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P5 Maths Cheat Sheet

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The short version

Every formula and rule a P5 child needs: 48 of them across 12 topics, on 6 A4 pages to print free. The PSLE paper gives no formula list, so your child has to know each one by heart.

$P5 Maths Cheat Sheet, page 1 of 6: formulas for whole numbers and four operations; and fractions and division$

Every P5 maths formula, by topic

Whole Numbers and Four Operations

Term 1Whole Numbers and Four Operations guide

Rule	Example
Numbers to 10 million2 030 005: two million, thirty thousand and five	See it drawn
Order of operations $(\;\;) \;\to\; \times\ \div \;\to\; +\ -$ Brackets first. Then × and ÷ from left to right, then + and −.	$24 - 6 \times 3 =$ $24 - 18 =$ $6$ $(24 - 6) \times 3 =$ $18 \times 3 =$ $54$ $36 \div 4 \times 3 =$ $9 \times 3 =$ $27$
× or ÷ by multiples of 10 $\times\, 300 \;\to\; \times\, 3,\ \text{then} \times\, 100$ Split off the zeros: use the digit, then the 10, 100 or 1000.	$23 \times 300 =$ $23 \times 3 \times 100 =$ $6900$ $5600 \div 70 =$ $560 \div 7 =$ $80$

Fractions and Division

Term 1Fractions and Division guide

Rule	Example
Division as a fractionA whole number ÷ a whole number can be written as a fraction.	$3 \div 5 =$ $\frac{3}{5}$ $9 \div 4 =$ $\frac{9}{4} =$ $2\frac{1}{4}$ See it drawn
Fraction to decimalMake the bottom 10, 100 or 1000, or divide.	$\frac{3}{4} =$ $\frac{75}{100} =$ $0.75$ $7 \div 8 =$ $0.875$ See it drawn
Fraction of a quantity"Of" means ×. Or find 1 unit first.	$\frac{3}{5} \times 40 =$ $24$ 1 unit → $40 \div 5 =$ $8$ 3 units → $3 \times 8 =$ $24$ See it drawn
Fraction × fractionNumerator × numerator, denominator × denominator, then simplify.	$\frac{2}{3} \times \frac{3}{4} =$ $\frac{6}{12} =$ $\frac{1}{2}$ $\frac{5}{4} \times \frac{6}{5} =$ $\frac{30}{20} =$ $1\frac{1}{2}$ See it drawn
Add or subtract mixed numbersWholes first, then the fractions over the same denominator.	$2\frac{1}{3} + 1\frac{3}{4} =$ $3 + \frac{13}{12} =$ $4\frac{1}{12}$ $3\frac{3}{4} - 1\frac{1}{3} =$ $2 + \frac{5}{12} =$ $2\frac{5}{12}$
Mixed number × whole numberMake it an improper fraction first.	$2\frac{1}{4} \times 6 =$ $\frac{9}{4} \times 6 =$ $13\frac{1}{2}$

Decimals

Term 3 · revisionDecimals guide

Rule	Example
× or ÷ by 10, 100, 1000× moves every digit 1, 2 or 3 places left. ÷ moves them right.	$2.375 \times 100 =$ $237.5$ $46.2 \div 100 =$ $0.462$ $0.35 \times 60 =$ $0.35 \times 6 \times 10 =$ $21$ See it drawn
Changing unitsTo a bigger unit, ÷. To a smaller unit, ×.	3.8 kg → $3.8 \times 1000 =$ $3800\,\text{g}$ See it drawn

Percentage

Term 3Percentage guide

Rule	Example
Percent means out of 100To a percentage, × 100%. Back to a decimal, ÷ 100.	$45\% =$ $\frac{45}{100} =$ $0.45$ $0.08 \times 100\% =$ $8\%$ See it drawn
Part as a percentage $\frac{\text{part}}{\text{whole}} \times 100\%$	18 out of 24 → $\frac{18}{24} \times 100\% =$ $75\%$ See it drawn
Fractions as percentages	$\frac{1}{4} =$ $25\%$ $\frac{1}{5} =$ $20\%$ $\frac{1}{8} =$ $12.5\%$ See it drawn
Percentage of a quantity	15% of $60 → $\frac{15}{100} \times 60 =$ $\text{\textdollar}9$ See it drawn
DiscountPrice after discount = usual price − discount	20% off $45 → $\frac{20}{100} \times 45 =$ $\text{\textdollar}9$ pay → $45 - 9 =$ $\text{\textdollar}36$ See it drawn
GSTPrice with GST = price + GST. Use the rate the question gives.	9% GST on $200 → $\frac{9}{100} \times 200 =$ $\text{\textdollar}18$ pay → $200 + 18 =$ $\text{\textdollar}218$ See it drawn
Annual interestA percentage of the money saved, paid each year.	3% a year on $2500 → $\frac{3}{100} \times 2500 =$ $\text{\textdollar}75$ after 1 year → $2500 + 75 =$ $\text{\textdollar}2575$ See it drawn

