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Primary 5 Maths Mock Paper in English: Fractions, Equations, Area and Volume
TUTORZONE ORIGINAL MOCK PAPER · PRIMARY 5 MATHEMATICS (ENGLISH) · EDB UNITS 5N1-5D1
Written to the EDB P5 learning units 5N1-5D1: 22 questions, 60 marks, 60 minutes, questions and answers in English throughout. Covers fraction multiplication and division, mixed fraction operations, decimals, simple equations, the area of triangles, parallelograms and trapeziums, volume, circle properties and bar charts.
What does the Primary 5 paper cover?
Direct answer: the EDB P5 units: fraction multiplication, division and mixed operations, decimals, simple equations, the area of triangles, parallelograms and trapeziums, the volume of cubes and cuboids, circle radius/diameter/circumference and bar charts – 22 questions, 60 marks, 60 minutes, in English. Circle area is P6.
This paper at a glance (sections, marks and timing)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Section A Quick computation | 12 short questions, 1 mark each: fraction multiplication and division, fraction of a quantity, solving equations, triangle and parallelogram area, volume, decimal-fraction conversion, radius from diameter | 12 | 14 min |
| Section B Short questions | 5 questions, 3 marks each: trapezium area, two-step equations, cube volume, unitary method, fraction multiplication | 15 | 16 min |
| Section C Word problems | 5 questions for 33 marks: fraction of a quantity, dividing by a unit fraction, forming and solving an equation, area and perimeter, volume and capacity | 33 | 30 min |
The table above describes how this paper is laid out; it is not an official examination structure from the EDB or any school. P5 pacing: 22 questions in 60 minutes. The three biggest leaks all come from one missing step: forgetting to halve in triangle area, forgetting to invert-and-multiply in fraction division, and applying an operation to only one side of an equation. Fix the routine: formula first, numbers second, unit last.
How this paper was built
The paper follows the P5 units in the EDB Learning Content of Primary Mathematics (2017): Number (5N1-5N5), Algebra (5A1-5A2), Measures (5M1-5M2), Shape and Space (5S1-5S2) and Data Handling (5D1). All questions are original.
Scope: circles are limited to the radius, diameter and circumference relationships (5S1); the area of a circle belongs to P6 (6M5). Volume covers cubes and cuboids only (5M2); equations use whole-number coefficients (5A2).
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Section A Quick computation | 12 | 14 min | Simplify every fraction; write the formula before substituting in area questions |
| Section B Short questions | 15 | 16 min | The unitary method has a fixed two-line shape: find one, then multiply |
| Section C Word problems | 33 | 30 min | Equation answers must define x; volume answers must end in the capacity unit |
How is the 60 minutes split?
Direct answer: 14 minutes for Section A, 16 for B and 30 for C, with seven minutes each for the equation and volume questions and six for the fraction context question.
Section A: Quick computation (12 questions, 1 mark each)
Answer only; simplify all fractions.
Question 1 (1 mark)
1/2 × 3/5 = ?
Question 2 (1 mark)
3/4 ÷ 1/8 = ?
Question 3 (1 mark)
2/3 of 45 = ?
Question 4 (1 mark)
Solve x + 7 = 15.
Question 5 (1 mark)
Solve 4x = 36.
Question 6 (1 mark)
Find the area of a triangle with base 12 cm and height 7 cm.
Question 7 (1 mark)
Find the area of a parallelogram with base 9 cm and height 5 cm.
Question 8 (1 mark)
Find the volume of a cuboid 6 cm by 4 cm by 3 cm.
Question 9 (1 mark)
Write 0.35 as a fraction in its simplest form.
Question 10 (1 mark)
The diameter of a circle is 14 cm. What is its radius?
Question 11 (1 mark)
1/6 of 54 = ?
Question 12 (1 mark)
0.6 × 100 = ?
Section B: Short questions (5 questions, 3 marks each)
Write the formula or equation before substituting.
Question 1 (3 marks)
Find the area of a trapezium with parallel sides 8 cm and 12 cm and height 5 cm.
Question 2 (3 marks)
Solve 3x − 4 = 20.
Question 3 (3 marks)
Find the volume of a cube of edge 5 cm.
Question 4 (3 marks)
4 books cost $52. What is the cost of 7 books?
Question 5 (3 marks)
5/8 × 4/15 = ?
Section C: Word problems (5 questions, 33 marks)
Define x in equation questions; give units for area and volume; split (a)(b)(c).
Question 1 (6 marks)
A tank holds 48 L of water and is 3/4 full. (a) How much water is in the tank? (b) One third of that water is used. How much water is left, and what fraction of the tank is that?
Question 2 (6 marks)
3/4 kg of flour is put into small bags of 1/8 kg each. How many bags are needed?
Question 3 (7 marks)
Peter has x marbles. Mary has 3 times as many as Peter. Together they have 48 marbles. (a) Write an equation. (b) Find x. (c) How many marbles does Mary have?
Question 4 (7 marks)
A rectangular field is 15 m by 10 m. A rectangular pond 6 m by 4 m is dug inside it. (a) Find the area of the grass. (b) Find the perimeter of the field.
Question 5 (7 marks)
A tank is 30 cm long, 20 cm wide and 15 cm high. (a) Find its volume in cm³. (b) Write that volume in litres. (c) How much water is in it when it is half full?
