Ordinary level 2025 Centre mock mathematics 2
Ordinary level 2025 Centre mock mathematics 2
Mathematics Examination Questions
Question 1
(i) Solve for $x$ in the equation $7^{x^2} = 7^{10x-25}$.
(ii) Given the polynomial $P(x) = 2x^3 + ax^2 + bx + 6$ has factors $(2x – 1)$ and $(x + 2)$
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a. Find the values of $a$ and $b$.
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b. Find the other factor of $P(x)$.
Question 2
(i) Write down the first four terms of the binomial expansion of $(2 – \frac{1}{2}x)^5$ in ascending powers of $x$.
(ii) A committee of 2 men and 3 women is to be chosen from 5 men and 4 women. How many different committees can be formed?
(iii) In how many ways can the letters of the word PHOTOSYNTHESIS be arranged?
Question 3
(i) The transformation $T$ is defined as $T: (x, y) \rightarrow (-2x + 3y, 3x – y)$. Find:
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a. The image of the point $(-5, -3)$ under $T$.
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b. The point whose image is $(6, -7)$ under $T$.
(ii) The binary operation $*$ is defined on the set of rational numbers by:
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c. Find the value of $-3 * 2$ and state whether or not $*$ is associative.
Question 4
Given that $x, 2x + 1, 4x – 1$ are consecutive terms of an AP, and that the $20^{\text{th}}$ term of this progression is $79$:
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a. Find the value of $x$ and state clearly the common difference.
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b. Find the sum of the first ten terms of the progression.
(ii) The third term of a GP is $\frac{1}{12}$ and the sixth term is $\frac{1}{96}$:
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c. Find the first term and the common ratio.
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d. Calculate the sum to infinity of this progression.
Question 5
A telephone Company produces $x$ Techno phones and $Y$ Samsung phones. Given that it takes $2$ hours to assemble a Techno phone and an Hour to assemble a Samsung phone and the company works for a maximum of $120$ hours per week. Given also that the company can package at most $60$ phones in a cartoon, and the profit per phone is $8000\text{frs}$ per Techno and $6000\text{frs}$ for Samsung and that the total profit made per cartoon is at least $180000$.
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a. Show that the profit made from a cartoon is satisfied by $4x + 3y \geq 90$.
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b. Write 2 inequalities that satisfy these conditions.
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c. On a graph paper and using a scale of $1\text{cm}$ for $5$ units on the X-axis and $1\text{cm}$ for $10$ units on the y-axis, shed so as to leave the unshaded the region represented by the inequalities.