Rate

Term 3Rate guide

Rule	Example
Rate $\text{total} \div \text{number of units}$ The amount for 1 unit.	$42 for 6 kg → $42 \div 6 =$ $\text{\textdollar}7$ See it drawn
Total amount $\text{rate} \times \text{number of units}$	9 kg → $7 \times 9 =$ $\text{\textdollar}63$ See it drawn
Number of units $\text{total} \div \text{rate}$	$35 → $35 \div 7 =$ $5\,\text{kg}$ See it drawn

Number and Shape Patterns

Term 4Number and Shape Patterns guide

Rule	Example
Number pattern: any termTo reach the 20th term, add 19 jumps to the first term.	20th term → $4 + 19 \times 7 =$ $137$ See it drawn
Shape patternFigure 1 is 4 sticks. Each new square adds 3 sticks.	Figure 10 → $4 + 9 \times 3 =$ $31$ See it drawn
Repeating patternDivide by the length of the repeat. The remainder is the place: R 2 is the 2nd shape, a triangle.	50th, repeat of 4 → $50 \div 4 =$ $12\text{ R }2$ See it drawn

Area of Triangle

Term 2Area of Triangle guide

Rule	Example
Area of a triangle $\tfrac{1}{2} \times \text{base} \times \text{height}$	$\frac{1}{2} \times 12 \times 7 =$ $42\,\text{cm}^{2}$ See it drawn
The height can be outsideIt is always at right angles to the base.	$\frac{1}{2} \times 4 \times 6 =$ $12\,\text{cm}^{2}$ See it drawn
Half of its rectangleSame base and height as the rectangle: half its area.	$\frac{1}{2} \times 10 \times 6 =$ $30\,\text{cm}^{2}$ See it drawn
Composite figuresSplit into rectangles, squares and triangles. Add, or take away.	$8 \times 4 + \frac{1}{2} \times 8 \times 3 =$ $44\,\text{cm}^{2}$ See it drawn

Volume of Cube and Cuboid

Term 2Volume of Cube and Cuboid guide

Rule	Example
Volume in unit cubesEach cube is 1 cm³. This block is 3 cubes long, 2 wide and 2 high.	$3 \times 2 \times 2 =$ $12\,\text{cm}^{3}$ See it drawn
Volume of a cuboid $\text{length} \times \text{breadth} \times \text{height}$	$10 \times 6 \times 4 =$ $240\,\text{cm}^{3}$ See it drawn
Volume of a cube $\text{edge} \times \text{edge} \times \text{edge}$	$6 \times 6 \times 6 =$ $216\,\text{cm}^{3}$ See it drawn
Water in a tankVolume of water = length × breadth × height of the water	$30 \times 20 \times 12 =$ $7200\,\text{cm}^{3}$ See it drawn
Water added or taken outVolume = length × breadth × the change in height	$30 \times 20 \times 5 =$ $3000\,\text{cm}^{3}$ See it drawn
Litres and cm³ $1\,\ell = 1000\,\text{cm}^{3}$ 1 mℓ = 1 cm³	$7200 \div 1000 =$ $7.2\,\ell$

Shapes and Spatial Reasoning

Term 2Shapes and Spatial Reasoning guide

Rule	Example
Count cubes layer by layerCount each layer, from the bottom up.	bottom to top → $6 + 4 + 2 =$ $12$ See it drawn
Front and side viewsLook straight at one face. Draw only the squares you see.	See it drawn
Cubes to fill a boxCubes the full box holds − cubes already in it	$4 \times 3 \times 2 - 9 =$ $15$ See it drawn

Angles

Term 3Angles guide

Rule	Example
Angles on a straight lineThey add up to 180°.	a → $180 - 125 =$ $55\degree$ See it drawn
Angles at a pointThey add up to 360°.	$360 - 150 - 95 =$ $115\degree$ See it drawn
Vertically opposite angles are equalSo a = 110°.	See it drawn
Angles in a right angleThey add up to 90°.	a → $90 - 28 =$ $62\degree$ See it drawn

