Free resource · PSLE (Primary 1 to 6)

PSLE Math Formulas and Formula Sheet (0008): Free PDF

There is no formula sheet in the PSLE Mathematics paper (0008), so pupils must recall every formula themselves. They need to know the formulas for perimeter, area and volume, the circumference and area of a circle, the angle facts for triangles and quadrilaterals, and the rules for fractions, percentage, ratio, rate and average. Calculators are allowed in Paper 2 only, not in Paper 1.

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$First page of the PSLE Math Formulas PDF$

Written for PSLE Standard Mathematics (0008). Items marked Standard Mathematics only are not in PSLE Foundation Mathematics (0038). P1 to P6 shows the level where the syllabus first teaches each one.

No formula list: memorise

Formulas the PSLE Mathematics paper does not give you

There is no formula list in the PSLE Mathematics paper, so these all have to be known by heart. Each one is in the syllabus.

Whole numbers

Order of operationsP5. Within each step, work from left to right. Practise without a calculator: $brackets first, then \times and \div, then + and -$

Fractions

Equivalent fractionsP3. Multiply or divide the numerator and the denominator by the same number: $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
Mixed number to improper fractionP4: $2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$

Fraction of a quantityP4 and P5: $\frac{3}{4} of 20 = \frac{3}{4} \times 20 = 15$
Adding and subtracting unlike fractionsP4 and P5. Change to the same denominator first: $\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$
Multiplying fractionsP5. Multiply the numerators, then multiply the denominators: $\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$
Dividing fractionsP6. Turn the number you divide by upside down (4 becomes 1/4), then multiply. Practise without a calculator: $\frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4} = \frac{1}{6}, \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{5}{6}$

Decimals

Fractions and decimalsP4 and P5. A fraction is the numerator divided by the denominator: $0.1 = \frac{1}{10}, 0.01 = \frac{1}{100}, 0.001 = \frac{1}{1000}, \frac{3}{4} = 3 \div 4 = 0.75$

Percentage

Part of a whole as a percentageP5: $\frac{part}{whole} \times 100%$
Percentage of a quantityP5. For example, 15% of 80 is 15 ÷ 100 × 80 = 12: $\frac{percentage}{100} \times whole$

Finding the wholeP6, Standard Mathematics only. For example, if 20% is 30, the whole is 30 ÷ 20 × 100 = 150: $whole = \frac{part}{percentage} \times 100$
Percentage increase or decreaseP6, Standard Mathematics only. Always divide by the original value: $\frac{increase or decrease}{original value} \times 100%$
DiscountP5: $discount = \frac{percentage discount}{100} \times usual price, sale price = usual price - discount$
GSTP5. Use the GST rate given in the question: $GST = \frac{GST rate}{100} \times price before GST, price with GST = price before GST + GST$
Annual interestP5. Amount after 1 year = amount saved + interest: $interest for 1 year = \frac{interest rate}{100} \times amount saved$

Ratio

Equivalent ratios and simplest formP6, Standard Mathematics only. Multiply or divide every term by the same number: $6 : 9 = (6 \div 3) : (9 \div 3) = 2 : 3$
Dividing a quantity in a given ratioP6, Standard Mathematics only. For a ratio of 2 : 3 there are 5 parts in total: $1 part = \frac{total}{total number of parts}$

Ratio and fractionP6, Standard Mathematics only: $A : B = 2 : 3 means A = \frac{2}{3} of B and A = \frac{2}{5} of the total$

Rate

RateP5. Rate is the amount per unit, for example $3 per kg. Number of units = total amount ÷ rate: $rate = \frac{total amount}{number of units}, total amount = rate \times number of units$

Average

AverageP6: $average = \frac{total value}{number of items}, total value = average \times number of items$

Algebra

Writing and simplifying expressionsP6, Standard Mathematics only: $3 \times a = 3 a, a \div 3 = \frac{a}{3}, 2 a + 5 a - a = 6 a$

Substitution and simple equationsP6, Standard Mathematics only. Do the same thing to both sides of an equation: $if a = 4, 3 a + 2 = 3 \times 4 + 2 = 14, 3 a + 2 = 14, 3 a = 12, a = 4$

Measurement: units

Length, mass and volume of liquidP3 and P5: $1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, 1 ℓ = 1000 ml$

TimeP2 (hours and minutes) and P3 (seconds, 24-hour clock): $1 h = 60 min, 1 min = 60 s$

Measurement: perimeter and area

RectangleP3: $perimeter = 2 \times (length + breadth), area = length \times breadth$

