Whole Numbers
0 practice questions
- Evaluate expressions with brackets and all four operations
- Round to the nearest 10, 100, 1000 and estimate answers
- Check if an answer is reasonable
Primary 6 Mathematics syllabus: topics and practice questions
These are the topics and skills of Primary 6 Mathematics in the MOE syllabus, with 38 original practice questions. Each topic below has a sample question: try it, then open the worked answer.
Number & Algebra
Fractions
3 practice questions
- Find a fraction of a whole number
- Find the whole when a fraction of it is known
- Divide a proper fraction by a whole number
- Divide a whole number or fraction by a proper fraction
- Solve "remainder" problems (fraction of what is left)
- Solve problems with before-and-after changes
Sample question
Find 3/5 of 200.
Show the answer and working
Answer: 120
How:
200 ÷ 5 = 40
40 × 3 = 120
Why: The 5 tells us to split 200 into 5 equal parts, so one part is 200 ÷ 5. We want 3 of those parts, so we multiply one part by 3.
Decimals
3 practice questions
- Multiply and divide decimals by whole numbers
- Convert between fractions and decimals
- Solve multi-step money and measurement problems with decimals
Sample question
Calculate 4.25 × 6.
Show the answer and working
Answer: 25.5
How:
425 × 6 = 2550
4.25 has 2 decimal places, so 4.25 × 6 = 25.50 = 25.5
Why: 4.25 is 425 hundredths. 6 lots of 425 hundredths is 2550 hundredths, which is 25.5.
Percentage
3 practice questions
- Find a percentage of a quantity
- Express one quantity as a percentage of another
- Find the whole given a part and its percentage
- Find percentage increase and decrease
- Solve discount, GST and service charge problems
Sample question
Find 15% of 80.
Show the answer and working
Answer: 12
How:
15/100 × 80 = 12
Why: 15% means 15 hundredths, so we take 15 hundredths of 80.
Ratio
3 practice questions
- Find the value of one unit from a total
- Write and simplify ratios of two or three quantities
- Convert between ratios and fractions of a whole
- Solve problems where one quantity is unchanged
- Solve problems where the total is unchanged
- Solve problems where the difference is unchanged
Sample question
Ali and Ben share 50 stickers in the ratio 3 : 2. How many stickers does Ali get?
Show the answer and working
Answer: 30
How:
Total units: 3 + 2 = 5
1 unit = 50 ÷ 5 = 10
Ali: 3 units = 30
Why: The ratio 3 : 2 means the stickers are split into equal units: 3 for Ali and 2 for Ben. The 50 stickers fill all 5 units, so one unit is 50 ÷ 5.
Rate
0 practice questions
- Find rate, total amount or number of units
- Solve problems with tiered rates (e.g. charges)
Speed
3 practice questions
- Find distance, time or speed
- Convert between minutes and hours in speed problems
- Find average speed for a whole journey
- Solve problems with two objects moving towards or after each other
Sample question
A car travels 180 km in 3 hours. What is its average speed?
Show the answer and working
Answer: 60 km/h
How:
180 km ÷ 3 h = 60 km/h
Why: In 3 hours the car goes 180 km, so in 1 hour it goes a third of that distance.
Factors & Multiples
0 practice questions
- Find common factors and common multiples
- Solve grouping and repeating-cycle problems
Algebra
0 practice questions
- Use a letter to represent an unknown number
- Simplify linear expressions
- Evaluate an expression by substitution
- Solve simple linear equations
Patterns
0 practice questions
- Find a rule for a pattern
- Find the nth term of a pattern
Problem Solving
3 practice questions
- Use the model (bar) method
- Use guess and check / make a table
- Work backwards
- Use the "assumption" method
Sample question
Sam and Tina have 84 marbles altogether. Tina has 12 more marbles than Sam. How many marbles does Sam have?
Show the answer and working
Answer: 36
How:
Take away the difference: 84 − 12 = 72
Two equal bars: 72 ÷ 2 = 36
Why: Without Tina's extra 12 marbles, both bars are the same length, and together they make 72.
Measurement & Geometry
Length
0 practice questions
- Convert between km, m and cm
Mass
0 practice questions
- Convert between kg and g and solve mass problems
Volume
4 practice questions
- Find volume by counting unit cubes
- Find volume using length × breadth × height
- Find a missing dimension from the volume
- Convert between cm³, ml and litres
- Solve tank-filling and water-level problems
Sample question
A cuboid is 4 cm long, 3 cm wide and 2 cm high. Find its volume.
Show the answer and working
Answer: 24 cm³
How:
One layer: 4 × 3 = 12 cubes
2 layers: 12 × 2 = 24 cm³
Why: The bottom layer holds 4 rows of 3 unit cubes. The cuboid is 2 cubes high, so there are 2 such layers.
