@STUDYSMARTERPRO
MATH
MATH LITERACY
@STUDYSMARTERPRO
LITERACY
GR
GR 12
12
PAPER
PAPER 22
IEB/CAPS
IEB/CAPS
Page 1 of 57
, (5
(5 QUESTIONS)
QUESTIONS) PAPER
PAPER 22 150
150 MARKS
MARKS
33 HOURS
HOURS
General Math Skills
Perform basic calculations (add, subtract, multiply, divide)
Use a calculator effectively
Substitute values into formulas and equations
Select the correct formula for problems
Simplify expressions
Calculate with measured values
Estimate values from graphs or tables
Understand key terms: area, perimeter, volume, radius, scale, floor plan,
elevation plan, layout plan
Be able to read and understand diagrams/maps/plans
Conversions
↔ ↔
Convert units of length (e.g., cm mm, m cm, km m) ↔
↔
Convert units of area (e.g., cm² mm²)
↔ ↔
Convert units of volume (e.g., cm³ mm³, m³ liters)
Convert time units (seconds, minutes, hours, days, weeks, months)
Convert temperature between Celsius and Fahrenheit
↔
Convert between measurement systems (metric imperial)
Convert units using different scales
Use conversion factors from tables
Ensure consistent units before calculating
Temperature
Read and interpret temperature from thermometers, dials, weather reports
Packaging
Understand packaging/stacking rules (no fractional, squashed, or cut items)
Compare packaging by wasted space (volume) and material (surface area)
Choose the most cost-effective packaging option
Time
Read and interpret time from watches, clocks, stopwatches
Understand time formats and time of day
Calculate elapsed time
Use calendars for days, weeks, months
Interpret timetables for departure, arrival, travel times
Estimate travel durations
Page 2 of 57
,Measurement (Length, Area, Volume, Perimeter)
Estimate and measure lengths and distances accurately
Calculate perimeter (sum of sides) with correct units
Calculate area (multiply two sides), understanding squared units
Calculate volume (multiply three sides), understanding cubed units
Work with 2D shapes:
Find radius (diameter ÷ 2)
Use π = 3.142
Adjust formula for semicircles (divide by 2)
Break complex figures into smaller parts, calculate, then sum
Apply perimeter, area, or volume in projects even if calculation type isn’t stated
Calculate quantities for tasks (e.g., paint needed) using surface area/volume and
conversions
Maps & Plans
Understand and use number and bar scales (advantages and
disadvantages)
Determine scales and calculate actual lengths/distances
Measure accurately from plans, diagrams, drawings
Identify features and locations using keys and grid references
Describe positions relative to surroundings
Use compass directions
Give and interpret travel directions
Estimate distances using map scales
Calculate travel costs (fuel quantity and price)
Calculate average speed
Use maps and distance charts to find shortest routes
Plan trips combining time and distance calculations
Decide appropriate stopping points (consider fatigue, petrol, time)
Critique travel routes and suggest alternatives
Describe items shown on plans
Evaluate the design of structures shown on plan
finance topics are included when they have a direct link to other main
sections.
Specifically, you might see finance concepts like:
Income
Expenditure
Profit/Loss
Income-and-Expenditure statements
Budgets
Cost price and Selling price
These finance elements are only included if they are directly connected to
Measurement or Maps and Plans.
AA Accuracy CA
CA Continued accuracy
MM Method MA
MA Method accuracy
MCA
MCA Method continued accuracy RR Rounding
Show full working (every step). Markers award M even if final is wrong.
Write formulas clearly (e.g. % = (part ÷ whole) × 100).
Label intermediate answers (monthly = …, total instalments = …). This helps carry-
through marks.
Box final answers so the marker sees them easily.
Include units and state rounding (e.g. “Rounded to 2 dp”). Page 3 of 57
If you use a wrong number earlier, use it consistently — you may still get later marks.
,RATIOS
RATIOS
1. Definition
A ratio compares two or more quantities.
It tells us how many times one quantity is in relation to another.
