← IGCSE Computer Science Paper 2

Arithmetic operators + - * / ^ (7a)

Arithmetic operators: add, subtract, multiply, divide and power. ^ is worked out first, then * and /, then + and -. Brackets change or clarify the order.

Part of: IGCSE Computer Science 0478 — 7a Program Development Life Cycle — Module 31

Understanding Arithmetic operators + - * / ^ (7a) in IGCSE Computer Science Paper 2

What it does: 3 * 4 gives 12 first, then 2 is added, so Total is 14 and not 20. Without brackets, English / 2 would be done first. The brackets make the two marks add up before dividing by 2. Cambridge pseudocode uses ^ for powers, so Radius ^ 2 means Radius squared. The area is Pi multiplied by Radius squared. Radius * 2 only doubles the radius. Multiplication is done before addition: 3 * 4 = 12, then 2 + 12 = 14. Brackets are worked out first: 2 + 3 = 5, then 5 * 4 = 20. Percentage = Score * 100 / MaxMark, which gives 75. With + the division happens first, giving a wrong answer.

Common mistakes: ^ raises Score to the power of 100, which gives a huge number. To turn the score into a percentage you multiply by 100, so it should be Score * 100 / 80. Radius * 2 doubles the radius. The area of a circle needs the radius squared, so the power operator is needed: Pi * Radius ^ 2.

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Learning
Duo
Which symbol raises a number to a power in Cambridge pseudocode?
^**
Matches
Average ← Maths + English / 2
↓
Without brackets, English / 2 is worked out before the addition, so this is not the average of the two marks. It should be (Maths + English) / 2.
Applying
Meanings
Term
+ - * / ^
Meaning
Arithmetic operators: add, subtract, multiply, divide and power. ^ is worked out first, then * and /, then + and -. Brackets change or clarify the order.
Practice
Answer ← Score * 100 / MaxMark
Testing
Gaps
Answer ← Score 100 / MaxMark
Check Answer
Spots
1Score ← 56
2Answer ← Score ^ 100 / 80

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Quick Questions

1. Which symbol raises a number to a power in Cambridge pseudocode?
A. **
B. ^ ✓
Cambridge pseudocode uses ^ for powers, so Radius ^ 2 means Radius squared.
2. Which line correctly calculates the area of a circle?
A. Area ← Pi * Radius ^ 2 ✓
B. Area ← Pi * Radius * 2
The area is Pi multiplied by Radius squared. Radius * 2 only doubles the radius.
3. What is the value of 2 + 3 * 4?
A. 20
B. 14 ✓
Multiplication is done before addition: 3 * 4 = 12, then 2 + 12 = 14.
4. What is the value of (2 + 3) * 4?
A. 20 ✓
B. 14
Brackets are worked out first: 2 + 3 = 5, then 5 * 4 = 20.
5. Score is 45 and MaxMark is 60. Which line gives the percentage?
A. Answer ← Score * 100 / MaxMark ✓
B. Answer ← Score + 100 / MaxMark
Percentage = Score * 100 / MaxMark, which gives 75. With + the division happens first, giving a wrong answer.

Match the Pairs

Answer ← Score * 100 / MaxMark → Multiplies Score by 100, then divides the result by MaxMark to work out a percentage
Area ← Pi * Radius ^ 2 → Squares Radius first (power), then multiplies the result by Pi
Multiplication and division are worked out before addition and subtraction, so 3 is multiplied by 4 first → Total ← 2 + 3 * 4
Brackets make the order clear and force the addition to be done first → Average ← (Maths + English) / 2
Average ← Maths + English / 2 → Without brackets, English / 2 is worked out before the addition, so this is not the average of the two marks. It should be (Maths + English) / 2.
Area ← (Pi * Radius) ^ 2 → The brackets make Pi * Radius be multiplied first and then squared, so Pi is squared too. It should be Pi * Radius ^ 2.

Key Term

+ - * / ^
Arithmetic operators: add, subtract, multiply, divide and power. ^ is worked out first, then * and /, then + and -. Brackets change or clarify the order.

Fill in the Blanks

1. Answer ← Score * 100 / MaxMark
Hint: Type the operator that multiplies two values.
2. Area ← Pi * Radius ^ 2
Hint: Type the operator that raises a value to a power.
3. Average ← (Maths + English) / 2
Hint: Type the operator that divides the total by the number of marks.
4. Total ← (Cost + Tax) * Quantity
Hint: Type the operator that adds the tax inside the brackets.
5. Change ← Paid - Cost
Hint: Type the operator that subtracts the cost from the amount paid.

Spot the Error

Question 1
A Score ← 56
B Answer ← Score ^ 100 / 80
C OUTPUT Answer
Line B — ^ raises Score to the power of 100, which gives a huge number. To turn the score into a percentage you multiply by 100, so it should be Score * 100 / 80.
Question 2
A Radius ← 5
B Pi ← 3.14
C Area ← Pi * Radius * 2
D OUTPUT Area
Line C — Radius * 2 doubles the radius. The area of a circle needs the radius squared, so the power operator is needed: Pi * Radius ^ 2.
Question 3
A INPUT Length
B INPUT Width
C Area ← Length * Width
D Perim ← 2 * Length + Width
E OUTPUT Perim
Line D — Without brackets, 2 * Length is worked out first and then Width is added. Brackets are needed so both sides are added before doubling: 2 * (Length + Width).
Question 4
A M1 ← 70
B M2 ← 80
C M3 ← 90
D Mean ← M1 + M2 + M3 / 3
E OUTPUT Mean
Line D — Division is done before addition, so only M3 is divided by 3. The three marks must be added inside brackets first: (M1 + M2 + M3) / 3.
Question 5
A Distance ← 150
B Speed ← Distance // 3
C OUTPUT Speed
Line B — // starts a comment in Cambridge pseudocode, so the division would not happen. The divide operator is a single /, so it should be Distance / 3.

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