Day 1 · Starting point
Complete the 15 starting questions without the answers. Mark them and choose three priorities from the topic summary.
Free GCSE maths · online and printable
Working towards Grade 4: a two-week maths pack
Start with a manageable check, find useful priorities and practise one clear skill each day. For Foundation students and families building confidence with core GCSE maths.
This is a selected practice resource, not a full specification, mock paper or grade prediction. Completing it cannot guarantee a grade. Ask your teacher which tier and topics are appropriate.
Robinson Tuition · www.robinsontuition.com/gcse-grade-4-revision
Use the pack on paper
Choose the sections you need. Your browser can print or save them as a PDF. Questions include working space; worked answers begin separately.
Choose A4, standard margins and 100% scale. Switch off browser headers and footers if you prefer. No answers or notes are sent anywhere.
How to use this pack
- Try the questions on paper first. Follow each calculator label and keep your working.
- Open the worked answer when you are ready. Compare the method as well as the result; equivalent correct methods count.
- Record where you worked independently, needed a hint, made an error or skipped. Use the topic map to choose what to practise next.
Marks are suggested maximums for these original practice questions, not an exam-board mark scheme. The worked steps show the method; ask a teacher if you are unsure about partial credit. No score from this page changes Maths Streak or tracker progress.
Open your two-week plan
Your two-week plan
Move days to fit school, homework and rest. If a session feels too long, split it. A missed day is a reason to adjust the plan, not to double the next day’s workload.
Day 2 · Arithmetic and signs
Spend 5 minutes on brackets and powers, then complete a BIDMAS workout. Rework two errors without looking at the solution.
Day 3 · Fractions
Read the fraction examples. Practise equivalent fractions and addition using a common denominator, then check each denominator.
Day 4 · Decimals and percentages
Convert five values between fraction, decimal and percentage forms. Complete the linked workout and explain one conversion aloud.
Day 5 · Percentage change
Practise finding the change, dividing by the original amount and multiplying by 100. Check which amount is the original.
Day 6 · Ratio and units
Convert quantities to matching units and simplify ratios. Draw a bar model for one sharing question.
Day 7 · Catch-up and retrieval
Redo three missed questions from days 2–6 with the answers covered. Take a break after checking; use this as a catch-up day.
Day 8 · Proportion
Find the value of one unit before scaling up. Complete the proportion workout and check the units of each answer.
Day 9 · Substitution
Write substituted negative numbers in brackets. Complete the substitution workout and check powers before multiplication.
Day 10 · Linear equations
Undo operations on both sides. Solve the linked questions, then substitute two answers into their original equations.
Day 11 · Angles
Read the angle examples. Write the fact used beside every calculation in the angles workout.
Day 12 · Area and volume
Rework starting questions 11 and 12. Complete a prism-volume workout and label each answer with square or cubic units as appropriate.
Day 13 · Data and chance
Rework starting questions 13–15. Complete an averages workout, then explain a probability using favourable and total equally likely outcomes.
Day 14 · End check and next steps
Complete the 13 different end-check questions. Mark and compare methods on the shared skills, not raw totals. Choose two topics to keep practising next week.
Starting assessment
15 original questions · 32 suggested marks · 30–40 minutes
Work on paper. Write a reason or method, even when the final answer is short. Leave a question and return later if needed.
Starting assessment · Question 1
Work out 5 × 22
Working
Starting assessment · Question 2
Work out −3 + 8
Working
Starting assessment · Question 3
Find the number that is exactly halfway between 14 and 58
Working
Starting assessment · Question 4
Write 0.45 as a percentage.
Working
Starting assessment · Question 5
Kane buys a bike for £250.
A year later he sells the bike for £210.
Work out his percentage loss.
Working
Starting assessment · Question 6
Write down the ratio 45 cm : 1.5 m in its simplest form.
Working
Starting assessment · Question 7
3 kg of potatoes cost £2.64.
Work out the cost of 7 kg of these potatoes.
Working
Starting assessment · Question 8
E = 3a − 2b
Work out the value of E when a = −4 and b = 5.
