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PSLE Maths Cheat Sheet

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The short version

The formulas and rules from P3 to P6 that your child must know by heart for the PSLE: 77 of them across 18 topics, on 11 A4 pages to print free. The PSLE paper gives no formula list, and recalling formulae is the first thing it assesses.

PSLE Maths Cheat Sheet, page 1 of 11: formulas for the four operations; and factors and multiples, exam rules and units

From SEAB's PSLE Maths syllabus

PSLE Maths: the formula list, calculators, units and working

No formula list

SEAB's syllabus for the paper lists no formula sheet: recalling formulae is the first thing it assesses.

A calculator in Paper 2 only

Paper 1, Booklets A and B, is done without one.

The unit is given

Each answer's unit is printed, and the answer must be in that unit.

Working earns marks

A wrong answer with the correct method can still score a mark, and long questions ask for every step.

The PSLE Maths paper, broken down

The PSLE maths formulas to know by heart, by topic

The Four Operations

P4 to P5Whole Numbers and Four Operations guide

Rule	Example
Order of operations $(\;\;) \;\to\; \times\ \div \;\to\; +\ -$ Brackets first. Then × and ÷, 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 $\times 300 = \times 3 \times 100$ Split off the zeros: use the digit, then the 10, 100 or 1000.	$23 \times 300 =$ $23 \times 3 \times 100 =$ $6900$ $5600 \div 70 =$ $560 \div 7 =$ $80$
RoundingLook at the next digit. 5 or more, round up.	nearest 10 → $36\,482 \approx$ $36\,480$ nearest 100 → $36\,482 \approx$ $36\,500$ nearest 1000 → $36\,482 \approx$ $36\,000$ See it drawn

Factors and Multiples

P4Factors and Multiples guide

Rule	Example
Common factorsList the factors of each number in pairs. The ones in both lists are common factors.	See it drawn
Common multiplesList the multiples of each number. The ones in both lists are common multiples.	See it drawn

Fractions

P3 to P6Fractions guide

Rule	Example
Simplest formDivide the numerator and the denominator by the same number, until no number divides both.	$\frac{6}{9} =$ $\frac{6 \div 3}{9 \div 3} =$ $\frac{2}{3}$ See it drawn
Mixed number to improper fractionEach whole is 5 fifths. Count all the fifths.	fifths → $2 \times 5 + 3 =$ $13$ $2\frac{3}{5} =$ $\frac{13}{5}$ See it drawn
Add or subtract fractionsSame denominators first. Then add or take away the numerators.	$\frac{2}{3} + \frac{1}{4} =$ $\frac{8}{12} + \frac{3}{12} =$ $\frac{11}{12}$ $\frac{7}{10} - \frac{2}{5} =$ $\frac{7}{10} - \frac{4}{10} =$ $\frac{3}{10}$ See it drawn
Division as a fractionA whole number ÷ a whole number is a fraction.	$3 \div 5 =$ $\frac{3}{5}$ $9 \div 4 =$ $\frac{9}{4} =$ $2\frac{1}{4}$ 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. A mixed number: make it improper first.	$\frac{2}{3} \times \frac{3}{4} =$ $\frac{6}{12} =$ $\frac{1}{2}$ $\frac{5}{4} \times \frac{6}{5} =$ $\frac{30}{20} =$ $1\frac{1}{2}$ $2\frac{1}{4} \times 6 =$ $\frac{9}{4} \times 6 =$ $13\frac{1}{2}$ See it drawn
Fraction ÷ whole number: share it out	$\frac{3}{4} \div 2 =$ $\frac{3}{8}$ See it drawn
Whole ÷ fraction: how many fit?	$2 \div \frac{2}{3} =$ $3$ See it drawn
÷ a fraction: Keep, Change, Flip	$\frac{3}{4} \div \frac{3}{8} =$ $\frac{3}{4} \times \frac{8}{3} =$ $2$