Do the answers show formulas and steps?
Direct answer: yes. Area answers write (base x height) / 2 or (a + b) / 2 x height first, equation answers work line by line (3x = 24, so x = 8), and volume answers finish with the litre conversion.
Section A answers and marks
Question 1
3/10. Multiply numerators and denominators: (1 × 3) / (2 × 5).
Question 2
6. Dividing by 1/8 is multiplying by 8: 3/4 × 8 = 6.
Question 3
30. 45 ÷ 3 = 15, then 15 × 2.
Question 4
x = 8. Subtract 7 from both sides; check 8 + 7 = 15.
Question 5
x = 9. Divide both sides by 4; check 4 × 9 = 36.
Question 6
42 cm². (12 × 7) ÷ 2 – the halving is the step most often forgotten.
Question 7
45 cm². Base × height; no halving for a parallelogram.
Question 8
72 cm³. 6 × 4 × 3.
Question 9
7/20. 35/100, then divide top and bottom by 5.
Question 10
7 cm. The radius is half the diameter.
Question 11
9. 54 ÷ 6.
Question 12
60.0. Multiplying by 100 moves the decimal point two places right.
Section B answers and marks
Question 1
(8 + 12) ÷ 2 × 5 = 50 cm². Add the parallel sides, halve, then multiply by the height.
Question 2
3x = 24, so x = 8. Add 4 to both sides first, then divide.
Question 3
5 × 5 × 5 = 125 cm³.
Question 4
One book: $52 ÷ 4 = $13. Seven books: $13 × 7 = $91. This is the unitary method – find one, then multiply.
Question 5
4/8 = 1/2 and 5/15 = 1/3, so the answer is 1/2 × 1/3 = 1/6.
Section C answers and marks
Question 1
(a) 48 ÷ 4 × 3 = 36 L. (b) 36 ÷ 3 = 12 L used, so 36 − 12 = 24 L left, which is half the tank.
Question 2
3/4 ÷ 1/8 = 3/4 × 8 = 6 bags. Dividing by a unit fraction multiplies.
Question 3
(a) x + 3x = 48. (b) 4x = 48, so x = 12. (c) 3 × 12 = 36 marbles. Check: 12 + 36 = 48.
Question 4
(a) 15 × 10 = 150 and 6 × 4 = 24, so the grass is 126 m². (b) (15 + 10) × 2 = 50 m.
Question 5
(a) 30 × 20 × 15 = 9000 cm³. (b) 1000 cm³ = 1 L, so 9 L. (c) Half of 9000 cm³ = 4500 cm³ = 4.5 L.
Where do P5 marks usually go?
Direct answer: forgetting to halve triangle area, not inverting in fraction division, changing only one side of an equation, and mixing volume with capacity units. All four are one missing step, not missing knowledge.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Forgetting to halve in triangle area | Writing 12 x 7 = 84 cm² | The whole item is wrong | Write (base x height) / 2 before substituting |
| Not inverting in fraction division | 3/4 / 1/8 worked as 3/32 | Out by a factor of 48 | Dividing by a fraction is multiplying by its reciprocal |
| Changing one side of an equation only | 3x – 4 = 20 turned into 3x = 20 | The answer is wrong | Add 4 to both sides, then divide both sides by 3 |
| Confusing volume with capacity units | 9000 cm³ written as 9000 L | Out by a factor of 1000 | 1000 cm³ = 1 L; convert before writing the answer |
How to use this paper
Timed in blocks of 14 / 16 / 30 minutes, keeping seven minutes each for the equation question and the volume question.
Marking: check the formula or equation line first, then the number. An answer with no formula line is marked zero and redone.
Seven days later: log the errors and add three more questions – one triangle area, one fraction division, one two-step equation.
What comes after this paper?
Direct answer: log the errors, redo after seven days, then move to the P6 paper. If two or more fraction operation questions were wrong, drill six more fraction calculations first.
FAQ
Why no circle area at P5?
Because the EDB puts circle area in P6 (unit 6M5, pi taken as 22/7 or 3.14). P5 covers the radius, diameter and circumference relationships only (5S1).
How should fraction division be taught?
Start from meaning: dividing by 1/8 asks how many eighths fit. 3/4 kg into 1/8 kg bags gives 6 bags, and the invert-and-multiply rule follows from that.
Must the equation question define x?
School papers usually require it, and an undefined x loses a mark even when the number is right – which is how this paper’s scheme is written.
Which paper next?
The P6 paper: percentages, speed, circle area and circumference, angles, symmetry, averages and statistical charts.
Official references
| Resource | What to check |
|---|---|
| https://www.edb.gov.hk/attachment/en/curriculum-development/kla/ma/curr/pmc2017_e.pdf | EDB Learning Content of Primary Mathematics (2017): P5 units 5N1-5D1 |
| https://www.tutorzone.com.hk/en-primary-maths-p4-mock-2027/ | Primary 4 paper: factors, multiples, perimeter and area |
| https://www.tutorzone.com.hk/en-primary-maths-p6-mock-paper/ | Primary 6 paper: percentages, speed, circle area and statistics |
Related: practice area · Primary 4 paper · Primary 6 paper
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