Working
Starting assessment · Question 9
Solve 3(x + 4) = 27
Working
Starting assessment · Question 10
Two angles fit together on a straight line. One of the angles is 64° and the other angle is y°.
- Work out the value of y.
- Give a reason for your answer.
Working
Starting assessment · Question 11
A rectangle is made from three identical squares placed side by side in a row.
The perimeter of the rectangle is 48 cm.
Work out the area of the rectangle.
Working
Starting assessment · Question 12
A cuboid has a volume of 180 cm3.
The base of the cuboid measures 6 cm by 5 cm.
Work out the height of the cuboid.
Working
Starting assessment · Question 13
A bar chart shows how the students in class 8R travel to school. The table gives the height of each bar.
| Method | Number of students |
|---|---|
| Walk | 12 |
| Car | 18 |
| Bus | 6 |
- Write down the number of students who travel by bus.
- Write down the ratio of the number of students who walk to the number who travel by car. Give your ratio in its simplest form.
Working
Starting assessment · Question 14
A bag contains 4 green counters, 7 yellow counters and 9 white counters.
A counter is taken from the bag at random.
Find the probability that the counter is not green.
Working
Starting assessment · Question 15
Here are four numbers.
6 11 9 14
Work out the mean of these numbers.
Working
End-of-plan check
13 original questions · 30 suggested marks · 20–30 minutes
Work on paper. Write a reason or method, even when the final answer is short. Leave a question and return later if needed.
End-of-plan check · Question 1
Work out 18 ÷ (2 + 4)
Working
End-of-plan check · Question 2
Work out 4 − 9
Working
End-of-plan check · Question 3
- One of these fractions is not equivalent to 35
610 915 1225 1525
Write down this fraction.
- Work out 25 + 13
Working
End-of-plan check · Question 4
A trader buys a table for £68.
She sells the table for £85.
Work out her percentage profit.
Working
End-of-plan check · Question 5
Each month Tom is paid £1800.
He saves 20% of the £1800.
He splits the rest between rent and bills in the ratio 5 : 3.
Work out how much Tom spends on rent each month.
Working
End-of-plan check · Question 6
Work out the value of x2 + 7x when x = 6.
Working
End-of-plan check · Question 7
Solve 4(2x − 3) = 36
Working
End-of-plan check · Question 8
Three angles meet at a point. Two of the angles are 145° and 118°. The third angle is x°.
Work out the value of x. Give a reason for your answer.
Working
End-of-plan check · Question 9
Priya buys 12 tickets in a school raffle.
A total of 400 tickets are sold.
One ticket is picked at random to win the prize.
Work out the probability that Priya does not win the prize.
Working
End-of-plan check · Question 10
A shoe shop records the sizes of the last eight pairs of trainers it sold.
5 7 6 5 8 5 9 6
- Write down the modal shoe size.
- Work out the range of the shoe sizes.
Working
End-of-plan check · Question 11
A rectangle has length 9 cm and width 4 cm.
- Work out the area of the rectangle.
- Work out the perimeter of the rectangle.
Working
End-of-plan check · Question 12
The cross-section of a prism is a right-angled triangle with base 8 cm and height 5 cm.
The length of the prism is 12 cm.
Work out the volume of the prism.
Working
End-of-plan check · Question 13
A bar chart shows the number of pets sold by a pet shop on four days. The table gives the height of each bar.
| Day | Pets sold |
|---|---|
| Monday | 14 |
| Tuesday | 8 |
| Wednesday | 11 |
| Thursday | 17 |
- Write down the day on which the fewest pets were sold.
- Work out how many more pets were sold on Thursday than on Tuesday.
Working
Turn your answers into priorities
Record “independent”, “partly”, “revisit” or “skipped” beside each question. A single answer is only one piece of evidence. Start with two or three topics where the method was unclear, and retry a different question after practice. If you are unsure about partial marks, ask a teacher to look at your working.