Decimals

P4 to P5Decimals guide

Rule	Example
Decimals and fractionsDecimal to fraction: over 10, 100 or 1000, then simplify. Fraction to decimal: divide.	$0.35 =$ $\frac{35}{100} =$ $\frac{7}{20}$ $7 \div 8 =$ $0.875$ See it drawn
Rounding decimalsLook at the next digit. 5 or more, round up.	nearest whole number → $5.374 \approx$ $5$ 1 decimal place → $5.374 \approx$ $5.4$ 2 decimal places → $5.374 \approx$ $5.37$ See it drawn
× 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, ×.	4500 cm → $4500 \div 100 =$ $45\,\text{m}$ See it drawn

Percentage

P5 to P6Percentage guide

Rule	Example
Part as a percentage $\frac{\text{part}}{\text{whole}} \times 100\%$	18 out of 24 → $\frac{18}{24} \times 100\% =$ $75\%$ See it drawn
Percentage of a quantity	15% of $60 → $\frac{15}{100} \times 60 =$ $\text{\textdollar}9$ See it drawn
30% is $45: find 10%, then 100%	10% → $45 \div 3 =$ $\text{\textdollar}15$ 100% → $15 \times 10 =$ $\text{\textdollar}150$ See it drawn
Percentage change $\frac{\text{change}}{\text{original}} \times 100\%$	$40 to $50 → $10 \div 40 \times 100\% =$ $25\%$ $50 to $40 → $10 \div 50 \times 100\% =$ $20\%$ 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

P5Rate guide

Rule	Example
Rate $\text{total} \div \text{number of units}$ The amount for 1 unit. Number of units = total ÷ rate.	$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

Ratio

P6Ratio guide

Rule	Example
Share $84 in the ratio 3 : 4. Find 1 unit first.3 + 4 = 7 units in all.	1 unit → $84 \div 7 =$ $\text{\textdollar}12$ A → $3 \times 12 =$ $\text{\textdollar}36$ B → $4 \times 12 =$ $\text{\textdollar}48$ See it drawn
Boys : girls = 3 : 5	boys as a fraction of girls → $3 \div 5 =$ $\frac{3}{5}$ boys as a fraction of all → $3 \div 8 =$ $\frac{3}{8}$ See it drawn
Simplest form: ÷ every term by the same number	$12 : 18 =$ $12 \div 6 : 18 \div 6 =$ $2 : 3$ $12 : 18 : 24 =$ $2 : 3 : 4$
Equivalent ratios: × or ÷ every term by the same number	$2 : 5 =$ $2 \times 3 : 5 \times 3 =$ $6 : 15$ 3 : 4 = ? : 20 → $3 \times (20 \div 4) =$ $15$

Algebra

P6Algebra guide

Rule	Example
A letter stands for an unknown number $3a = 3 \times a, \quad \frac{a}{3} = a \div 3$	See it drawn
Add or take away like terms only $5a + 2 - 2a + 4 = 3a + 6$
Substitute a = 4 into 3a + 6	$3 \times 4 + 6 =$ $18$
Solve 2x + 5 = 17: undo each step, then check	2x → $17 - 5 =$ $12$ x → $12 \div 2 =$ $6$ check → $2 \times 6 + 5 =$ $17$ See it drawn

Number and Shape Patterns

P5Number and Shape Patterns guide

Rule	Example
Number pattern: the nth term $\text{first} + (n - 1) \times \text{jump}$ The 20th term is 19 jumps after the first.	20th term → $4 + 19 \times 7 =$ $137$ See it drawn
Repeating patternDivide by the length of the repeat. The remainder is the place in the repeat.	50th, repeat of 4 → $50 \div 4 =$ $12\text{ R }2$ See it drawn

Time

P3Time guide

Rule	Example
24-hour clockAfter 12 noon, add 12 to the hour. Midnight is 00 00.	$3.15\text{ p.m.} =$ $15\ 15$ See it drawn
How long it takesCount on to the next hour, then whole hours, then the minutes left.	9.45 a.m. to 11.15 a.m. → $15\,\text{min} + 1\,\text{h} + 15\,\text{min} =$ $1\,\text{h}\ 30\,\text{min}$ See it drawn

