Parent guidesUnderstand the exam
The common types of PSLE Maths questions
The short version
PSLE Maths questions come in two kinds. Topic questions test one part of the syllabus, such as the area of a quarter circle or a price after GST. Problem sums are word problems solved with a method, such as before and after or units and parts. Each type links the page that teaches it, where there is one.
- Topic types
- 23
- Problem sums
- 10
- Levels
- P1 to P6
PSLE-style questions
Mathematics
Each question tagged with its type
- 1
Aiden had $60. He spent of it on a book, then of the remainder on lunch. How much did he spend on lunch?
Topic question: Fraction of what is left - 2
Ravi is 13 years old. His cousin is 25 years old. How many years ago was his cousin 3 times as old as Ravi?
Problem sum: What stays the same? - 3
Look at the pattern 5, 8, 11, 14, … What is the 10th term?
Topic question: Patterns - 4
A factory makes 900 bicycles and tricycles with 2140 wheels in all. A bicycle has 2 wheels and a tricycle has 3. How many tricycles are there?
Problem sum: Supposition - 5
The average mass of 4 parcels is 18 kg. A fifth parcel is added and the average becomes 19 kg. What is the mass of the fifth parcel?
Topic question: Average
What are the common types of PSLE Maths questions?
Two kinds: topic questions and problem sums. A topic question tests one part of the syllabus. A problem sum is a word problem solved with a method, and it can draw on several topics at once.
| Topic question23 types, in 3 strands | Problem sum10 types, in 3 groups | |
|---|---|---|
| Tests | One part of the syllabus, such as area or percentage | A method, which can draw on several topics |
| Reads like | "Find the area of the shaded part." | A story that changes: "at first", "the same amount" |
| Taught on | Each topic's page, P4 to P6 | The page that teaches its method, from P1 |
PSLE Maths topic questions, by strand
By the strands of MOE's syllabus, each type with the year it is first taught and, where the topic page has one, its own example and answer.
Number and Algebra
10 typesOrder of operations
From P5
A sum that mixes +, −, × and ÷, with or without brackets, worked in the right order.
Example
Find the value of 5 + 3 × 10.
Answer: 35 · The slip gives: 80
Multiplying and dividing decimals by 10, 100, 1000 and their multiples
From P5
The digits move by place value (÷ 400 is ÷ 4, then ÷ 100), and measurements are written in decimals.
Example
Find the value of 8.4 ÷ 400.
Answer: 0.021 · The slip gives: 2.1
Fraction of what is left
From P5
A second fraction is taken of what remains, never of the whole amount.
Example
Aiden had $60. He spent of it on a book, then of the remainder on lunch. How much did he spend on lunch?
Answer: $12 · The slip gives: $20
Dividing fractions
From P6
A fraction divided by a whole number or by a fraction. Dividing by a fraction less than 1 gives a bigger answer.
Example
Find the value of .
Answer: · The slip gives:
Discount, GST and interest
From P5
A percentage of an amount, then the price or the total after it.
Finding the whole from a percentage
From P6
The amount after a change is given, so it stands for 80% or 120% of the whole, never 100%.
Example
A bag costs $60 after a 20% discount. What was the original price?
Answer: $75 · The slip gives: $72
Dividing a quantity in a ratio
From P6
A total is shared in a ratio, so the parts are added first: 3 : 4 is 7 parts.
Example
A car park holds cars and motorcycles in the ratio 3 : 4. There are 28 vehicles in all. How many cars are there?
Answer: 12 cars · The slip gives: 21 cars
Rate
From P5
Any two of the rate, the total and the number of units give the third.
Example
A tap fills a tank at 4.5 litres per minute. How much water flows in 1 h 20 min?
Answer: 360 litres · The slip gives: 90 litres
Number and shape patterns
From P5
Find the rule, then use it for a far term instead of listing every term.
Example
Look at the pattern 5, 8, 11, 14, … What is the 10th term?
Answer: 32 · The slip gives: 35
Algebra: expressions and equations
From P6
Write an expression in n, simplify it, find its value for a given n, or solve a simple equation.
Example
A blue ribbon is n cm long. A red ribbon is 3 cm longer than the blue one. Write the length of the red ribbon, in terms of n.