Starting assessment: question-to-topic map
Q1: BIDMAS (Order of Operations)
Evidence / next step: ____________________
Practise this skill (Foundation)
Q2: Negative Numbers
Evidence / next step: ____________________
Practise this skill (Foundation)
Q3: Fractions
Evidence / next step: ____________________
Practise this skill (Foundation)
Q4: Fractions, Decimals and Percentages
Evidence / next step: ____________________
Practise this skill (Foundation)
Q5: Percentage Change
Evidence / next step: ____________________
Practise this skill (Foundation)
Q6: Writing and Simplifying Ratio
Evidence / next step: ____________________
Practise this skill (Foundation)
Q7: Proportion
Evidence / next step: ____________________
Practise this skill (Foundation)
Q8: Substitution
Evidence / next step: ____________________
Practise this skill (Foundation)
Q9: Solving Equations
Evidence / next step: ____________________
Practise this skill (Foundation)
Q10: Angles
Evidence / next step: ____________________
Practise this skill (Foundation)
Q11: Area and Perimeter
Evidence / next step: ____________________
Practise this skill (Foundation)
Q12: Volume of a Prism
Evidence / next step: ____________________
Practise this skill (Foundation)
Q13: Bar Charts
Evidence / next step: ____________________
Practise this skill (Foundation)
Q14: Probability
Evidence / next step: ____________________
Practise this skill (Foundation)
Q15: Averages
Evidence / next step: ____________________
Practise this skill (Foundation)
End-of-plan check: question-to-topic map
Q1: BIDMAS (Order of Operations)
Evidence / next step: ____________________
Practise this skill (Foundation)
Q2: Negative Numbers
Evidence / next step: ____________________
Practise this skill (Foundation)
Q3: Fractions
Evidence / next step: ____________________
Practise this skill (Foundation)
Q4: Percentage Change
Evidence / next step: ____________________
Practise this skill (Foundation)
Q5: Ratio
Evidence / next step: ____________________
Practise this skill (Foundation)
Q6: Substitution
Evidence / next step: ____________________
Practise this skill (Foundation)
Q7: Solving Equations
Evidence / next step: ____________________
Practise this skill (Foundation)
Q8: Angles
Evidence / next step: ____________________
Practise this skill (Foundation)
Q9: Probability
Evidence / next step: ____________________
Practise this skill (Foundation)
Q10: Averages
Evidence / next step: ____________________
Practise this skill (Foundation)
Q11: Area and Perimeter
Evidence / next step: ____________________
Practise this skill (Foundation)
Q12: Volume of a Prism
Evidence / next step: ____________________
Practise this skill (Foundation)
Q13: Bar Charts
Evidence / next step: ____________________
Practise this skill (Foundation)
For a guided summary, try the short topic check. Neither this pack nor that check predicts a GCSE grade or assesses the whole course.
Compare skills, not totals
The checks use different tasks and difficulty, so a raw total is not a like-for-like grade measure. For each skill record independent, partly, revisit or skipped. Decimal conversion (starting Q4) and unit proportion (starting Q7) need a separate workout recheck.
Order of operations · Starting Q1 → End Q1
Before: __________ After: __________ Next step: __________
Negative numbers · Starting Q2 → End Q2
Before: __________ After: __________ Next step: __________
Fractions · Starting Q3 → End Q3
Before: __________ After: __________ Next step: __________
Percentage change · Starting Q5 → End Q4
Before: __________ After: __________ Next step: __________
Ratio · Starting Q6 → End Q5
Before: __________ After: __________ Next step: __________
Substitution · Starting Q8 → End Q6
Before: __________ After: __________ Next step: __________
Equations · Starting Q9 → End Q7
Before: __________ After: __________ Next step: __________
Angles · Starting Q10 → End Q8
Before: __________ After: __________ Next step: __________
Area and perimeter · Starting Q11 → End Q11
Before: __________ After: __________ Next step: __________
Volume · Starting Q12 → End Q12
Before: __________ After: __________ Next step: __________
Charts · Starting Q13 → End Q13
Before: __________ After: __________ Next step: __________
Probability · Starting Q14 → End Q9
Before: __________ After: __________ Next step: __________
Averages · Starting Q15 → End Q10
Before: __________ After: __________ Next step: __________
Mistake-review sheet
Choose useful errors, not just the hardest questions. Cover the answer and redo the question after writing the corrected method.