Example: If a recipe uses 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is 2:1.
2. Writing Ratios
Ratios can be written as:
→
a : b “a to b”
→
a/b as a fraction
→
a to b in words
3. Simplifying Ratios
Divide both numbers by their greatest common factor (GCF).
→
Example: 12:8 divide both by 4 3:2 →
4. Types of Ratios
→
1. Part-to-part compares parts of a whole
→
Example: 3 boys and 2 girls boys:girls = 3:2
→
2. Part-to-whole compares part to the total
→
Example: 3 boys, 2 girls boys:total = 3:5
5. Using Ratios
Scaling up or down: Multiply or divide each part of the ratio by the same number.
→
Example: 2:3 scaled up by 4 8:12
Sharing / dividing in a ratio:
Total ÷ sum of ratio parts × each part
→
Example: Share R120 in ratio 2:3 sum = 5
First part: 2/5 × 120 = 48
Second part: 3/5 × 120 = 72
6. Converting Ratios to Fractions / Percentages
Example: 3:2
Fraction of first part = 3/(3+2) = 3/5
Fraction of second part = 2/5
Percentage of first part = 3/5 × 100 = 60%
Page 4 of 57
, PAPER
PAPER 11 AND
AND 22
RATES/
RATES/ PER/PROPORTION
PER/PROPORTION
1.PETROL
1.PETROL QUESTIONS
QUESTIONS (P2 « MAPS)
(P2« MAPS)
2.DISTANCE
2.DISTANCE ,SPEED
,SPEED AND
AND TIME
TIME QUESTIONS
QUESTIONS
3.MIXED
3.MIXED QUESTIONS
QUESTIONS
1. What Is a Rate?
Look for "per" (per = divide) A rate compares two different quantities
using the word per.
Ask: What do they want? Per unit or “Per” means for every and in math, it
total? means divide (÷).
Ask:
“Per what?” So when you see “per”:
Then say: The thing before “per” is the amount
The thing after “per” is the time, distance,
“For every 1 ___, there are ___.” person, item etc.
What two things are being compared? Example: A printer prints 120 pages per
Two different units (like km and hours, or 3 minutes.
litres and seconds). What is the rate in pages per minute?
2. What does the word per come after? 1: What do I have?
It comes after the amount (example: 60 120 pages
km per hour). 3 minutes
3. Which value goes on top? I want: pages per 1 minute
The total amount (example: 60 km). 2: Set up as a fraction
120 ÷ 3 = 40
4. Which value goes on bottom? Answer: 40 pages per minute
The per unit (example: 1 hour).
Units:
Speed: km/h or m/s
Distance: km or m
Time: hours or seconds
Fuel consumption , eg 13l/ km, then
make a triangle to find your own
formula or use direct proportion
13 l - 1km
? - 60 km
EXAMPLE 1
Comparing Batsmen
Question: Musee: 450 runs/7 games. James: 330 runs/5 games. Better batsman?
Solution:
≈
Musee: 450 ÷ 7 64.28 runs/game
James: 330 ÷ 5 = 66 runs/game
Conclusion: James is better.
Page 5 of 57
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,Scenario:
Jane is an avid go-kart racer who often goes racing at the local track. The track length is 250 m. Her
maximum speed is 65 km/h, her average lap time is 30 seconds, and the lap record is 20.741 seconds.
The data below shows information relating to Jane’s last race.
Track length: 250 m
Maximum speed: 65 km/h
Average lap time: 30 s
Lap record: 20,741 seconds
Questions
5.1Determine how many laps Jane must do to cover a total distance of 1,5 km.
5.2Using the average lap time, determine in minutes how long it will take her to cover a total distance of 1,5
km.
5.3Determine, rounded to the nearest second, how much slower she drove compared to her lap record.
5.1 – Number of Laps to Cover 1,5 km
1 – Convert total distance to meters:
1,5 km × 1000 = 1500 m
2 – Divide total distance by lap length:
1500 m ÷ 250 m = 6 laps
Answer: 6 laps
: Always convert km to meters to match the lap length units.