SquareP3: $perimeter = 4 \times length, area = length \times length$
Missing side of a rectangleP4: $breadth = area \div length or breadth = perimeter \div 2 - length$
Side of a squareP4. For example, a square of area 49 cm² has sides of 7 cm. The √ sign is P6, Standard Mathematics only: $side = perimeter \div 4 or side = area$
Area of a triangleP5. The height is at right angles to the base: $\frac{1}{2} \times base \times height$

Measurement: circles

Circumference of a circleP6, Standard Mathematics only. Diameter = 2 × radius: $π \times diameter = 2 \times π \times radius$
Area of a circleP6, Standard Mathematics only. Use the value of π the question gives: $π \times radius \times radius$

SemicircleP6, Standard Mathematics only. The perimeter includes the straight edge: $area = \frac{1}{2} \times π \times radius \times radius, perimeter = \frac{1}{2} \times π \times diameter + diameter$
Quarter circleP6, Standard Mathematics only. The perimeter includes the two straight edges: $area = \frac{1}{4} \times π \times radius \times radius, perimeter = \frac{1}{4} \times 2 \times π \times radius + 2 \times radius$

Measurement: volume

Volume of a cuboidP5 and P6: $length \times breadth \times height = base area \times height$

Volume of a cubeP5. Finding the edge from the volume, and the ∛ sign, are P6, Standard Mathematics only: $edge \times edge \times edge, edge = 3 volume$
Finding a missing dimensionP6, Standard Mathematics only: $height = \frac{volume}{base area}, length = \frac{volume}{breadth \times height}, area of a face = \frac{volume}{the other dimension}$
Water in a rectangular tankP5. Also 1 ml = 1 cm³: $volume of water = length \times breadth \times height of water, 1000 cm^{3} = 1 ℓ$

Geometry: angles

Angles on a straight lineP5: $angles on a straight line add up to 18 0^{\circ}$
Angles at a pointP5: $angles at a point add up to 36 0^{\circ}$

Vertically opposite anglesP5: $vertically opposite angles are equal$

Geometry: triangles

Angle sum of a triangleP5. In a right-angled triangle, the other 2 angles add up to 90°: $the 3 angles of a triangle add up to 18 0^{\circ}$
Isosceles triangleP5: $2 equal sides, and the 2 angles opposite them are equal$

Equilateral triangleP5: $3 equal sides, and each angle is 6 0^{\circ}$

Geometry: quadrilaterals

Rectangle and squareP4. A square also has 4 equal sides: $all 4 angles are 9 0^{\circ}, opposite sides are equal and parallel$

ParallelogramP5, Standard Mathematics only. Opposite sides are parallel and equal: $opposite angles are equal, neighbouring angles add up to 18 0^{\circ}$
RhombusP5, Standard Mathematics only. A rhombus is a parallelogram with 4 equal sides: $4 equal sides, opposite angles are equal, neighbouring angles add up to 18 0^{\circ}$
TrapeziumP5, Standard Mathematics only: $one pair of parallel sides, the 2 angles on each non-parallel side add up to 18 0^{\circ}$

Inside the PDF

4 A4 pages, ready to print. Tap a page to open the PDF there.

Questions students ask

Is a formula sheet given in PSLE Math?

No. The SEAB exam format for PSLE Mathematics (0008) does not include a list of formulae, and its first assessment objective asks pupils to "recall mathematical facts, concepts, rules and formulae". Every formula on this page has to be learnt by heart.

Can I use a calculator in PSLE Math?

Only in Paper 2. Paper 1 has two booklets and calculators are not allowed. Paper 2 has one booklet and calculators are allowed. The syllabus also lists some skills, such as the order of operations and dividing fractions, as done without a calculator, so practise these by hand.

Which value of π should I use in PSLE Math?

Neither the SEAB exam format nor the MOE syllabus fixes one value of π. Read each circle question carefully and use the value of π that the question tells you to use.

Is speed in the PSLE Math syllabus?

No. The 2021 Primary Mathematics syllabus, which applies to Primary 6 from 2026, does not list speed. It covers rate instead, as the amount of a quantity per unit of another quantity, from Primary 5. The area of a parallelogram or a trapezium is not listed either.

Is this sheet for Foundation Mathematics too?

Mostly. It is written for PSLE Standard Mathematics (0008). Items marked Standard Mathematics only, such as ratio, algebra, circles and the properties of a parallelogram, rhombus and trapezium, are not in PSLE Foundation Mathematics (0038). Everything else applies to both.

Keep revising

Source

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