Geometry

P4 to P6Angles in Geometrical Figures guide

Rule	Example
Angles in a right angleThey add up to 90°. Every corner of a rectangle is 90°.	∠y → $90 - 35 =$ $55\degree$ See it drawn
Angles on a straight line $a + b = 180\degree$	See it drawn
Angles at a point $a + b + c = 360\degree$	See it drawn
Vertically opposite angles are equal	See it drawn
Angles in a triangle $a + b + c = 180\degree$	See it drawn
Isosceles triangle: 2 equal sides, 2 equal base angles	See it drawn
Equilateral triangle: every angle is 60°	$180 \div 3 =$ $60\degree$ See it drawn
Angles in a quadrilateral $a + b + c + d = 360\degree$	See it drawn
Parallelogram, rhombus: opposite angles are equal $a + b = 180\degree$	See it drawn
Trapezium: the angles between parallel sides $a + b = 180\degree$	See it drawn
Cube6 equal square faces. A dotted line is a hidden edge.	See it drawn
Cuboid6 rectangle faces, in 3 matching pairs.	See it drawn

Area & Perimeter

P3 to P5Area of Triangle guide

Rule	Example
Rectangle: area A, perimeter P $A = l \times b \qquad P = 2l + 2b$ l = length, b = breadth. Breadth from the area: A ÷ l.	$7 \times 4 =$ $28\,\text{cm}^{2}$ $7 + 4 + 7 + 4 =$ $22\,\text{cm}$ breadth → $84 \div 12 =$ $7\,\text{cm}$ See it drawn
Square: area A, perimeter P $A = s \times s \qquad P = 4 \times s$ s = side. The side from the perimeter: P ÷ 4.	$6 \times 6 =$ $36\,\text{cm}^{2}$ $4 \times 6 =$ $24\,\text{cm}$ side → $36 \div 4 =$ $9\,\text{cm}$ See it drawn
Area of a triangle $A = \tfrac{1}{2} \times b \times h$ b = base, h = 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
Composite figuresArea: split into rectangles, then add. Perimeter: the outside edge only.	area → $10 \times 4 + 5 \times 3 =$ $55\,\text{cm}^{2}$ perimeter → $10 + 4 + 5 + 3 + 5 + 7 =$ $34\,\text{cm}$ See it drawn

Volume

P5 to P6Volume of Cube and Cuboid guide

Rule	Example
Volume of a cuboid $V = l \times b \times h$ a cube: edge × edge × edge	See it drawn
Height of a cuboid $h = V \div \text{base area}$	360 cm³, base 40 cm² → $360 \div 40 =$ $9\,\text{cm}$ See it drawn
Area of a face $A = V \div h$	480 cm³, h = 6 cm → $480 \div 6 =$ $80\,\text{cm}^{2}$ See it drawn
Edge of a cube $\text{edge} = \sqrt[3]{V}$	343 cm³ → $\sqrt[3]{343} =$ $7\,\text{cm}$ See it drawn
Water added or taken outWater added or taken out = l × b × 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	$7200 \div 1000 =$ $7.2\,\ell$

Circles

P6π =

\frac{22}{7}

Circles guide

Rule	Example
Diameter and radius $d = 2r$	See it drawn
Circumference: the distance around $C = \pi d = 2\pi r$	$2 \times \pi \times 7 =$ $44\,\text{cm}$ See it drawn
Area of a circle $A = \pi r^{2}$	$\pi \times 7 \times 7 =$ $154\,\text{cm}^{2}$ See it drawn
Half circle: perimeter $\tfrac{1}{2}\pi d + d$	$\frac{1}{2} \times \pi \times 14 + 14 =$ $36\,\text{cm}$ See it drawn
Quarter circle: perimeter $\tfrac{1}{2}\pi r + 2r$	$\frac{1}{2} \times \pi \times 7 + 2 \times 7 =$ $25\,\text{cm}$ See it drawn
Half or quarter circle: area $\tfrac{1}{2}\pi r^{2} \text{ or } \tfrac{1}{4}\pi r^{2}$	$\frac{1}{4} \times \pi \times 14^{2} =$ $154\,\text{cm}^{2}$ See it drawn
Composite figuresArea: add or take away. Perimeter: the outside edge only.	square − quarter circle → $14 \times 14 - 154 =$ $42\,\text{cm}^{2}$ See it drawn