5.2 – Time to Cover 1,5 km Using Average Lap Time
1 – Multiply number of laps by average lap time:
30 s × 6 laps = 180 s
2 – Convert seconds to minutes:
180 s ÷ 60 = 3 minutes
Answer: 3 minutes
: Ensure units are consistent; seconds can be converted to minutes for easier interpretation.
5.3 – Time Slower Compared to Lap Record
1 – Subtract lap record from average lap time:
30 s – 20.741 s = 9.259 s
2 – Round to nearest second:
≈ 9s
Answer: 9 seconds slower
: Always round final time to the nearest second as instructed.
1. Calculating Time on a Calculator
When you use formulas like:
Time= Speed/Distance
Your calculator might give the answer in hours,
minutes, seconds, or decimal hours depending
on the mode.
Decimal hours: 1.5 hours = 1 hour 30
minutes (0.5 × 60 = 30 minutes)
Seconds format: 1 hour 30 minutes = 5400
seconds (1 × 3600 + 30 × 60)
Page 6 of 57
,5.4.1
Jane races against a friend. Jane drives at an average speed of 62 km/h, while her friend drives at 54 km/h.
After 10 laps, Jane wins. Show that she beats her friend by roughly 22 seconds.
5.4.2
The track has a rectangular middle section and two semi-circles on either side. Some dimensions are given.
Calculate the outer perimeter of the track, rounded to the nearest meter.
5.4.3
Jane’s go-kart has a 9-litre fuel tank and uses ½ a tank per 10-lap race. Determine her fuel consumption in
litres per km.
5.5.1
Jane has two tyre options with diameters 27,94 cm and 25,4 cm. Calculate the difference in circumference
between the two tyres.
5.5.2
Calculate the number of full rotations made by Tyre A (25,4 cm) in one lap of the racetrack.
5.5.3
A set of tyres needs to be replaced after every 10 km. Determine after how many complete races (10 laps
per race) Jane must replace her tyres.
5.4.1 – Time Difference Between Jane and Friend 5.4.2 – Outer Perimeter of Track
(10 Laps) 1 – Circumference of two semi-circles:
1 – Calculate total distance for 10 laps: C = 2 × π × r, where r = 17,5 m
250 m × 10 = 2500 m = 2,5 km 2 × 3.142 × 17.5 = 109.985 m
2 – Convert speed to km/s (or calculate time in 2 – Add lengths of rectangular sides:
seconds): 2 × 70 m = 140 m
Time = Distance ÷ Speed × 3600 (to get seconds) 3 – Total perimeter:
Jane: 2,5 ÷ 62 × 3600 = 145.16 s
Friend: 2,5 ÷ 54 × 3600 = 166.67 s
≈
109.985 + 140 250 m
Answer: 250 m
3 – Calculate time difference: : Semi-circles together make one full circle. Add
≈
166.67 – 145.16 = 21.51 s 22 s
Answer: Jane beats her friend by roughly 22
straight sides for total perimeter.
seconds 5.4.3 – Fuel Consumption in Litres per km
1 – Fuel used per race:
½ tank of 9 L = 4.5 L
2 – Distance per race:
5.5.1 – Difference in Tyre Circumference 10 laps × 250 m = 2500 m = 2,5 km
1 – Calculate difference using π × diameter: 3 – Fuel consumption per km:
Answer: 8 cm
≈
π × 27.94 cm – π × 25.4 cm = π × 2.54 8 cm 4.5 ÷ 2.5 = 1.8 L/km
Answer: 1.8 L/km
: Difference in circumference = π × difference in : Always convert distance to km to match
diameters. litres/km units.
5.5.2 – Number of Rotations for Tyre A (25,4 cm)
1 – Convert lap distance to cm:
250 m × 100 = 25,000 cm
2 – Divide lap distance by tyre circumference:
≈
25,000 ÷ (π × 25.4) 313,3
3 – Round down to full rotations:
≈ 313 full rotations
Answer: 313 rotations
: Only full rotations count; ignore decimal for rotation
count.