Properties of Triangles

Term 4Properties of Triangles guide

Rule	Example
Angles in a triangleThey add up to 180°.	$180 - 65 - 48 =$ $67\degree$ See it drawn
Isosceles triangle2 equal sides, 2 equal base angles.	$180 - 65 - 65 =$ $50\degree$ See it drawn
Equilateral triangle3 equal sides. Every angle is 60°.	$180 \div 3 =$ $60\degree$ See it drawn
Right-angled triangleThe other two angles add up to 90°.	a → $90 - 34 =$ $56\degree$ See it drawn

Parallelogram, Rhombus and Trapezium

Term 4Parallelogram, Rhombus and Trapezium guide

Rule	Example
ParallelogramOpposite sides parallel and equal. Angles next to each other add up to 180°.	a → $180 - 64 =$ $116\degree$ See it drawn
RhombusAll 4 sides equal. Opposite angles equal: a = 58°.	See it drawn
TrapeziumOne pair of parallel sides. The angles between them add up to 180°.	a → $180 - 72 =$ $108\degree$ See it drawn

P5 maths revision notes, topic by topic

Whole Numbers and Four Operations

Term 1

Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones
2 0 3 0 0 0 5
Numbers to 10 million2 030 005: two million, thirty thousand and five
Order of operations $(\;\;) \;\to\; \times\ \div \;\to\; +\ -$ Brackets first. Then × and ÷ from left to right, then + and −.Example $24 - 6 \times 3 =$ $24 - 18 =$ $6$ $(24 - 6) \times 3 =$ $18 \times 3 =$ $54$ $36 \div 4 \times 3 =$ $9 \times 3 =$ $27$
× or ÷ by multiples of 10 $\times\, 300 \;\to\; \times\, 3,\ \text{then} \times\, 100$ Split off the zeros: use the digit, then the 10, 100 or 1000.Example $23 \times 300 =$ $23 \times 3 \times 100 =$ $6900$ $5600 \div 70 =$ $560 \div 7 =$ $80$

Millions	Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
2	0	3	0	0	0	5

Fractions and Division

Term 1

Division as a fractionA whole number ÷ a whole number can be written as a fraction. $3 \div 5 =$ $\frac{3}{5}$ $9 \div 4 =$ $\frac{9}{4} =$ $2\frac{1}{4}$
Fraction to decimalMake the bottom 10, 100 or 1000, or divide. $\frac{3}{4} =$ $\frac{75}{100} =$ $0.75$ $7 \div 8 =$ $0.875$
Fraction of a quantity"Of" means ×. Or find 1 unit first. $\frac{3}{5} \times 40 =$ $24$ 1 unit → $40 \div 5 =$ $8$ 3 units → $3 \times 8 =$ $24$
Fraction × fractionNumerator × numerator, denominator × denominator, then simplify. $\frac{2}{3} \times \frac{3}{4} =$ $\frac{6}{12} =$ $\frac{1}{2}$ $\frac{5}{4} \times \frac{6}{5} =$ $\frac{30}{20} =$ $1\frac{1}{2}$
Add or subtract mixed numbersWholes first, then the fractions over the same denominator. $2\frac{1}{3} + 1\frac{3}{4} =$ $3 + \frac{13}{12} =$ $4\frac{1}{12}$ $3\frac{3}{4} - 1\frac{1}{3} =$ $2 + \frac{5}{12} =$ $2\frac{5}{12}$
Mixed number × whole numberMake it an improper fraction first. $2\frac{1}{4} \times 6 =$ $\frac{9}{4} \times 6 =$ $13\frac{1}{2}$

Decimals

Term 3 · revision

Hundreds Tens Ones . Tenths Hundredths Thousandths
2.375 2 . 3 7 5
× 100 2 3 7 . 5
× or ÷ by 10, 100, 1000× moves every digit 1, 2 or 3 places left. ÷ moves them right. $2.375 \times 100 =$ $237.5$ $46.2 \div 100 =$ $0.462$ $0.35 \times 60 =$ $0.35 \times 6 \times 10 =$ $21$
cm
4500
÷ 100
m
45
÷ 1000
km
0.045
Changing unitsTo a bigger unit, ÷. To a smaller unit, ×.3.8 kg → $3.8 \times 1000 =$ $3800\,\text{g}$