Shapes and Spatial Reasoning

P5Shapes 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

Graphs & Tables

P3 to P4Tables and Line Graphs guide

Rule	Example
Read the scale firstFind what one step on the scale is worth first.	half of a step of 10 → $10 \div 2 =$ $5$ Tuesday → $20 + 5 =$ $25$ See it drawn
Read a line graphRead each point against the scale. The steepest rise is the biggest change.	Wed to Thu → $70 - 40 =$ $30$ See it drawn

Pie Charts

P4Pie Charts guide

Rule	Example
A sector is a fraction of the wholeA right-angle mark is a quarter of the circle. A straight line across the centre cuts it in half.	See it drawn
A part from the totalPart = fraction × total. Total = part ÷ fraction.	a quarter of 120 → $\frac{1}{4} \times 120 =$ $30$ total → $4 \times 18 =$ $72$ See it drawn

Average

P6Average guide

Rule	Example
Average $\text{total} \div \text{number}$	$(12 + 15 + 18) \div 3 =$ $15$ See it drawn
Total from the average $\text{average} \times \text{number}$	3 numbers, average 14 → $14 \times 3 =$ $42$ See it drawn

PSLE maths revision notes, topic by topic

The Four Operations

P4 to P5

Order of operations $(\;\;) \;\to\; \times\ \div \;\to\; +\ -$ Brackets first. Then × and ÷, 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 $\times 300 = \times 3 \times 100$ Split off the zeros: use the digit, then the 10, 100 or 1000.Example $23 \times 300 =$ $23 \times 3 \times 100 =$ $6900$ $5600 \div 70 =$ $560 \div 7 =$ $80$
Point Value
36 482 36482
RoundingLook at the next digit. 5 or more, round up.nearest 10 → $36\,482 \approx$ $36\,480$ nearest 100 → $36\,482 \approx$ $36\,500$ nearest 1000 → $36\,482 \approx$ $36\,000$

Point	Value
36 482	36482

Factors and Multiples

Factors
20 1, 2, 4, 5, 10, 20
30 1, 2, 3, 5, 6, 10, 15, 30
Both 1, 2, 5, 10
Common factorsList the factors of each number in pairs. The ones in both lists are common factors.
Multiples
4 4, 8, 12, 16, 20, 24
6 6, 12, 18, 24, 30, 36
Both 12, 24
Common multiplesList the multiples of each number. The ones in both lists are common multiples.

	Factors
20	1, 2, 4, 5, 10, 20
30	1, 2, 3, 5, 6, 10, 15, 30
Both	1, 2, 5, 10

	Multiples
4	4, 8, 12, 16, 20, 24
6	6, 12, 18, 24, 30, 36
Both	12, 24

Fractions

P3 to P6

Simplest formDivide the numerator and the denominator by the same number, until no number divides both. $\frac{6}{9} =$ $\frac{6 \div 3}{9 \div 3} =$ $\frac{2}{3}$
Mixed number to improper fractionEach whole is 5 fifths. Count all the fifths.fifths → $2 \times 5 + 3 =$ $13$ $2\frac{3}{5} =$ $\frac{13}{5}$
Add or subtract fractionsSame denominators first. Then add or take away the numerators. $\frac{2}{3} + \frac{1}{4} =$ $\frac{8}{12} + \frac{3}{12} =$ $\frac{11}{12}$ $\frac{7}{10} - \frac{2}{5} =$ $\frac{7}{10} - \frac{4}{10} =$ $\frac{3}{10}$
Division as a fractionA whole number ÷ a whole number is a fraction. $3 \div 5 =$ $\frac{3}{5}$ $9 \div 4 =$ $\frac{9}{4} =$ $2\frac{1}{4}$
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. A mixed number: make it improper first. $\frac{2}{3} \times \frac{3}{4} =$ $\frac{6}{12} =$ $\frac{1}{2}$ $\frac{5}{4} \times \frac{6}{5} =$ $\frac{30}{20} =$ $1\frac{1}{2}$ $2\frac{1}{4} \times 6 =$ $\frac{9}{4} \times 6 =$ $13\frac{1}{2}$
Fraction ÷ whole number: share it out $\frac{3}{4} \div 2 =$ $\frac{3}{8}$
Whole ÷ fraction: how many fit? $2 \div \frac{2}{3} =$ $3$
÷ a fraction: Keep, Change, Flip $\frac{3}{4} \div \frac{3}{8} =$ $\frac{3}{4} \times \frac{8}{3} =$ $2$

