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Primary 5 Mathematics syllabus: topics and practice questions

These are the topics and skills of Primary 5 Mathematics in the MOE syllabus, with 55 original practice questions. Each topic below has a sample question: try it, then open the worked answer.

Number & Algebra

Whole Numbers

9 practice questions

  • Read, write and compare numbers up to 10 million
  • Multiply and divide by 10, 100, 1000 and their multiples
  • Use order of operations

Sample question

Write three million, forty thousand and five hundred in numerals.
Show the answer and working

Answer: 3040500

How:
Millions: 3
Thousands: 040 (forty thousand)
Ones: 500
3 040 500

Why: Forty thousand has no hundred thousands, so a 0 must hold that place. Without it, the 4 would slide into the hundred-thousands place.

Fractions

7 practice questions

  • Understand a ÷ b as the fraction a/b
  • Add and subtract mixed numbers
  • Multiply a fraction by a whole number or a fraction

Sample question

Write 7 ÷ 4 as a mixed number.
Fraction picture: a bar split into 4 equal parts with 4 shaded (1), a bar split into 4 equal parts with 3 shaded (3/4).13/4
Show the answer and working

Answer: 1 34

How:
7 ÷ 4 = 74
7 = 4 + 3, so 74 = 1 34

Why: Sharing 7 wholes among 4 gives each 1 whole and 3 quarters, because 7 = 1 × 4 + 3.

Decimals

3 practice questions

  • Multiply and divide decimals by 10, 100, 1000

Sample question

Work out 3.06 × 100.
Show the answer and working

Answer: 306

How:
3.06 × 100 = 306

Why: Each digit becomes 100 times bigger: 3 ones become 3 hundreds and 6 hundredths become 6 ones.

Percentage

5 practice questions

  • Express part of a whole as a percentage
  • Find discount and GST

Sample question

Express 720 as a percentage.
Show the answer and working

Answer: 35

How:
720 = 35100 = 35%

Why: Multiplying the top and bottom by 5 gives an equal fraction out of 100, which is the percentage.

Ratio

5 practice questions

  • Find and write ratios
  • Find equivalent ratios

Sample question

A choir has 12 boys and 17 girls. Write the ratio of the number of boys to the number of girls.
Show the answer and working

Answer: 12:17

How:
Boys : Girls = 12 : 17

Why: The question names boys first, so the 12 goes first. 12 and 17 have no common factor, so the ratio is already in its simplest form.

Rate

3 practice questions

  • Find rate as an amount per unit

Sample question

A tap fills 72 ℓ of water in 6 minutes. How many litres of water does it fill in 1 minute?
Show the answer and working

Answer: 12 ℓ

How:
72 ÷ 6 = 12 ℓ per minute

Why: The water flows at the same rate every minute, so we share the 72 ℓ equally among the 6 minutes.

Measurement & Geometry

Area

3 practice questions

  • Find the area of a triangle

Sample question

Find the area of the right-angled triangle.
Diagram. Triangle with sides marked 10 cm, 6 cm; angle at point 1 is a right angle. Not drawn to scale.10 cm6 cmNot drawn to scale
Show the answer and working

Answer: 30 cm²

How:
12 × 10 × 6 = 30 cm²

Why: The triangle is half of a 10 cm by 6 cm rectangle, so its area is half of 60 cm².

Volume

5 practice questions

  • Build solids with unit cubes and find their volume
  • Find the volume of liquid in a rectangular tank

Sample question

The cuboid is made of 1-cm cubes. What is its volume?
3D picture. A cuboid built from unit cubes (length 5 cm, breadth 2 cm, height 3 cm).5 cm2 cm3 cm
Show the answer and working

Answer: 30 cm³

How:
One layer: 5 × 2 = 10 cubes
3 layers: 10 × 3 = 30 cubes = 30 cm³

Why: Each 1-cm cube is 1 cm³. Every layer has the same number of cubes, so multiply one layer by the number of layers.

Angles

3 practice questions

  • Use angles on a straight line, at a point and vertically opposite angles

Sample question

The figure shows a straight line. Find the unknown angle.
Diagram. Label: 47°. Label: ?. Not drawn to scale.47°?Not drawn to scale
Show the answer and working

Answer: 133 °

How:
180° − 47° = 133°

Why: The two angles together make the straight line, which is 180°.

Triangles

3 practice questions

  • Find unknown angles in a triangle

Sample question

Two angles of a triangle are 58° and 71°. Find the third angle.
Diagram. Triangle; angle at point 1 is 58°; angle at point 2 is 71°; angle at point 3 is ?. Not drawn to scale.58°71°?Not drawn to scale
Show the answer and working

Answer: 51 °

How:
58° + 71° = 129°
180° − 129° = 51°

Why: Whatever its shape, a triangle's three angles always total 180°.

Quadrilaterals

3 practice questions

  • Find unknown angles in quadrilaterals

Sample question

ABCD is a parallelogram. Angle DAB is 68°. Find angle ABC.
Diagram. Four-sided shape ABCD; angle at A is 68°; angle at B is ?. Not drawn to scale.68°?ABCDNot drawn to scale
Show the answer and working

Answer: 112 °

How:
180° − 68° = 112°

Why: AD is parallel to BC, so the two angles at the ends of AB add up to 180°.

Statistics

Average

3 practice questions

  • Find the average of a set of data

Sample question

Find the average of 14, 18, 25 and 31.
Show the answer and working

Answer: 22

How:
14 + 18 + 25 + 31 = 88
88 ÷ 4 = 22

Why: The average is the amount each would have if the total were shared out equally.

Tables

3 practice questions

  • Read and complete tables

Sample question

The table shows the number of pupils in two clubs. How many girls are in the Art Club?
Table: Pupils in two clubs. Columns: Club, Boys, Girls, Total. Chess: Boys 12, Girls 9, Total 21. Art: Boys 8, Girls missing, Total 23.Pupils in two clubsClubBoysGirlsTotalChess12921Art8?23
Show the answer and working

Answer: 15

How:
23 − 8 = 15

Why: The Art Club has 23 pupils, and 8 of them are boys, so the rest are girls.

Practise all 55 Primary 5 questions

With an account, practice adapts to your child: hints one step at a time, feedback on the mistake behind a wrong answer, review of older topics and a Primary 5 mock paper.

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