Free P4 Maths paper: Factors and multiples
A full Paper 1 and Paper 2 at the level of a very hard P4 end-of-year paper, in the PSLE format, for Singapore P4 pupils. 29 of the 100 marks are on factors and multiples; the rest cover the other P4 topics, as a real paper does.
Free. No sign-up to start. Untimed, like homework, and your answers save as you type. No calculator in either paper, as P4 pupils do not use one. Paper 2 follows Paper 1. The score shows the moment Paper 2 is handed in, and a parent can unlock the full diagnosis and have it emailed.
What is in the paper
| Questions | Marks | Calculator | Time | |
|---|---|---|---|---|
| Paper 1 multiple choice, then short answers | 30 | 50 | No | 1 h 10 min |
| Paper 2 short answers, then structured questions | 15 | 50 | No | 1 h 20 min |
The focus: 29 marks on factors and multiples, across both papers, from one-mark multiple choice to a five-mark final question. Also in the paper: Whole numbers, Area and perimeter, Measurement, Angles, Data tables and graphs, Pie charts, Nets and solids, Symmetry, Decimals, Fractions.
Timing is up to you. Sit it in one go against the PSLE times for exam practice, or spread it over a few evenings as homework is.
Where the marks go in factors and multiples
Factors and multiples look easy until a question needs the smallest number that fits both, or the largest equal groups. P4 papers hide them in word problems: lights flashing together, cards shared with none left over, numbers that leave the same remainder.
The mistakes this paper looks for
- Multiplying two numbers to get their smallest common multiple (4 and 6 first meet at 12, not 24)
- Forgetting that 1 and the number itself are factors
- Mixing up factors and multiples
Try a question from this paper
Paper 1, Question 15 (2 marks). When some pupils are put into groups of 9, 8 pupils are left over. When they are put into groups of 6, 5 pupils are left over. There are more than 75 pupils. What is the smallest possible number of pupils?
- 90
- 80
- 89
- 107
Show the answer
(3) 89
8 left over in groups of 9 means 1 more pupil would make another full group. The same is true for groups of 6.
So the number of pupils + 1 is a common multiple of 9 and 6: 18, 36, 54, and so on.
The smallest number more than 75 is 90 − 1 = 89.
What the report tells you
- The score for each paper and the total, with the PSLE Achievement Level band as a guide, two years early.
- Factors and multiples skill by skill, apart from the rest of the paper.
- What we diagnosed: the mistakes the wrong answers point to, such as taking a fraction of the wrong group or treating an hour as 100 minutes.
- Three things to work on, and every question with its correct answer.
The score is free for everyone. The full diagnosis is sent to a parent's email, and nothing else is done with the details.
Planning ahead for P5 and P6?
Wei Jie's crash courses start in the November before P6, the year of the PSLE, so there is no course for P4 yet. Until then, the free P5 papers are the next step up, and questions are welcome on WhatsApp.