Decimals

P4 to P5

Decimals and fractionsDecimal to fraction: over 10, 100 or 1000, then simplify. Fraction to decimal: divide. $0.35 =$ $\frac{35}{100} =$ $\frac{7}{20}$ $7 \div 8 =$ $0.875$
Point Value
5.374 5.374
Rounding decimalsLook at the next digit. 5 or more, round up.nearest whole number → $5.374 \approx$ $5$ 1 decimal place → $5.374 \approx$ $5.4$ 2 decimal places → $5.374 \approx$ $5.37$
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, ×.4500 cm → $4500 \div 100 =$ $45\,\text{m}$

Point	Value
5.374	5.374

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

Percentage

P5 to P6

Part as a percentage $\frac{\text{part}}{\text{whole}} \times 100\%$ Example18 out of 24 → $\frac{18}{24} \times 100\% =$ $75\%$
Percentage of a quantity15% of $60 → $\frac{15}{100} \times 60 =$ $\text{\textdollar}9$
30% is $45: find 10%, then 100%10% → $45 \div 3 =$ $\text{\textdollar}15$ 100% → $15 \times 10 =$ $\text{\textdollar}150$
Percentage change $\frac{\text{change}}{\text{original}} \times 100\%$ Example$40 to $50 → $10 \div 40 \times 100\% =$ $25\%$ $50 to $40 → $10 \div 50 \times 100\% =$ $20\%$
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

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

Ratio

Share $84 in the ratio 3 : 4. Find 1 unit first.3 + 4 = 7 units in all.1 unit → $84 \div 7 =$ $\text{\textdollar}12$ A → $3 \times 12 =$ $\text{\textdollar}36$ B → $4 \times 12 =$ $\text{\textdollar}48$
Boys : girls = 3 : 5boys as a fraction of girls → $3 \div 5 =$ $\frac{3}{5}$ boys as a fraction of all → $3 \div 8 =$ $\frac{3}{8}$
Simplest form: ÷ every term by the same number $12 : 18 =$ $12 \div 6 : 18 \div 6 =$ $2 : 3$ $12 : 18 : 24 =$ $2 : 3 : 4$
Equivalent ratios: × or ÷ every term by the same number $2 : 5 =$ $2 \times 3 : 5 \times 3 =$ $6 : 15$ 3 : 4 = ? : 20 → $3 \times (20 \div 4) =$ $15$

Algebra

A letter stands for an unknown number $3a = 3 \times a, \quad \frac{a}{3} = a \div 3$
Add or take away like terms only $5a + 2 - 2a + 4 = 3a + 6$
Substitute a = 4 into 3a + 6 $3 \times 4 + 6 =$ $18$
Solve 2x + 5 = 17: undo each step, then check2x → $17 - 5 =$ $12$ x → $12 \div 2 =$ $6$ check → $2 \times 6 + 5 =$ $17$

Number and Shape Patterns

Number pattern: the nth term $\text{first} + (n - 1) \times \text{jump}$ The 20th term is 19 jumps after the first.Example20th term → $4 + 19 \times 7 =$ $137$
Repeating patternDivide by the length of the repeat. The remainder is the place in the repeat.50th, repeat of 4 → $50 \div 4 =$ $12\text{ R }2$