	Hundreds	Tens	Ones	.	Tenths	Hundredths	Thousandths
2.375			2	.	3	7	5
× 100	2	3	7	.	5

Percentage

Term 3

Percent means out of 100To a percentage, × 100%. Back to a decimal, ÷ 100. $45\% =$ $\frac{45}{100} =$ $0.45$ $0.08 \times 100\% =$ $8\%$
Part as a percentage $\frac{\text{part}}{\text{whole}} \times 100\%$ Example18 out of 24 → $\frac{18}{24} \times 100\% =$ $75\%$
Fractions as percentages $\frac{1}{4} =$ $25\%$ $\frac{1}{5} =$ $20\%$ $\frac{1}{8} =$ $12.5\%$
Percentage of a quantity15% of $60 → $\frac{15}{100} \times 60 =$ $\text{\textdollar}9$
DiscountPrice after discount = usual price − discount20% off $45 → $\frac{20}{100} \times 45 =$ $\text{\textdollar}9$ pay → $45 - 9 =$ $\text{\textdollar}36$
GSTPrice with GST = price + GST. Use the rate the question gives.9% GST on $200 → $\frac{9}{100} \times 200 =$ $\text{\textdollar}18$ pay → $200 + 18 =$ $\text{\textdollar}218$
Annual interestA percentage of the money saved, paid each year.3% a year on $2500 → $\frac{3}{100} \times 2500 =$ $\text{\textdollar}75$ after 1 year → $2500 + 75 =$ $\text{\textdollar}2575$

Rate

Term 3

Rate $\text{total} \div \text{number of units}$ The amount for 1 unit.Example$42 for 6 kg → $42 \div 6 =$ $\text{\textdollar}7$
Total amount $\text{rate} \times \text{number of units}$ Example9 kg → $7 \times 9 =$ $\text{\textdollar}63$
Number of units $\text{total} \div \text{rate}$ Example$35 → $35 \div 7 =$ $5\,\text{kg}$

Number and Shape Patterns

Term 4

Number pattern: any termTo reach the 20th term, add 19 jumps to the first term.20th term → $4 + 19 \times 7 =$ $137$
Shape patternFigure 1 is 4 sticks. Each new square adds 3 sticks.Figure 10 → $4 + 9 \times 3 =$ $31$
Repeating patternDivide by the length of the repeat. The remainder is the place: R 2 is the 2nd shape, a triangle.50th, repeat of 4 → $50 \div 4 =$ $12\text{ R }2$

Area of Triangle

Term 2

Area of a triangle $\tfrac{1}{2} \times \text{base} \times \text{height}$ Example $\frac{1}{2} \times 12 \times 7 =$ $42\,\text{cm}^{2}$
The height can be outsideIt is always at right angles to the base. $\frac{1}{2} \times 4 \times 6 =$ $12\,\text{cm}^{2}$
Half of its rectangleSame base and height as the rectangle: half its area. $\frac{1}{2} \times 10 \times 6 =$ $30\,\text{cm}^{2}$
Composite figuresSplit into rectangles, squares and triangles. Add, or take away. $8 \times 4 + \frac{1}{2} \times 8 \times 3 =$ $44\,\text{cm}^{2}$

Volume of Cube and Cuboid

Term 2

Volume in unit cubesEach cube is 1 cm³. This block is 3 cubes long, 2 wide and 2 high. $3 \times 2 \times 2 =$ $12\,\text{cm}^{3}$
Volume of a cuboid $\text{length} \times \text{breadth} \times \text{height}$ Example $10 \times 6 \times 4 =$ $240\,\text{cm}^{3}$
Volume of a cube $\text{edge} \times \text{edge} \times \text{edge}$ Example $6 \times 6 \times 6 =$ $216\,\text{cm}^{3}$
Water in a tankVolume of water = length × breadth × height of the water $30 \times 20 \times 12 =$ $7200\,\text{cm}^{3}$
Water added or taken outVolume = length × breadth × the change in height $30 \times 20 \times 5 =$ $3000\,\text{cm}^{3}$
Litres and cm³ $1\,\ell = 1000\,\text{cm}^{3}$ 1 mℓ = 1 cm³Example $7200 \div 1000 =$ $7.2\,\ell$

Shapes and Spatial Reasoning

Term 2

Count cubes layer by layerCount each layer, from the bottom up.bottom to top → $6 + 4 + 2 =$ $12$
Front and side viewsLook straight at one face. Draw only the squares you see.
Cubes to fill a boxCubes the full box holds − cubes already in it $4 \times 3 \times 2 - 9 =$ $15$