Answer: n + 3 · The slip gives: 3n
Measurement and Geometry
10 typesAngles on a line and at a point
From P5
Unknown angles from angles on a straight line, at a point and vertically opposite.
Example
Three angles meet at a point. Two of them add up to 120°. Find the third angle.
Answer: 240° · The slip gives: 60°
Angles in triangles
From P5
The angle sum of 180° with isosceles, equilateral and right-angled triangles.
Angles in parallelograms, rhombuses and trapeziums
From P5
Unknown angles from the properties marked on the figure.
Example
A parallelogram has an angle of 70°. What is the angle next to it?
Answer: 110° · The slip gives: 70°
Unknown angles in composite figures
From P6
Several shapes joined together, one angle found at a time, each from a rule.
Area of a triangle: base and perpendicular height
From P5
Half of base × perpendicular height, never the sloping side, also inside figures made of several shapes.
Example
A triangle has a base of 6 cm and a sloping side of 5 cm. Its perpendicular height, meeting the base at a right angle, is 4 cm. Find its area.
Answer: 12 cm² · The slip gives: 15 cm²
Area and perimeter of composite figures
From P4
Figures made of rectangles and squares, split or completed to find a missing side, area or perimeter.
Half and quarter circles, and shaded areas
From P6
Circumference and area of circles, semicircles and quarter circles, and figures made of several shapes.
Example
A semicircle has a diameter of 14 cm. Find its perimeter. (Take )
Answer: 36 cm · The slip gives: 22 cm
Volume and water in a tank
From P5
The volume of cubes and cuboids in cm³ and litres, including water filling a tank.
A missing side from the volume
From P6
The volume is given and a side, a cube's edge or a base area is the unknown.
Example
A cube has a volume of 216 cm³. Find the length of one edge.
Answer: 6 cm · The slip gives: 72 cm
Counting cubes and views
From P5
Count the cubes in a stack, the cubes still needed to fill it, or what it looks like from the front or the side.
Statistics
3 typesAverage: find the total first
From P6
Average × number of items = total, the step these questions turn on.
Example
The average mass of 4 parcels is 18 kg. A fifth parcel is added and the average becomes 19 kg. What is the mass of the fifth parcel?
Answer: 23 kg · The slip gives: 4 kg
Reading pie charts
From P4
A fraction of the pie is the same fraction of the total.
Example
A pie chart shows the favourite fruit of 40 pupils. The apple sector is exactly a quarter of the circle. How many pupils chose apple?
Answer: 10 · The slip gives: 4
Tables and line graphs
From P4
Values, differences and changes read from a table or a line graph.
What types of problem sums are there?
In three groups, by what your child does: draw a model, make a calculated guess, or work another way.
Draw a model
5 typesBasic models
From P1
Parts and a whole, or two amounts compared, drawn as bars.
Example
Find the smaller of two numbers whose sum is 6294 and whose difference is 1350.
Answer: 2472. Two bars lined up on the left, the longer 1350 more. Take that off: 6294 − 1350 = 4944 is two equal bars, and 4944 ÷ 2 = 2472.
Fractions and ratio models
From P4
A fraction or a ratio of an amount, drawn as equal units.
Change models
From P1
The amounts change, and the question asks about before or after.
Example
Class A had 15 more pupils than B. After 24 moved from A to B, B had 4 times as many as A. How many did B have at first?
Answer: 20. After the move B leads by 24 + 24 − 15 = 33. That is 3 units, so 1 unit is 11 and B ends with 44.
What stays the same?
From P3
Amounts change, but the total, the difference or one amount does not.
Example
Ravi is 13 years old. His cousin is 25 years old. How many years ago was his cousin 3 times as old as Ravi?
Answer: 7. The age gap stays 25 − 13 = 12, which was 2 units then: 1 unit = 6. Ravi was 6, 13 − 6 = 7 years ago.
Units and Parts
From P3
Fractions of two different wholes, compared as units and parts.
Example
Ravi has 2 boxes and 5 packets holding 819 buttons in total. A box holds 4 times as many as a packet. How many buttons are in each packet?