Time

12-hour 24-hour
9.05 a.m. 09 05
12 noon 12 00
3.15 p.m. 15 15
midnight 00 00
24-hour clockAfter 12 noon, add 12 to the hour. Midnight is 00 00. $3.15\text{ p.m.} =$ $15\ 15$
Span Gap
9.45 a.m. → 10 a.m. 15 min
10 a.m. → 11 a.m. 1 h
11 a.m. → 11.15 a.m. 15 min
How long it takesCount on to the next hour, then whole hours, then the minutes left.9.45 a.m. to 11.15 a.m. → $15\,\text{min} + 1\,\text{h} + 15\,\text{min} =$ $1\,\text{h}\ 30\,\text{min}$

12-hour	24-hour
9.05 a.m.	09 05
12 noon	12 00
3.15 p.m.	15 15
midnight	00 00

Span	Gap
9.45 a.m. → 10 a.m.	15 min
10 a.m. → 11 a.m.	1 h
11 a.m. → 11.15 a.m.	15 min

Geometry

P4 to P6

Angles in a right angleThey add up to 90°. Every corner of a rectangle is 90°.∠y → $90 - 35 =$ $55\degree$
Angles on a straight line $a + b = 180\degree$
Angles at a point $a + b + c = 360\degree$
Vertically opposite angles are equal
Angles in a triangle $a + b + c = 180\degree$
Isosceles triangle: 2 equal sides, 2 equal base angles
Equilateral triangle: every angle is 60° $180 \div 3 =$ $60\degree$
Angles in a quadrilateral $a + b + c + d = 360\degree$
Parallelogram, rhombus: opposite angles are equal $a + b = 180\degree$
Trapezium: the angles between parallel sides $a + b = 180\degree$
Cube6 equal square faces. A dotted line is a hidden edge.
Cuboid6 rectangle faces, in 3 matching pairs.

Area & Perimeter

P3 to P5

Rectangle: area A, perimeter P $A = l \times b \qquad P = 2l + 2b$ l = length, b = breadth. Breadth from the area: A ÷ l.Example $7 \times 4 =$ $28\,\text{cm}^{2}$ $7 + 4 + 7 + 4 =$ $22\,\text{cm}$ breadth → $84 \div 12 =$ $7\,\text{cm}$
Square: area A, perimeter P $A = s \times s \qquad P = 4 \times s$ s = side. The side from the perimeter: P ÷ 4.Example $6 \times 6 =$ $36\,\text{cm}^{2}$ $4 \times 6 =$ $24\,\text{cm}$ side → $36 \div 4 =$ $9\,\text{cm}$
Area of a triangle $A = \tfrac{1}{2} \times b \times h$ b = base, h = 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. $\frac{1}{2} \times 4 \times 6 =$ $12\,\text{cm}^{2}$
Composite figuresArea: split into rectangles, then add. Perimeter: the outside edge only.area → $10 \times 4 + 5 \times 3 =$ $55\,\text{cm}^{2}$ perimeter → $10 + 4 + 5 + 3 + 5 + 7 =$ $34\,\text{cm}$

Volume

P5 to P6

Volume of a cuboid $V = l \times b \times h$ a cube: edge × edge × edge
Height of a cuboid $h = V \div \text{base area}$ Example360 cm³, base 40 cm² → $360 \div 40 =$ $9\,\text{cm}$
Area of a face $A = V \div h$ Example480 cm³, h = 6 cm → $480 \div 6 =$ $80\,\text{cm}^{2}$
Edge of a cube $\text{edge} = \sqrt[3]{V}$ Example343 cm³ → $\sqrt[3]{343} =$ $7\,\text{cm}$
Water added or taken outWater added or taken out = l × b × 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 $7200 \div 1000 =$ $7.2\,\ell$