Review 1
Question / topic: __________________________________________
Error: knowledge / method / accuracy / timing / skipped
What happened? __________________________________________
Corrected method: ________________________________________
________________________________________________________
Next practice and date: ____________________________________
Review 2
Question / topic: __________________________________________
Error: knowledge / method / accuracy / timing / skipped
What happened? __________________________________________
Corrected method: ________________________________________
________________________________________________________
Next practice and date: ____________________________________
Review 3
Question / topic: __________________________________________
Error: knowledge / method / accuracy / timing / skipped
What happened? __________________________________________
Corrected method: ________________________________________
________________________________________________________
Next practice and date: ____________________________________
Review 4
Question / topic: __________________________________________
Error: knowledge / method / accuracy / timing / skipped
What happened? __________________________________________
Corrected method: ________________________________________
________________________________________________________
Next practice and date: ____________________________________
Worked answers
Keep this section covered until you have tried the questions. A matching final answer does not establish that all the reasoning is correct.
Credit an equivalent correct method. A correct method can earn its checkpoint even if later arithmetic is wrong; only award an accuracy checkpoint when its stated result is correct. Do not award the same checkpoint twice. For a proof, the reasons are essential. This original guidance is not an exam-board scheme.
Starting assessment · Answer 1: BIDMAS (Order of Operations)
Starting assessment · Answer 1
1 suggested marks · compare each step, not just the final answer.
Indices come before multiplication
2² = 4
5 × 4 = 20
20
Suggested marking checkpoints
- 1 mark: Correct value 20.
Next practice: BIDMAS (Order of Operations) workout · Learn this method
Starting assessment · Answer 2: Negative Numbers
Starting assessment · Answer 2
1 suggested marks · compare each step, not just the final answer.
Start at -3 on a number line and move 8 to the right
-3 + 8 = 5
5
Suggested marking checkpoints
- 1 mark: Correct value 5.
Next practice: Negative Numbers workout · Learn this method
Starting assessment · Answer 3: Fractions
Starting assessment · Answer 3
2 suggested marks · compare each step, not just the final answer.
Write both fractions with denominator 8: 14 = 28.
Add them: 28 + 58 = 78.
Halve the total: 78 divided by 2 = 716.
716
Suggested marking checkpoints
- 1 mark: Add the fractions correctly using a common denominator, or find their difference correctly.
- 1 mark: Halve the total, or add half the difference to the smaller fraction, to obtain 7/16.
Next practice: Fractions workout · Learn this method
Starting assessment · Answer 4: Fractions, Decimals and Percentages
Starting assessment · Answer 4
1 suggested marks · compare each step, not just the final answer.
0.45 × 100 = 45, so 0.45 = 45%.
45%
Suggested marking checkpoints
- 1 mark: 45%.
Next practice: Fractions, Decimals and Percentages workout · Learn this method
Starting assessment · Answer 5: Percentage Change
Starting assessment · Answer 5
3 suggested marks · compare each step, not just the final answer.
Loss = 250 − 210 = £40.
Percentage loss = 40 ÷ 250 = 0.16.
0.16 × 100 = 16%.
16%
Suggested marking checkpoints
- 1 mark: Loss £40.
- 1 mark: Divide the loss by the original £250.
- 1 mark: Convert to 16%.
Next practice: Percentage Change workout · Learn this method
Starting assessment · Answer 6: Writing and Simplifying Ratio
Starting assessment · Answer 6
2 suggested marks · compare each step, not just the final answer.
Convert to the same units: 1.5 m = 150 cm.
The ratio is 45 : 150.
The highest common factor of 45 and 150 is 15.
45 ÷ 15 = 3 and 150 ÷ 15 = 10, so the ratio is 3 : 10.
3 : 10
Suggested marking checkpoints
- 1 mark: Convert both lengths to matching units: 45:150 or 0.45:1.5.
- 1 mark: Simplest ratio 3:10.
Next practice: Writing and Simplifying Ratio workout · Learn this method
Starting assessment · Answer 7: Proportion
Starting assessment · Answer 7
3 suggested marks · compare each step, not just the final answer.
1 kg costs 2.64 ÷ 3 = £0.88.
