Free P4 Maths paper: Word problems: supposition, excess and shortage
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 word problems: supposition, excess and shortage; 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 word problems: supposition, excess and shortage, across both papers, from one-mark multiple choice to a five-mark final question. Also in the paper: Whole numbers, Measurement, Symmetry, Nets and solids, Area and perimeter, Decimals, Data tables and graphs, Fractions, Pie charts, Angles.
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 supposition word problems
Supposition and excess and shortage are the heuristics P4 papers use for their hardest word problems. Assume every item is the cheaper one, then correct; or share two ways and compare what is left over and what is short.
The mistakes this paper looks for
- Dividing by the price of one item instead of the difference in prices
- Taking the difference of what is left over and what is short, when one way leaves some over and the other runs short (they add)
- Answering with the other item's count
Try a question from this paper
Paper 1, Question 11 (2 marks). Some pupils are sitting on benches in a hall. If 3 pupils sit on each bench, 12 pupils have no seat. If 4 pupils sit on each bench, 1 bench is left empty and the other benches are full. How many pupils are there?
- 16
- 48
- 60
- 51
Show the answer
(3) 60
With 4 on each bench, the empty bench has 1 × 4 = 4 seats not used.
Going from 3 to 4 a bench seats the 12 pupils with no seat and leaves 4 seats unused: 12 + 4 = 16 more seats.
Each bench gives 1 more seat, so there are 16 benches.
Pupils: 3 × 16 = 48, and 48 + 12 = 60
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.
- Word problems: supposition, excess and shortage 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.