5.5.3 – Number of Races Before Tyres Need Replacement
1 – Distance per race:
10 laps × 250 m = 2500 m = 2,5 km
2 – Divide tyre lifespan by race distance:
10 km ÷ 2,5 km = 4 races
Answer: 4 complete races Page 7 of 57
, Jane has a choice of two different-sized tyres for her
go-kart. The diameters of each tyre are provided.
5.5.1. Calculate the difference in circumference between
the two tyres.
5.5.2. Calculate the number of full rotations made by
Tyre A in one lap on the racetrack.
5.5.3. A set of tyres needs to be replaced after every 10
km. Determine after how many complete races (10 laps)
Jane must replace her tyres.
5.5.1 – Difference in Circumference
Step 1 – Use the formula for circumference:
Circumference = π × diameter
Step 2 – Calculate difference:
≈
π × 27.94 cm – π × 25.4 cm = π × 2.54 8 cm
Answer: 8 cm
Notes: The difference in circumference equals π times the difference in
diameters.
5.5.2 – Number of Full Rotations of Tyre A
Step 1 – Convert lap distance to cm:
1 lap = 250 m × 100 = 25,000 cm
Step 2 – Divide lap distance by tyre circumference:
≈
25,000 ÷ (π × 25.4) 313.3
Step 3 – Round to full rotations:
≈ 313 full rotations
Answer: 313 rotations
Notes: Only full rotations are counted; decimal portion is ignored.
5.5.3 – Number of Races Before Tyres Must Be Replaced
Step 1 – Distance per race (10 laps):
10 laps × 250 m = 2500 m = 2.5 km
Step 2 – Divide tyre lifespan by race distance:
10 km ÷ 2.5 km = 4 races
Answer: 4 complete races
Notes: Divide the total tyre lifespan by the distance covered per race to
determine the number of races before replacement.
Page 8 of 57
MATH
MATH LITERACY
@STUDYSMARTERPRO
LITERACY
GR
GR 12
12
PAPER
PAPER 22
IEB/CAPS
IEB/CAPS
Page 1 of 57
, (5
(5 QUESTIONS)
QUESTIONS) PAPER
PAPER 22 150
150 MARKS
MARKS
33 HOURS
HOURS
General Math Skills
Perform basic calculations (add, subtract, multiply, divide)
Use a calculator effectively
Substitute values into formulas and equations
Select the correct formula for problems
Simplify expressions
Calculate with measured values
Estimate values from graphs or tables
Understand key terms: area, perimeter, volume, radius, scale, floor plan,
elevation plan, layout plan
Be able to read and understand diagrams/maps/plans
Conversions
↔ ↔
Convert units of length (e.g., cm mm, m cm, km m) ↔
↔
Convert units of area (e.g., cm² mm²)
↔ ↔
Convert units of volume (e.g., cm³ mm³, m³ liters)
Convert time units (seconds, minutes, hours, days, weeks, months)
Convert temperature between Celsius and Fahrenheit
↔
Convert between measurement systems (metric imperial)
Convert units using different scales
Use conversion factors from tables
Ensure consistent units before calculating
Temperature
Read and interpret temperature from thermometers, dials, weather reports
Packaging
Understand packaging/stacking rules (no fractional, squashed, or cut items)
Compare packaging by wasted space (volume) and material (surface area)
Choose the most cost-effective packaging option
Time
Read and interpret time from watches, clocks, stopwatches
Understand time formats and time of day
Calculate elapsed time
Use calendars for days, weeks, months
Interpret timetables for departure, arrival, travel times
Estimate travel durations
Page 2 of 57
,Measurement (Length, Area, Volume, Perimeter)
Estimate and measure lengths and distances accurately
Calculate perimeter (sum of sides) with correct units
Calculate area (multiply two sides), understanding squared units
Calculate volume (multiply three sides), understanding cubed units
Work with 2D shapes:
Find radius (diameter ÷ 2)
Use π = 3.142
Adjust formula for semicircles (divide by 2)
Break complex figures into smaller parts, calculate, then sum
Apply perimeter, area, or volume in projects even if calculation type isn’t stated
Calculate quantities for tasks (e.g., paint needed) using surface area/volume and
conversions
Maps & Plans
Understand and use number and bar scales (advantages and
disadvantages)
Determine scales and calculate actual lengths/distances
Measure accurately from plans, diagrams, drawings
Identify features and locations using keys and grid references
Describe positions relative to surroundings
Use compass directions
Give and interpret travel directions
Estimate distances using map scales
Calculate travel costs (fuel quantity and price)
Calculate average speed
Use maps and distance charts to find shortest routes
Plan trips combining time and distance calculations
Decide appropriate stopping points (consider fatigue, petrol, time)
Critique travel routes and suggest alternatives
Describe items shown on plans
Evaluate the design of structures shown on plan
finance topics are included when they have a direct link to other main
sections.