7 kg costs 7 × £0.88 = £6.16.
£6.16
Suggested marking checkpoints
- 1 mark: Set up a valid proportional route: unit price £2.64 ÷ 3, or scale factor 7/3.
- 1 mark: Use that unit price for 7 kg (or a correct scale factor 7/3).
- 1 mark: £6.16.
Next practice: Proportion workout · Learn this method
Starting assessment · Answer 8: Substitution
Starting assessment · Answer 8
2 suggested marks · compare each step, not just the final answer.
Substitute the values: E = 3 × (-4) - 2 × 5.
E = -12 - 10 = -22.
-22
Suggested marking checkpoints
- 1 mark: Substitute 3 × (−4) − 2 × 5.
- 1 mark: −22.
Next practice: Substitution workout · Learn this method
Starting assessment · Answer 9: Solving Equations
Starting assessment · Answer 9
2 suggested marks · compare each step, not just the final answer.
Divide both sides by 3: x + 4 = 9
Subtract 4 from both sides: x = 5
x = 5
Suggested marking checkpoints
- 1 mark: Valid first transformation, such as x + 4 = 9.
- 1 mark: x = 5.
Next practice: Solving Equations workout · Learn this method
Starting assessment · Answer 10: Angles
Starting assessment · Answer 10
2 suggested marks · compare each step, not just the final answer.
Angles on a straight line add up to 180°.
y = 180 − 64 = 116.
(a) 116; (b) angles on a straight line add up to 180 degrees
Suggested marking checkpoints
- 1 mark: 116°.
- 1 mark: Reason: angles on a straight line total 180°.
Next practice: Angles workout · Learn this method
Starting assessment · Answer 11: Area and Perimeter
Starting assessment · Answer 11
3 suggested marks · compare each step, not just the final answer.
Let each square have side s cm. The rectangle is 3s cm long and s cm wide.
Perimeter = 2 × (3s + s) = 8s, so 8s = 48 and s = 6.
The rectangle is 18 cm by 6 cm, so its area = 18 × 6 = 108 cm².
108 cm²
Suggested marking checkpoints
- 1 mark: Represent the rectangle as 3s by s and perimeter as 8s.
- 1 mark: Find s = 6 cm, hence dimensions 18 cm and 6 cm.
- 1 mark: Area 108 cm².
Next practice: Area and Perimeter workout · Learn this method
Starting assessment · Answer 12: Volume of a Prism
Starting assessment · Answer 12
3 suggested marks · compare each step, not just the final answer.
Area of the base = 6 × 5 = 30 cm²
Volume = base area × height, so 30 × height = 180
Height = 180 ÷ 30 = 6 cm
6 cm
Suggested marking checkpoints
- 1 mark: Base area 30 cm².
- 1 mark: Use height = volume ÷ base area.
- 1 mark: Height 6 cm.
Next practice: Volume of a Prism workout · Learn this method
Starting assessment · Answer 13: Bar Charts
Starting assessment · Answer 13
3 suggested marks · compare each step, not just the final answer.
a) The bus bar has height 6.
b) Walk : Car = 12 : 18. Divide both sides by 6 to get 2 : 3.
(a) 6; (b) 2 : 3
Suggested marking checkpoints
- 1 mark: (a) 6 students.
- 1 mark: (b) Start with walk:car = 12:18.
- 1 mark: Simplify to 2:3.
Next practice: Bar Charts workout · Learn this method
Starting assessment · Answer 14: Probability
Starting assessment · Answer 14
2 suggested marks · compare each step, not just the final answer.
Total number of counters = 4 + 7 + 9 = 20.
Counters that are not green = 7 + 9 = 16.
P(not green) = 1620 = 45
45
Suggested marking checkpoints
- 1 mark: Identify 16 non-green counters out of 20.
- 1 mark: Probability 16/20 = 4/5 (equivalent fraction or 0.8 acceptable).
Next practice: Probability workout · Learn this method
Starting assessment · Answer 15: Averages
Starting assessment · Answer 15
2 suggested marks · compare each step, not just the final answer.
Total: 6 + 11 + 9 + 14 = 40.