Circles

\frac{22}{7}

Diameter and radius $d = 2r$
Circumference: the distance around $C = \pi d = 2\pi r$ Example $2 \times \pi \times 7 =$ $44\,\text{cm}$
Area of a circle $A = \pi r^{2}$ Example $\pi \times 7 \times 7 =$ $154\,\text{cm}^{2}$
Half circle: perimeter $\tfrac{1}{2}\pi d + d$ Example $\frac{1}{2} \times \pi \times 14 + 14 =$ $36\,\text{cm}$
Quarter circle: perimeter $\tfrac{1}{2}\pi r + 2r$ Example $\frac{1}{2} \times \pi \times 7 + 2 \times 7 =$ $25\,\text{cm}$
Half or quarter circle: area $\tfrac{1}{2}\pi r^{2} \text{ or } \tfrac{1}{4}\pi r^{2}$ Example $\frac{1}{4} \times \pi \times 14^{2} =$ $154\,\text{cm}^{2}$
Composite figuresArea: add or take away. Perimeter: the outside edge only.square − quarter circle → $14 \times 14 - 154 =$ $42\,\text{cm}^{2}$

Shapes and Spatial Reasoning

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.

Graphs & Tables

P3 to P4

Category Number of cups
Mon 30
Tue 25
Wed 40
Read the scale firstFind what one step on the scale is worth first.half of a step of 10 → $10 \div 2 =$ $5$ Tuesday → $20 + 5 =$ $25$
Series 1
Mon 20
Tue 30
Wed 40
Thu 70
Fri 60
Read a line graphRead each point against the scale. The steepest rise is the biggest change.Wed to Thu → $70 - 40 =$ $30$

Category	Number of cups
Mon	30
Tue	25
Wed	40

	Series 1
Mon	20
Tue	30
Wed	40
Thu	70
Fri	60

Pie Charts

Category Share Value
half ? ?
quarter ? ?
quarter ? ?
A sector is a fraction of the wholeA right-angle mark is a quarter of the circle. A straight line across the centre cuts it in half.
Category Share Value
? ? ?
half ? ?
quarter ? ?
A part from the totalPart = fraction × total. Total = part ÷ fraction.a quarter of 120 → $\frac{1}{4} \times 120 =$ $30$ total → $4 \times 18 =$ $72$

Category	Share	Value
half	?	?
quarter	?	?
quarter	?	?

Category	Share	Value
?	?	?
half	?	?
quarter	?	?

Average

Average $\text{total} \div \text{number}$ Example $(12 + 15 + 18) \div 3 =$ $15$
Total from the average $\text{average} \times \text{number}$ Example3 numbers, average 14 → $14 \times 3 =$ $42$

Every formula, level by level

This sheet keeps what to know by heart. The level sheets hold all 253 formulas and rules, one level at a time.

$P6 Maths Cheat Sheet, page 1 of 4: formulas for fractions, ratio and percentage$
P6 Maths Cheat Sheet
36 formulas and rules · 8 topics · 6 problem-sum methods · 4 A4 pages
- Fractions
- Ratio
- Percentage
- Algebra
- Angles in Geometrical Figures
- Circles
- Volume of Cube and Cuboid
- Average
See every formula
$P5 Maths Cheat Sheet, page 1 of 6: formulas for whole numbers and four operations; and fractions and division$
P5 Maths Cheat Sheet
48 formulas and rules · 12 topics · 6 problem-sum methods · 6 A4 pages
- Whole Numbers and Four Operations
- Fractions and Division
- Decimals
- Percentage
- Rate
- Number and Shape Patterns
- Area of Triangle
- Volume of Cube and Cuboid
- Shapes and Spatial Reasoning
- Angles
- Properties of Triangles
- Parallelogram, Rhombus and Trapezium
See every formula
P4 Maths Cheat Sheet
48 formulas and rules · 12 topics · 5 problem-sum methods · 7 A4 pages
- Numbers to 100 000
- Factors and Multiples
- Four Operations of Whole Numbers
- Fractions
- Decimals
- Angles
- Rectangles and Squares
- Area and Perimeter
- Nets
- Symmetry
- Tables and Line Graphs
- Pie Charts
See every formula
P3 Maths Cheat Sheet
45 formulas and rules · 10 topics · 5 problem-sum methods · 8 A4 pages
- Numbers to 10 000
- Money
- Multiplication and Division
- Fractions
- Angles
- Perpendicular and Parallel Lines
- Length, Mass and Volume
- Area and Perimeter
- Time
- Bar Graphs
See every formula
P2 Maths Cheat Sheet
35 formulas and rules · 12 topics · 2 problem-sum methods · 7 A4 pages
- Numbers to 1000
- Addition and Subtraction within 1000
- Multiplication and Division
- Multiplication Tables of 3 and 4
- Fractions
- Money
- Length
- Mass
- Time
- Volume
- Shapes and Patterns
- Picture Graphs
See every formula
P1 Maths Cheat Sheet
41 formulas and rules · 13 topics · 2 problem-sum methods · 8 A4 pages
- Numbers to 10
- Addition and Subtraction within 10
- Ordinal Numbers and Position
- Numbers to 20
- Addition and Subtraction within 20
- Numbers to 100
- Addition and Subtraction within 100
- Multiplication and Division
- Money
- Shapes
- Length
- Time
- Picture Graphs
See every formula