Answer: 63. A packet is 1 unit and a box is 4, so 8 + 5 = 13 units = 819. 1 unit = 819 ÷ 13 = 63.
Make a calculated guess
3 typesGuess and Check
From P3
Try a value, check it against every fact, then adjust.
Example
Jar A has 5 marbles and Jar B has 17. A turn adds 9 to A or 5 to B. What is the fewest turns to make them equal?
Answer: 6. Check each total Jar B reaches: 17, 22 and 27 fail, but 32 works. That is 3 turns for Jar A and 3 for Jar B.
Supposition
From P4
Two kinds and two totals: suppose every item is one kind, then fix the difference.
Example
A factory makes 900 bicycles and tricycles with 2140 wheels in all. A bicycle has 2 wheels and a tricycle has 3. How many tricycles are there?
Answer: 340. Assume all are bicycles: 1800 wheels, 340 short. Each tricycle adds 1 wheel, so there are 340 tricycles.
Excess and Shortage
From P4
Shared one way there are some left; shared another way, some are short.
Other strategies
2 typesWorking Backwards
From P1
Only the end is known, so each step is undone from the end.
Example
A notebook costs as much as a folder. A pen costs as much as the notebook. The pen costs $2.40. Find the cost of the folder.
Answer: $7.20. The notebook is 2 × $2.40 = $4.80, which is 2 thirds of the folder. So a third is $4.80 ÷ 2 = $2.40, and 3 thirds are $7.20.
Grouping
From P2
The items come in fixed sets, so the sets are counted.
Example
Farah had 3 times as many $2 notes as $5 notes, with $176 in total. How many $5 notes did she have?
Answer: 16. One set is three $2 notes and one $5 note, so $11. $176 ÷ $11 = 16 sets, and each set holds one $5 note.
Other names you may hear
- Remainder concept
- The branching method: a second fraction is taken of what is left. Fraction of what is left questions, worked
- Equal fractions
- Two fractions of different wholes made equal (2/5 of A = 1/3 of B), drawn as units. Not the equal stage method. P6 Ratio questions
- Repeated identity
- One person in two ratios, made the same number of units so the ratios join. P6 Ratio questions
- Number × value
- Items of different values, such as $2 and $5 notes, counted in sets. Grouping questions, worked
- Gap and difference
- The difference in each share, divided into the difference in total.
- Intervals
- Trees or lamp posts along a road: with one at each end, there is one gap fewer than the number of trees.
Where StudyLah fits
StudyLah practises the topic types one topic at a time. Topic Drill sets PSLE-style questions on the topic your child picks, and every question comes with Lah's worked solution, step by step. A wrong answer goes into the mistake book, where your child can try it again.
Questions about PSLE Maths question types
How do I tell which type a question is?
Read the question's last line first. It names what to find, and that points to the topic. Then read the words before it: "at first" and "the same amount" each call for a method.
What types of questions are in the PSLE Maths paper?
Multiple-choice, short-answer and structured questions: those are the paper's formats. The types on this page are what the questions are about, and they appear across the formats.
Is speed still in the PSLE Maths syllabus?
No. Speed, distance and time are not in the current primary syllabus. Rate, taught in P5, is.
What are pattern questions in PSLE Maths?
Questions that give the first few numbers or figures of a pattern and ask for a far term or for the rule. The rule finds the term without listing every one before it.
What are average questions in PSLE Maths?
Questions that link an average, the number of items and the total: average × number of items = total. When an item is added or removed, the new total is found first.
Is the equal stage method the same as equal fractions?
No. The equal stage method is for amounts that end up the same. Equal fractions compares a fraction of one amount with a fraction of another, such as 2/5 of A and 1/3 of B, and solves it with units.
What is repeated identity in PSLE Maths?
A ratio question where one person appears in two ratios. Their units are made the same in both, so the two ratios join into one.
What is the hardest PSLE Maths question ever?
No PSLE Maths question is officially the hardest. The hardest questions page goes through the hardest of each recent year, with their answers.
Now the practice has to happen.
These guides tell you what usually goes wrong. Your child's own practice tells you what's going wrong for them. StudyLah does the second part, and shows you the answer.