Mean: 40 divided by 4 = 10.
10
Suggested marking checkpoints
- 1 mark: Sum 40.
- 1 mark: Divide by 4 to obtain 10.
Next practice: Averages workout · Learn this method
End-of-plan check · Answer 1: BIDMAS (Order of Operations)
End-of-plan check · Answer 1
1 suggested marks · compare each step, not just the final answer.
Work out the brackets first: 2 + 4 = 6
18 ÷ 6 = 3
3
Suggested marking checkpoints
- 1 mark: 3.
Next practice: BIDMAS (Order of Operations) workout · Learn this method
End-of-plan check · Answer 2: Negative Numbers
End-of-plan check · Answer 2
1 suggested marks · compare each step, not just the final answer.
Start at 4 on a number line and move 9 to the left
4 - 9 = -5
-5
Suggested marking checkpoints
- 1 mark: −5.
Next practice: Negative Numbers workout · Learn this method
End-of-plan check · Answer 3: Fractions
End-of-plan check · Answer 3
3 suggested marks · compare each step, not just the final answer.
a) 610, 915 and 1525 all simplify to 35, but 1225 does not (35 = 1525, not 1225).
b) Use denominator 15: 25 = 615 and 13 = 515.
615 + 515 = 1115.
(a) 1225; (b) 1115
Suggested marking checkpoints
- 1 mark: (a) Identify 12/25.
- 1 mark: (b) Express the addends as 6/15 and 5/15.
- 1 mark: 11/15.
Next practice: Fractions workout · Learn this method
End-of-plan check · Answer 4: Percentage Change
End-of-plan check · Answer 4
3 suggested marks · compare each step, not just the final answer.
Profit = 85 − 68 = £17.
Percentage profit = 17 ÷ 68 = 0.25.
0.25 × 100 = 25%.
25%
Suggested marking checkpoints
- 1 mark: Profit £17.
- 1 mark: Divide by the original cost £68.
- 1 mark: 25%.
Next practice: Percentage Change workout · Learn this method
End-of-plan check · Answer 5: Ratio
End-of-plan check · Answer 5
3 suggested marks · compare each step, not just the final answer.
Savings = 20% of £1800 = £360, leaving 1800 − 360 = £1440.
Total parts = 5 + 3 = 8, so 1 part = 1440 ÷ 8 = £180.
Rent = 5 × £180 = £900.
£900
Suggested marking checkpoints
- 1 mark: After saving, £1440 remains.
- 1 mark: Divide the remainder into 8 parts (one part £180).
- 1 mark: Rent £900.
Next practice: Ratio workout · Learn this method
End-of-plan check · Answer 6: Substitution
End-of-plan check · Answer 6
2 suggested marks · compare each step, not just the final answer.
x2 = 6 × 6 = 36.
7x = 7 × 6 = 42.
36 + 42 = 78.
78
Suggested marking checkpoints
- 1 mark: Evaluate 6² and 7 × 6 correctly or write the fully substituted expression.
- 1 mark: 78.
Next practice: Substitution workout · Learn this method
End-of-plan check · Answer 7: Solving Equations
End-of-plan check · Answer 7
3 suggested marks · compare each step, not just the final answer.
Expand the bracket: 8x - 12 = 36
Add 12 to both sides: 8x = 48
Divide both sides by 8: x = 6
x = 6
Suggested marking checkpoints
- 1 mark: Valid first step: expand to 8x − 12 = 36 or divide to 2x − 3 = 9.
- 1 mark: Isolate the x-term: 8x = 48 or 2x = 12.
- 1 mark: x = 6.
Next practice: Solving Equations workout · Learn this method
End-of-plan check · Answer 8: Angles
End-of-plan check · Answer 8
2 suggested marks · compare each step, not just the final answer.
Angles around a point add up to 360°.
145 + 118 = 263.
x = 360 − 263 = 97.
x = 97 (angles around a point add up to 360 degrees)
Suggested marking checkpoints
- 1 mark: 97°.
- 1 mark: Reason: angles around a point total 360°.