Specifically, you might see finance concepts like:
Income
Expenditure
Profit/Loss
Income-and-Expenditure statements
Budgets
Cost price and Selling price
These finance elements are only included if they are directly connected to
Measurement or Maps and Plans.
AA Accuracy CA
CA Continued accuracy
MM Method MA
MA Method accuracy
MCA
MCA Method continued accuracy RR Rounding
Show full working (every step). Markers award M even if final is wrong.
Write formulas clearly (e.g. % = (part ÷ whole) × 100).
Label intermediate answers (monthly = …, total instalments = …). This helps carry-
through marks.
Box final answers so the marker sees them easily.
Include units and state rounding (e.g. “Rounded to 2 dp”). Page 3 of 57
If you use a wrong number earlier, use it consistently — you may still get later marks.
,RATIOS
RATIOS
1. Definition
A ratio compares two or more quantities.
It tells us how many times one quantity is in relation to another.
Example: If a recipe uses 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is 2:1.
2. Writing Ratios
Ratios can be written as:
→
a : b “a to b”
→
a/b as a fraction
→
a to b in words
3. Simplifying Ratios
Divide both numbers by their greatest common factor (GCF).
→
Example: 12:8 divide both by 4 3:2 →
4. Types of Ratios
→
1. Part-to-part compares parts of a whole
→
Example: 3 boys and 2 girls boys:girls = 3:2
→
2. Part-to-whole compares part to the total
→
Example: 3 boys, 2 girls boys:total = 3:5
5. Using Ratios
Scaling up or down: Multiply or divide each part of the ratio by the same number.
→
Example: 2:3 scaled up by 4 8:12
Sharing / dividing in a ratio:
Total ÷ sum of ratio parts × each part
→
Example: Share R120 in ratio 2:3 sum = 5
First part: 2/5 × 120 = 48
Second part: 3/5 × 120 = 72
6. Converting Ratios to Fractions / Percentages
Example: 3:2
Fraction of first part = 3/(3+2) = 3/5
Fraction of second part = 2/5
Percentage of first part = 3/5 × 100 = 60%
Page 4 of 57
, PAPER
PAPER 11 AND
AND 22
RATES/
RATES/ PER/PROPORTION
PER/PROPORTION
1.PETROL
1.PETROL QUESTIONS
QUESTIONS (P2 « MAPS)
(P2« MAPS)
2.DISTANCE
2.DISTANCE ,SPEED
,SPEED AND
AND TIME
TIME QUESTIONS
QUESTIONS
3.MIXED
3.MIXED QUESTIONS
QUESTIONS
1. What Is a Rate?
Look for "per" (per = divide) A rate compares two different quantities
using the word per.
Ask: What do they want? Per unit or “Per” means for every and in math, it
total? means divide (÷).
Ask:
“Per what?” So when you see “per”:
Then say: The thing before “per” is the amount
The thing after “per” is the time, distance,
“For every 1 ___, there are ___.” person, item etc.
