a) Write down two inequalities in terms of $x$ and $y$ that satisfy the above condition. (2 marks)

• b) On graph paper, taking 1 cm for one unit on the x-axis and 1 cm for 4 units on the y-axis, shade so as to leave the unshaded the region that satisfy the inequalities. (4 marks)

• c) Hence, find the greatest number of bottles of drinks that can be bought for the party. (2 marks)

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Question 6 (Trigonometry)

• (i) Prove that $\frac{1 – \cos 2x}{1 + \cos 2x} = \tan^2 x$. (3 marks)

• (ii) The function $f$ is defined by $f(\theta) = 2\cos \theta + \sin 2\theta$ for $0^\circ \leq \theta \leq 360^\circ$.

  • a) Copy and complete the following table: (2 marks)

θ	0∘	30∘	60∘	90∘	120∘	150∘	180∘	210∘	240∘	270∘	300∘	330∘	360∘
$f(\theta)$	2			0	-1.9		-2			0			2

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