Angles

Term 3

Angles on a straight lineThey add up to 180°.a → $180 - 125 =$ $55\degree$
Angles at a pointThey add up to 360°. $360 - 150 - 95 =$ $115\degree$
Vertically opposite angles are equalSo a = 110°.
Angles in a right angleThey add up to 90°.a → $90 - 28 =$ $62\degree$

Properties of Triangles

Term 4

Angles in a triangleThey add up to 180°. $180 - 65 - 48 =$ $67\degree$
Isosceles triangle2 equal sides, 2 equal base angles. $180 - 65 - 65 =$ $50\degree$
Equilateral triangle3 equal sides. Every angle is 60°. $180 \div 3 =$ $60\degree$
Right-angled triangleThe other two angles add up to 90°.a → $90 - 34 =$ $56\degree$

Parallelogram, Rhombus and Trapezium

Term 4

ParallelogramOpposite sides parallel and equal. Angles next to each other add up to 180°.a → $180 - 64 =$ $116\degree$
RhombusAll 4 sides equal. Opposite angles equal: a = 58°.
TrapeziumOne pair of parallel sides. The angles between them add up to 180°.a → $180 - 72 =$ $108\degree$

$P6 Maths Cheat Sheet, page 1 of 4: formulas for fractions, ratio and percentage$

The P6 sheet, for the PSLE year

The P6 sheet holds 36 more formulas and rules, across its 8 topics, on 4 A4 pages.

P6 Maths Cheat Sheet

P4 Maths Cheat Sheet, page 1 of 7: formulas for numbers to 100 000; and factors and multiples

The P4 Maths Cheat Sheet

The P4 sheet holds 48 more formulas and rules, across its 12 topics, on 7 A4 pages.

P4 Maths Cheat Sheet

P3 Maths Cheat Sheet, page 1 of 8: formulas for numbers to 10 000

The P3 Maths Cheat Sheet

The P3 sheet holds 45 more formulas and rules, across its 10 topics, on 8 A4 pages.

P3 Maths Cheat Sheet

The sheet

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$P5 Maths Cheat Sheet, page 1 of 6: formulas for whole numbers and four operations; and fractions and division$
P5 Maths Cheat Sheet, page 1 of 6: formulas for whole numbers and four operations; and fractions and division
P5 Maths Cheat Sheet, page 2 of 6: formulas for decimals and percentage
P5 Maths Cheat Sheet, page 3 of 6: formulas for rate; number and shape patterns; and area of triangle
P5 Maths Cheat Sheet, page 4 of 6: formulas for volume of cube and cuboid; and shapes and spatial reasoning
P5 Maths Cheat Sheet, page 5 of 6: formulas for angles; properties of triangles; and parallelogram, rhombus and trapezium
P5 Maths Cheat Sheet, page 6 of 6: problem-sum methods, exam rules and units

Download the free PDF6 A4 pages · PDF, 975 KB

Knowing the formula is half of it

The other half is spotting which one a question needs. StudyLah gives your child P5 questions on these topics, and Lah walks through each one step by step. Free: one Daily Practice and one Topic Drill every day, and one exam paper a month.

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Questions

Questions parents ask

What maths formulas does a P5 child need to know?

The 48 formulas and rules on this sheet, across whole numbers and four operations; fractions and division; area of triangle; volume of cube and cuboid; shapes and spatial reasoning; decimals; percentage; rate; angles; properties of triangles; parallelogram, rhombus and trapezium; and number and shape patterns. It also shows how to spot 6 problem-sum methods. The PSLE tests them too, with the P6 formulas.

P6 Maths Cheat Sheet

What topics are in P5 maths?

12 topics, in the order schools teach them: whole numbers and four operations; fractions and division; area of triangle; volume of cube and cuboid; shapes and spatial reasoning; decimals; percentage; rate; angles; properties of triangles; parallelogram, rhombus and trapezium; and number and shape patterns.

Primary 5 maths syllabus

Keep going

Sources: Ministry of Education, Singapore, Primary Mathematics Syllabus (Standard), updated October 2025. Singapore Examinations and Assessment Board, PSLE Mathematics (0008), for examination from 2026.

Updated 22 October 2026

Practise every topic on the P5 sheet

Free for every P5 child. Lah walks through each question.

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