What two things are being compared? Example: A printer prints 120 pages per
Two different units (like km and hours, or 3 minutes.
litres and seconds). What is the rate in pages per minute?
2. What does the word per come after? 1: What do I have?
It comes after the amount (example: 60 120 pages
km per hour). 3 minutes
3. Which value goes on top? I want: pages per 1 minute
The total amount (example: 60 km). 2: Set up as a fraction
120 ÷ 3 = 40
4. Which value goes on bottom? Answer: 40 pages per minute
The per unit (example: 1 hour).
Units:
Speed: km/h or m/s
Distance: km or m
Time: hours or seconds
Fuel consumption , eg 13l/ km, then
make a triangle to find your own
formula or use direct proportion
13 l - 1km
? - 60 km
EXAMPLE 1
Comparing Batsmen
Question: Musee: 450 runs/7 games. James: 330 runs/5 games. Better batsman?
Solution:
≈
Musee: 450 ÷ 7 64.28 runs/game
James: 330 ÷ 5 = 66 runs/game
Conclusion: James is better.
Page 5 of 57
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,Scenario:
Jane is an avid go-kart racer who often goes racing at the local track. The track length is 250 m. Her
maximum speed is 65 km/h, her average lap time is 30 seconds, and the lap record is 20.741 seconds.
The data below shows information relating to Jane’s last race.
Track length: 250 m
Maximum speed: 65 km/h
Average lap time: 30 s
Lap record: 20,741 seconds
Questions
5.1Determine how many laps Jane must do to cover a total distance of 1,5 km.
5.2Using the average lap time, determine in minutes how long it will take her to cover a total distance of 1,5
km.
5.3Determine, rounded to the nearest second, how much slower she drove compared to her lap record.
5.1 – Number of Laps to Cover 1,5 km
1 – Convert total distance to meters:
1,5 km × 1000 = 1500 m
2 – Divide total distance by lap length:
1500 m ÷ 250 m = 6 laps
Answer: 6 laps
: Always convert km to meters to match the lap length units.
5.2 – Time to Cover 1,5 km Using Average Lap Time
1 – Multiply number of laps by average lap time:
30 s × 6 laps = 180 s
2 – Convert seconds to minutes:
180 s ÷ 60 = 3 minutes
Answer: 3 minutes
: Ensure units are consistent; seconds can be converted to minutes for easier interpretation.
5.3 – Time Slower Compared to Lap Record
1 – Subtract lap record from average lap time:
30 s – 20.741 s = 9.259 s
2 – Round to nearest second:
≈ 9s
Answer: 9 seconds slower
: Always round final time to the nearest second as instructed.
1. Calculating Time on a Calculator
When you use formulas like:
Time= Speed/Distance
Your calculator might give the answer in hours,
minutes, seconds, or decimal hours depending
on the mode.
Decimal hours: 1.5 hours = 1 hour 30
minutes (0.5 × 60 = 30 minutes)
Seconds format: 1 hour 30 minutes = 5400
seconds (1 × 3600 + 30 × 60)
Page 6 of 57
,5.4.1
Jane races against a friend. Jane drives at an average speed of 62 km/h, while her friend drives at 54 km/h.
After 10 laps, Jane wins. Show that she beats her friend by roughly 22 seconds.
5.4.2
The track has a rectangular middle section and two semi-circles on either side. Some dimensions are given.
Calculate the outer perimeter of the track, rounded to the nearest meter.
5.4.3
Jane’s go-kart has a 9-litre fuel tank and uses ½ a tank per 10-lap race. Determine her fuel consumption in
litres per km.
5.5.1
Jane has two tyre options with diameters 27,94 cm and 25,4 cm. Calculate the difference in circumference
between the two tyres.
5.5.2
Calculate the number of full rotations made by Tyre A (25,4 cm) in one lap of the racetrack.
5.5.3
A set of tyres needs to be replaced after every 10 km. Determine after how many complete races (10 laps
per race) Jane must replace her tyres.
