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P6 Algebra Questions (with Worked Solutions)

Forming and solving simple algebraic expressions and equations — P6 prelim questions. Every question is from a real Singapore P6 preliminary exam, marked instantly, with step-by-step solutions.

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A few real algebra questions from P6 prelim papers. The full set — with marking and progress tracking — is inside SG Maths Exam.

St Nicholas 2025 · Paper 2 · Q16(a) · 3 marks

Paul and Zalim went out together with a total of \$140.20. Zalim spent 4 times as much money as Paul. The amount of money Paul had left was \$12 more than $\frac{1}{2}$ of what Zalim spent. The amount of money Zalim had left was $\frac{1}{5}$ of what Paul had left. (a) How much money did Paul spend?

Worked solution

Let Paul spend 1 unit, so Zalim spent 4 units. Paul left $= 2\text{ units} + \$12$ (half of Zalim's spending is 2 units). Zalim left $= \frac{1}{5}$ of Paul's left. Total money $= 1 + 4 + (2\text{ units} + 12) + \text{Zalim left} = \$140.20$. Solving, $37\text{ units} + \$12 + \$2.40 = \$140.20$, so $37\text{ units} = \$125.80$ and $1\text{ unit} = \$3.40$. Paul spent $5 \times \$3.40 = \$17$.

Tao Nan 2025 · Paper 1 Booklet A · Q12 · 2 marks

Ali had $y$ marbles. Bala had 5 more marbles than Ali. Charles had 3 times as many marbles as Ali. They had 45 marbles altogether. How many more marbles did Charles have than Bala?

1. 8
2. 10
3. 11
4. 15

Worked solution

\text{Ali} = y, \text{Bala} = y + 5, \text{Charles} = 3y
y + (y+5) + 3y = 45
5y + 5 = 45
y = 8
\text{Charles} - \text{Bala} = 3(8) - (8+5) = 24 - 13 = 11

St Nicholas 2025 · Paper 2 · Q16(b) · 2 marks

For Paul and Zalim, (b) How much money did Zalim have at first?

Worked solution

Zalim's money at first $= $ what he spent $+ $ what he had left $= 22\text{ units} + \$2.40 = 22 \times \$3.40 + \$2.40 = \$74.80 + \$2.40 = \$77.20$.

Nanyang 2025 · Paper 2 · Q1 · 2 marks

Jaslyn had $w$ stickers. Krishna had 34 more stickers than Jaslyn. They had 128 stickers altogether. How many stickers did Krishna have?

Worked solution

$w + (w + 34) = 128$
$2w + 34 = 128$
$2w = 94$
$w = 47$. Krishna had $47 + 34 = 81$ stickers.

Ai Tong 2025 · Paper 1 Booklet A · Q10 · 1 mark

Find the value of $\frac{m}{7} + 10$, where $m = 28$.

1. 11
2. 14
3. 17
4. 28

Worked solution

\frac{m}{7} + 10 = \frac{28}{7} + 10
= 4 + 10
= 14

Nan Hua 2025 · Paper 1 Booklet A · Q10 · 1 mark

A book costs $\$b$ more than a pen. The total cost of a book and 3 pens is $\$20$. Find the cost of a pen.

1. $\frac{20 - b}{3}$
2. $\frac{20}{4} - b$
3. $20 - 3b$
4. $\frac{20 - b}{4}$

Worked solution

\text{Let cost of pen} = \$p
\text{Book} = \$(p + b)
(p + b) + 3p = 20
4p + b = 20
p = \tfrac{20 - b}{4}

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