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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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Example Algebra questions

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 · 5 marks
(a)
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 — (a)
  1. 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 $5 \times \$3.40 = \$17$.
(b)
For Paul and Zalim, (b) How much money did Zalim have at first?
Worked solution — (b)
  1. Zalim's money at first $= $ what he spent $+ $ what he had left $= 22\text{ units} + \$2.40 = 22 \times \$3.40 + \$2.40 = \$74.80 + \$2.40 = \$77.20$.
Henry Park 2025 · Paper 1 Booklet A · Q15 · 2 marks
A pattern is formed using the letters A and H. The first 20 letters are shown. How many times does the letter A appear in the first 80 letters of the pattern?
Manual crop
  • 1. 50
  • 2. 52
  • 3. 53
  • 4. 57
Worked solution
  1. \(\text{Identify the repeating block from the first 20 letters}\)
  2. \(\text{Count A's per block, then scale to 80 letters}\)
  3. \(\text{Total A's} = 53\)
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
  1. \(\text{Ali} = y, \text{Bala} = y + 5, \text{Charles} = 3y\)
  2. \(y + (y+5) + 3y = 45\)
  3. \(5y + 5 = 45\)
  4. \(y = 8\)
  5. \(\text{Charles} - \text{Bala} = 3(8) - (8+5) = 24 - 13 = 11\)
St Nicholas 2025 · Paper 1 Booklet B · Q23 · 2 marks
(a)
Lina bought 3 packets of stickers. Each packet contained $y$ stickers. She kept 3 stickers for herself and gave the rest of the stickers equally to her 6 friends. (a) How many stickers did each friend receive in terms of $y$?
Worked solution — (a)
  1. Total stickers $= 3 \times y = 3y$. After keeping 3, $3y - 3$ are left. Each friend received $\frac{3y-3}{6}$ stickers.
(b)
Lina bought 3 packets of stickers, each containing $y$ stickers, kept 3 and gave the rest equally to her 6 friends. (b) Each friend received 8 stickers from Lina. Find the value of $y$.
Worked solution — (b)
  1. Stickers given out $= 8 \times 6 = 48$. Total stickers $= 48 + 3 = 51$. So $3y = 51$ and $y = 17$.
St Nicholas 2025 · Paper 2 · Q8 · 2 marks
(a)
The table shows the number of curry puffs sold at a shop last week. Monday to Friday: $2w$ per day. Saturday: $w + 40$. Sunday: $9w - 5$. (a) How many curry puffs were sold altogether last week? Express your answer in terms of $w$ in the simplest form.
Q8a
Worked solution — (a)
  1. Monday to Friday $= 5 \times 2w = 10w$. Adding Saturday and Sunday: $10w + (w + 40) + (9w - 5) = 20w + 35$.
(b)
For the curry puff sales table, (b) For each statement, indicate whether it is True, False or Not possible to tell.
Q8b
Worked solution — (b)
  1. Statement 1: Saturday $= w + 40$ and Monday $= 2w$
  2. whether $w + 40 > 2w$ depends on the value of $w$, so it is Not possible to tell. Statement 2: Monday sold $2w$ curry puffs at \$2 each $= \$4w$, so the statement is True.
Nanyang 2025 · Paper 1 Booklet B · Q30 · 2 marks
The mass of Parcel P is $x$ kg. The mass of Parcel Q is $3x$ kg. Parcel R is 3 kg lighter than Parcel Q. If $x = 12$, find the total mass of the 3 parcels.
Worked solution
  1. Parcel P $= x = 12$ kg. Parcel Q $= 3x = 36$ kg. Parcel R $= 3x - 3 = 33$ kg. Total $= 12 + 36 + 33 = 81$ kg.

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