5.4.1 – Time Difference Between Jane and Friend 5.4.2 – Outer Perimeter of Track
(10 Laps) 1 – Circumference of two semi-circles:
1 – Calculate total distance for 10 laps: C = 2 × π × r, where r = 17,5 m
250 m × 10 = 2500 m = 2,5 km 2 × 3.142 × 17.5 = 109.985 m
2 – Convert speed to km/s (or calculate time in 2 – Add lengths of rectangular sides:
seconds): 2 × 70 m = 140 m
Time = Distance ÷ Speed × 3600 (to get seconds) 3 – Total perimeter:
Jane: 2,5 ÷ 62 × 3600 = 145.16 s
Friend: 2,5 ÷ 54 × 3600 = 166.67 s
≈
109.985 + 140 250 m
Answer: 250 m
3 – Calculate time difference: : Semi-circles together make one full circle. Add
≈
166.67 – 145.16 = 21.51 s 22 s
Answer: Jane beats her friend by roughly 22
straight sides for total perimeter.
seconds 5.4.3 – Fuel Consumption in Litres per km
1 – Fuel used per race:
½ tank of 9 L = 4.5 L
2 – Distance per race:
5.5.1 – Difference in Tyre Circumference 10 laps × 250 m = 2500 m = 2,5 km
1 – Calculate difference using π × diameter: 3 – Fuel consumption per km:
Answer: 8 cm
≈
π × 27.94 cm – π × 25.4 cm = π × 2.54 8 cm 4.5 ÷ 2.5 = 1.8 L/km
Answer: 1.8 L/km
: Difference in circumference = π × difference in : Always convert distance to km to match
diameters. litres/km units.
5.5.2 – Number of Rotations for Tyre A (25,4 cm)
1 – Convert lap distance to cm:
250 m × 100 = 25,000 cm
2 – Divide lap distance by tyre circumference:
≈
25,000 ÷ (π × 25.4) 313,3
3 – Round down to full rotations:
≈ 313 full rotations
Answer: 313 rotations
: Only full rotations count; ignore decimal for rotation
count.
5.5.3 – Number of Races Before Tyres Need Replacement
1 – Distance per race:
10 laps × 250 m = 2500 m = 2,5 km
2 – Divide tyre lifespan by race distance:
10 km ÷ 2,5 km = 4 races
Answer: 4 complete races Page 7 of 57
, Jane has a choice of two different-sized tyres for her
go-kart. The diameters of each tyre are provided.
5.5.1. Calculate the difference in circumference between
the two tyres.
5.5.2. Calculate the number of full rotations made by
Tyre A in one lap on the racetrack.
5.5.3. A set of tyres needs to be replaced after every 10
km. Determine after how many complete races (10 laps)
Jane must replace her tyres.
5.5.1 – Difference in Circumference
Step 1 – Use the formula for circumference:
Circumference = π × diameter
Step 2 – Calculate difference:
≈
π × 27.94 cm – π × 25.4 cm = π × 2.54 8 cm
Answer: 8 cm
Notes: The difference in circumference equals π times the difference in
diameters.
5.5.2 – Number of Full Rotations of Tyre A
Step 1 – Convert lap distance to cm:
1 lap = 250 m × 100 = 25,000 cm
Step 2 – Divide lap distance by tyre circumference:
≈
25,000 ÷ (π × 25.4) 313.3
Step 3 – Round to full rotations:
≈ 313 full rotations
Answer: 313 rotations
Notes: Only full rotations are counted; decimal portion is ignored.
5.5.3 – Number of Races Before Tyres Must Be Replaced
Step 1 – Distance per race (10 laps):
10 laps × 250 m = 2500 m = 2.5 km
Step 2 – Divide tyre lifespan by race distance:
10 km ÷ 2.5 km = 4 races
Answer: 4 complete races
Notes: Divide the total tyre lifespan by the distance covered per race to
determine the number of races before replacement.
Page 8 of 57