The sheet

All 11 pages, full size

The PDF prints sharp on A4. Each page is also an image you can save or send.

PSLE Maths Cheat Sheet, page 1 of 11: formulas for the four operations; and factors and multiples, exam rules and units
$PSLE Maths Cheat Sheet, page 2 of 11: formulas for fractions$
PSLE Maths Cheat Sheet, page 2 of 11: formulas for fractions
PSLE Maths Cheat Sheet, page 3 of 11: formulas for decimals
PSLE Maths Cheat Sheet, page 4 of 11: formulas for percentage and rate
PSLE Maths Cheat Sheet, page 5 of 11: formulas for ratio; algebra; and number and shape patterns
PSLE Maths Cheat Sheet, page 6 of 11: formulas for time and geometry
PSLE Maths Cheat Sheet, page 7 of 11: formulas for area & perimeter
PSLE Maths Cheat Sheet, page 8 of 11: formulas for volume
PSLE Maths Cheat Sheet, page 9 of 11: formulas for circles; and shapes and spatial reasoning
PSLE Maths Cheat Sheet, page 10 of 11: formulas for graphs & tables and pie charts
PSLE Maths Cheat Sheet, page 11 of 11: formulas for average, problem-sum methods

Download the free PDF11 A4 pages · PDF, 1469 KB

Knowing the formula is half of it

The other half is spotting which one a question needs. StudyLah gives your child 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

PSLE Maths formulas: questions parents ask

Does the PSLE Maths paper give a formula list?

No. SEAB's syllabus for the paper lists no formula sheet, and recalling facts, rules and formulae is the first thing the paper assesses. It prints the unit each answer needs, never the formula.

Which formulas does my child need for the PSLE?

Every formula in the primary syllabus, because the PSLE assesses all of it. This sheet gathers the 77 to know by heart, from P3 to P6, and the level sheets hold all 253, one level at a time.

What topics are tested in PSLE Maths?

Every topic of the primary Maths syllabus, from P1 to P6, in its three strands: Number and Algebra; Measurement and Geometry; and Statistics. This sheet's 18 topics are the ones with a formula or rule to know by heart.

Syllabus & guides

Are P5 Maths topics tested in the PSLE?

Yes. The PSLE assesses the whole primary Maths syllabus, so P5 topics such as whole numbers and four operations; fractions and division; area of triangle; and volume of cube and cuboid are in it.

P5 Maths Cheat Sheet

Can my child use a calculator in PSLE Maths?

In Paper 2 only. Paper 1, Booklets A and B, is done without one.

The PSLE Maths paper, broken down

Which value of π should my child use?

The one the question gives: 3.14 or 22/7. Each circle example on this sheet says which it uses.

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's changing in 2026 PSLE Maths

Does my child need to show the working?

Yes. On a short question, a wrong answer with the correct method can still score a mark, and long questions ask for every step.

The PSLE Maths paper, broken down

Which unit conversions does my child need to know?

The answer has to be in the unit the question gives, so these have to be known: 1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, 1 ℓ = 1000 mℓ = 1000 cm³, 1 h = 60 min, 1 min = 60 s.

Does my child need the volume of a cylinder or a cone?

No. Primary Maths asks for the volume of cubes and cuboids only. Cylinders and cones appear only as shapes and nets.

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 24 October 2026

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