THE WESTMORLAND SECONDARY SCHOOL
Subject Name: Additional Mathematics
FORM 4
Date: Tuesday, November 18, 2025
Duration: 2 hours
1. This examination consists of SIX (6) questions.
2. You are expected to Answer ALL questions.
3. Number your responses carefully and identically (including any
associated parts) as they appear on the question paper.
4. Write your name and page number on EACH sheet of paper
used including any extra paper used.
5. You MUST write ALL your final answers with black or blue
ink pens.
6. You MUST collate and staple your pages in the correct order.
Note: All steps must be clearly shown for the full allotment of marks.
1.
i.
Factorize completely, 6𝑥 3 + 𝑥 2 − 5𝑥 − 2.
[6]
ii.
Solve for 𝑥, the following equation,
6𝑥 3 + 𝑥 2 − 5𝑥 − 2 = 0
[3]
2. The expression 6𝑥 3 − 4𝑥 2 + 𝑎𝑥 + 𝑏 leaves a remainder of 5 when
divided by 𝑥 − 1 and a remainder of 1 when divided by 𝑥 + 1. Find
the values of 𝑎 and 𝑏.
[6]
3. The polynomial 2𝑥 3 + 9𝑥 2 + 𝑎𝑥 + 3 has a factor 𝑥 + 3,
i. Find 𝑎.
[4]
ii. Show that (𝑥 + 1) is also a factor and find the third factor. [6]
4.
(𝑥 − 1)(2𝑥 + 1)(3𝑥 + 2)
i.
Expand and simplify
[4]
ii.
By using a calculator, evaluate
6 √2
5
+ √3
5. Solve 812𝑥+1 = 27𝑥
[3]
[4]
6. Given that 3𝑥 3 + 𝑎𝑥 2 + 𝑏𝑥 + 2 ≡ (3𝑥 2 + 1)(𝑥 + 2), where 𝑎 and 𝑏 are
constants, find 𝑎 and 𝑏.
[6]
END OF EXAMINATION