4 high-yield, syllabus-aligned questions on Algebraic processes, covering 11 individually creditable mark points. Each one shows the answer that scores full marks under our guide, which phrase earns which mark, and a common incomplete answer — so you can see the difference rather than guess at it.
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Every question and solution is reviewed by examiners versed in WAEC and JAMB, each with more than thirty years of experience.
Mark allocations are TopMarks’ own, written against the published syllabus and Chief Examiners’ reports. They are a guide to how these answers are usually credited, not an official marking scheme.
Solve3 marks
Solve the simultaneous equations: 3x + 2y = 16 and x - y = 2.
TopMarks model answer
From the second equation, x = y + 2. Substituting into the first equation: 3(y + 2) + 2y = 16, so 3y + 6 + 2y = 16, giving 5y = 10 and therefore y = 2. Substituting back, x = 2 + 2 = 4. Therefore x = 4 and y = 2.
Suggested marking guide
1A valid method started — substitution or elimination
2Correct value of y
3Correct value of x
The working, line by line
1From x - y = 2, make x the subject: x = y + 2 — Choose the equation where a variable already has coefficient 1 — it makes the substitution clean.
23(y + 2) + 2y = 16 → 5y + 6 = 16 → 5y = 10 → y = 2 — Expand the bracket before collecting terms.
3x = y + 2 = 4 — Substitute back into the SIMPLER equation, not the one you expanded.
4Check: 3(4) + 2(2) = 16 ✓ — Substituting both values into the equation you did not use costs ten seconds and catches almost every arithmetic slip.
Why it scores
Two of the three marks are for the working. And notice the free check at the end: a simultaneous-equation answer can always be verified by putting it back into the original equations, so there is no reason ever to hand in a wrong one.
A common incomplete answer
“x = 4 and y = 2”
What it costs: Two marks of three. Both values are correct, but nothing shows how they were obtained, so only the final answer mark can be given.
Key ideas to include: substitution, elimination, subject of the formula, check by substitution.
Factorise2 marks
Factorise completely: 6x² - 7x - 3.
TopMarks model answer
The product of the first and last coefficients is 6 x (-3) = -18, and the middle coefficient is -7. Two numbers with product -18 and sum -7 are -9 and +2. So 6x² - 7x - 3 = 6x² - 9x + 2x - 3 = 3x(2x - 3) + 1(2x - 3) = (2x - 3)(3x + 1).
Suggested marking guide
1Splits the middle term correctly
2Correct factors
The working, line by line
1Multiply the first and last coefficients: 6 x (-3) = -18 — This is the number you are factorising, not the -3 on its own.
2Find two numbers with product -18 and sum -7: these are -9 and +2 — Always check BOTH conditions. -9 x 2 = -18 ✓ and -9 + 2 = -7 ✓
36x² - 9x + 2x - 3 = 3x(2x - 3) + 1(2x - 3) — The bracket must come out identical from both halves. If it does not, you split the term the wrong way round — swap the two middle terms and try again.
4= (2x - 3)(3x + 1) — Expand mentally to check.
Why it scores
Expanding your factors back is a complete check that takes five seconds, which makes this a question you should never get wrong. The method mark is for the splitting line — a candidate who spots the factors by inspection and writes them down alone gets half the marks.
A common incomplete answer
“(2x - 3)(3x + 1)”
What it costs: One mark of two. The factorisation is correct, but the middle term is never split, so the method mark cannot be awarded.
Key ideas to include: splitting the middle term, common factor, product and sum, factorise completely.
Make3 marks
Make r the subject of the formula V = (1/3)πr²h.
TopMarks model answer
V = (1/3)πr²h. Multiply both sides by 3: 3V = πr²h. Divide both sides by πh: r² = 3V ÷ πh. Take the square root of both sides: r is the square root of (3V ÷ πh).
Suggested marking guide
1Clears the fraction by multiplying by 3
2Divides by πh to isolate r²
3Takes the square root
The working, line by line
1Multiply both sides by 3: 3V = πr²h — Deal with the fraction first. Everything after this is simple division.
2Divide both sides by πh: r² = 3V ÷ πh — Divide by EVERYTHING that multiplies r², which is π and h together.
3Square root both sides: r = √(3V ÷ πh) — The final operation undoes the square. Forgetting it leaves you with r², not r, which is not what was asked.
Why it scores
Rearranging is undoing operations in reverse order, and each undoing is a mark. The last step is the one most often forgotten: the question asked for r, and stopping at r² answers a different question.
A common incomplete answer
“3V = πr²h”
What it costs: Two marks of three. The first step is correct and credited, but r is never isolated and the square root is never taken, so r is not made the subject.
Key ideas to include: subject of the formula, inverse operations, clear the fraction, square root.
Solve3 marks
Solve the inequality 3(x - 2) ≤ 5x + 4.
TopMarks model answer
Expanding the bracket: 3x - 6 ≤ 5x + 4. Subtract 5x from both sides: -2x - 6 ≤ 4. Add 6 to both sides: -2x ≤ 10. Divide both sides by -2 and reverse the inequality sign, because dividing by a negative number reverses the inequality: x ≥ -5.
Suggested marking guide
1Expands the bracket correctly
2Collects the terms correctly
3Reverses the inequality on dividing by a negative
The working, line by line
13(x - 2) ≤ 5x + 4 → 3x - 6 ≤ 5x + 4 — Multiply BOTH terms inside the bracket by 3.
23x - 5x ≤ 4 + 6 → -2x ≤ 10 — Collect the x terms on one side and the numbers on the other.
3Divide by -2 AND reverse the sign: x ≥ -5 — This is the whole point of the question. Multiplying or dividing an inequality by a negative number flips the direction of the sign.
Why it scores
This inequality is set precisely because it forces a division by a negative number. If you would rather not risk it, collect the x terms on the side that keeps them positive instead: 3x - 6 ≤ 5x + 4 gives -10 ≤ 2x, so -5 ≤ x, which is the same answer with no sign reversal at all.
A common incomplete answer
“3x - 6 ≤ 5x + 4, so -2x ≤ 10 and x ≤ -5.”
What it costs: One mark of three. The expansion and the collection are both correct and credited, but the inequality sign was not reversed when dividing by -2, so the final answer points the wrong way.
Key ideas to include: inequality, expand the bracket, collect like terms, reverse the sign.
Practise Algebraic processes on real questions
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