Time
0 practice questions
- Find duration and use the 24-hour clock
Money
0 practice questions
- Solve multi-step money problems
Area
3 practice questions
- Find the area of a triangle using base and height
- Identify the height for a given base
- Find the area of a circle, semicircle and quadrant
Sample question
A triangle has a base of 12 cm and a height of 7 cm. Find its area.
Show the answer and working
Answer: 42 cm²
How:
1/2 × 12 × 7 = 42 cm²
Why: Any triangle fits exactly into half of a rectangle that has the same base and height, so its area is half of base × height.
Perimeter
3 practice questions
- Find the perimeter of rectilinear figures
- Find the perimeter of figures with curved edges
Sample question
A rectangle is 15 cm long and 8 cm wide. Find its perimeter.
Show the answer and working
Answer: 46 cm
How:
15 + 8 + 15 + 8 = 46 cm
Why: Walking all the way around the rectangle, you pass both lengths and both widths.
Angles
1 practice question
- Use angles on a straight line and at a point
- Use vertically opposite angles
Sample question
Two angles lie on a straight line. One of them is 128°. Find the other angle.
Show the answer and working
Answer: 52 °
How:
180° − 128° = 52°
Why: A straight line is half a full turn, and a full turn is 360°, so angles on a straight line make 180°.
Triangles
2 practice questions
- Use the angle sum of a triangle
- Use properties of isosceles and equilateral triangles
Sample question
In an isosceles triangle, the angle between the two equal sides is 40°. Find the size of each of the other two angles.
Show the answer and working
Answer: 70 °
How:
180° − 40° = 140°
140° ÷ 2 = 70°
Why: The other two angles share the 140° that is left, and in an isosceles triangle they are equal, so each gets half.
Quadrilaterals
0 practice questions
- Use properties of parallelograms, rhombuses and trapeziums to find unknown angles
Circles
0 practice questions
- Relate radius and diameter
- Find circumference and length of arcs
3D Solids
0 practice questions
- Identify prisms, pyramids, cylinders, cones and spheres
Nets
1 practice question
- Identify the net of a cube, cuboid, prism or pyramid
- Identify the solid formed by a net
Sample question
The net below is folded to make a solid. Which solid is it?
Show the answer and working
Answer: (B) Cuboid
How:
6 faces, all rectangles
Opposite faces match in pairs
So it folds into a cuboid
Why: When the net folds up, each face meets the face opposite it in size. Three pairs of matching rectangles make the six faces of a cuboid. The faces are not all squares, so it cannot be a cube.
Composite Figures
0 practice questions
- Find area by splitting a figure into parts
- Find area by subtracting a part from a whole
- Find shaded areas involving circles
Statistics
Tables
0 practice questions
- Read and complete tables
Bar Graphs
1 practice question
- Read and interpret bar graphs
Sample question
The bar graph shows the number of books four pupils read last month. How many more books did Chen read than Dev?
Show the answer and working
Answer: 9
How:
15 − 6 = 9
Why: "How many more" asks for the gap between the two bars, which is their difference.
Line Graphs
1 practice question
- Read and interpret line graphs, including trends
Sample question
The line graph shows the temperature during a day. Between which two times did the temperature rise the most?
Show the answer and working
Answer: (B) 10 am and 12 noon
How:
8–10 am: 27 − 24 = 3°C
10 am–12 noon: 31 − 27 = 4°C
12 noon–2 pm: 33 − 31 = 2°C
Why: Each period is 2 hours long, so the period with the largest difference is where the line is steepest.
Pie Charts
1 practice question
- Read pie charts given as fractions or percentages
- Find quantities from angles in a pie chart
Sample question
The pie chart shows how 240 pupils travel to school. How many pupils come by car?
Show the answer and working
Answer: 90
How:
Car: 1 − 1/4 − 3/8 = 3/8
3/8 × 240 = 90
Why: Every pupil is in exactly one sector, so the car sector is whatever fraction is left after walking and bus.
Data Interpretation
0 practice questions
- Compare and draw conclusions from data displays
Average
3 practice questions
- Find the average
- Find the total or a missing value from the average
- Solve problems where the average changes
Sample question
Find the average of 12, 15, 18 and 23.
Show the answer and working
Answer: 17
How:
Total: 12 + 15 + 18 + 23 = 68
Average: 68 ÷ 4 = 17
Why: The average is the amount each would have if the total were shared out equally.
Data Problem Solving
0 practice questions
- Combine data from more than one display
Practise all 38 Primary 6 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 6 mock paper.