Next practice: Angles workout · Learn this method
End-of-plan check · Answer 9: Probability
End-of-plan check · Answer 9
2 suggested marks · compare each step, not just the final answer.
The number of tickets that are not Priya's is 400 - 12 = 388.
P(Priya does not win) = 388400 = 97100
97100
Suggested marking checkpoints
- 1 mark: 388 non-winning tickets out of 400.
- 1 mark: 388/400 = 97/100 (0.97 acceptable).
Next practice: Probability workout · Learn this method
End-of-plan check · Answer 10: Averages
End-of-plan check · Answer 10
3 suggested marks · compare each step, not just the final answer.
a) Size 5 appears three times, more than any other size, so the mode is 5.
b) Range: 9 - 5 = 4.
(a) 5; (b) 4
Suggested marking checkpoints
- 1 mark: (a) Mode 5.
- 1 mark: (b) Identify highest 9 and lowest 5.
- 1 mark: Range 4.
Next practice: Averages workout · Learn this method
End-of-plan check · Answer 11: Area and Perimeter
End-of-plan check · Answer 11
2 suggested marks · compare each step, not just the final answer.
Area = length × width = 9 × 4 = 36 cm².
Perimeter = 2 × (9 + 4) = 2 × 13 = 26 cm.
(a) 36 cm^2; (b) 26 cm
Suggested marking checkpoints
- 1 mark: Area 36 cm².
- 1 mark: Perimeter 26 cm.
Next practice: Area and Perimeter workout · Learn this method
End-of-plan check · Answer 12: Volume of a Prism
End-of-plan check · Answer 12
3 suggested marks · compare each step, not just the final answer.
Area of the triangular cross-section = 12 × 8 × 5 = 20 cm²
Volume of a prism = area of cross-section × length
Volume = 20 × 12 = 240 cm³
240 cm³
Suggested marking checkpoints
- 1 mark: Triangular cross-section area ½ × 8 × 5 = 20 cm².
- 1 mark: Multiply the cross-section area by length 12.
- 1 mark: 240 cm³.
Next practice: Volume of a Prism workout · Learn this method
End-of-plan check · Answer 13: Bar Charts
End-of-plan check · Answer 13
2 suggested marks · compare each step, not just the final answer.
a) The shortest bar is Tuesday, with 8 pets.
b) 17 - 8 = 9 more pets.
(a) Tuesday; (b) 9
Suggested marking checkpoints
- 1 mark: (a) Tuesday.
- 1 mark: (b) 17 − 8 = 9.
Next practice: Bar Charts workout · Learn this method
Learn the methods
BIDMAS (Order of Operations)
Brackets identify a calculation to do as a unit. Next evaluate powers. Multiplication and division have equal priority: work left to right. Then add and subtract left to right. A fraction bar groups the whole numerator and denominator, so calculate each before dividing.
Use the worked answer for your question to follow these steps with numbers, then cover it and try the linked workout.
Negative Numbers
Picture a number line. Adding a positive number moves right; subtracting a positive number moves left. Crossing zero is allowed: from 4, nine steps left reaches −5. The minus sign can describe a negative number or an operation, so read its position carefully.
Use the worked answer for your question to follow these steps with numbers, then cover it and try the linked workout.
Fractions, Decimals and Percentages
Percent means out of 100. Multiply a decimal by 100 to express it as a percentage; divide a percentage by 100 to get a decimal. For a fraction, divide numerator by denominator first. For example, 0.45 means 45 hundredths, so it is 45%.
Use the worked answer for your question to follow these steps with numbers, then cover it and try the linked workout.
Proportion
When the unit price is constant, cost and quantity increase in the same ratio. Divide the known cost by the quantity to find the cost of one unit, then multiply by the required quantity. Keep the unit beside each value so you do not multiply by the original quantity again.
Use the worked answer for your question to follow these steps with numbers, then cover it and try the linked workout.
Bar Charts
Read the labelled frequency axis and its scale before comparing bars. Each bar represents one category; its height gives that category’s frequency. A difference asks for subtraction. A ratio compares the frequencies in the stated order, then divides both by a common factor.
Use the worked answer for your question to follow these steps with numbers, then cover it and try the linked workout.