Ordinary level 2026 south west regional mock mathematics 2

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SECTION B

ANSWER ALL QUESTIONS IN THIS SECTION.

EACH QUESTION CARRIES 15 MARKS

1. A certain business woman specializes in selling the following foodstuff, Beans, Potatoes, Rice, and Groundnuts, all measured in buckets. On a certain market day, each bucket of each of these items sold gave the following profits.

   $Beans = 1200\text{ FCFA}$, $Potatoes = \frac{3}{4}$ of the profit of beans, $Rice = 1350\text{ FCFA}$ and $Groundnuts = \frac{2}{3}$ of the profit of rice. Calculate

   a) the profit of a bucket of

   i). Potatoes

   ii) Groundnuts

   b). the total profit she made on that day from the sale of 8 buckets of Beans, 2 buckets of Potatoes, 5 buckets of groundnuts, and 7 buckets of rice.

   c). the percentage gain if the total cost price for the food items sold was $109000\text{ FCFA}$.

   From the total profit realized in (b) above, she used $\frac{2}{5}$ of this amount to buy her dress.

   d) Find the amount paid for the dress.

   She also uses $\frac{4}{9}$ of the remaining profit for her electricity bill and saved the rest.

   e). Calculate the amount

   i). paid for the electricity bill.

   ii) saved

   (15 marks)

2. a) Given the function, $y = 6 + 5x – x^2$

   i) Construct a table of values of $y$ against $x$ for $-3 \le x \le 7$ where $|\vec{i}| = |\vec{j}| = 1\text{cm}$

   ii) Draw the graph of $y = f(x)$

   iii) State the values of the $x$ for which $6 + 5x – x^2 = 0$

   iv) Determine the gradient of the curve at the point $(-2, -8)$

   v) Using the graph in (ii) above, solve the equation $3 + 4x – x^2 = 0$ (10 marks)

   b). Let a function, $g$, be defined in $\mathbb{R}$, the set of real numbers by $g(x) = ax^3 + 3x^2 + 4x – b$,

   When $g$ is divided by $(x + 1)$, the remainder is 0. Given also that $(x – 2)$ is a factor of $g(x)$.

   i) Find the values of $a$ and $b$.

   ii) Factorize $g(x)$ completely

   iii) Solve $g(x) = 0$.

Would you like me to help you solve the profit calculations in Question 1 or find the values of $a$ and $b$ using the Factor Theorem in Question 2(b)?