← IGCSE Computer Science Paper 2

Power operator ^

The power operator. Radius ^ 2 raises Radius to the power 2, meaning Radius * Radius. It is worked out before multiplication, so Pi * Radius ^ 2 squares Radius first.

Part of: IGCSE Computer Science 0478 — 8.1a Data Types and Variables — Module 28

Understanding Power operator ^ in IGCSE Computer Science Paper 2

What it does: Number ^ 2 means Number * Number, so the variable Square stores the square of Number. Radius ^ 2 is calculated first and the result is then multiplied by 3. It does not mean (3 * Radius) squared. The ^ operator raises a number to a power. Radius ^ 2 is Radius * Radius. It is not Radius * 2. Side ^ 3 means 4 * 4 * 4 = 64. Multiplying 4 by 3 gives 12, which is wrong. A square means a power of 2. A power of 3 gives a cube. Multiplying by 2 is not the same as raising to the power 2. Squaring needs ^ 2 or Radius * Radius.

Common mistakes: Cambridge pseudocode uses ^ for powers, not **. The line should be Square ← 5 ^ 2. The brackets make the multiplication happen first, so 12.56 is squared. Without them, only 4 is squared before multiplying by 3.14: Area ← 3.14 * 4 ^ 2.

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This module's key terms are also in a printable crossword (Modules 337–346) and word search (Modules 337–357).

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Learning
Duo
What does Radius ^ 2 mean in Cambridge pseudocode?
Radius multiplied by 2Radius multiplied by itself
Matches
Area ← Pi * Radius * 2
↓
Radius * 2 doubles the radius instead of squaring it. The power operator ^ is needed, so it should be Pi * Radius ^ 2.
Applying
Meanings
Term
^
Meaning
The power operator. Radius ^ 2 raises Radius to the power 2, meaning Radius * Radius. It is worked out before multiplication, so Pi * Radius ^ 2 squares Radius first.
Practice
CONSTANT Pi ← 3.14
Testing
Gaps
Answer ← Pi * Radius 2
Check Answer
Spots
1Square ← 5 ** 2
2Cube ← 5 ^ 3

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Quick Questions

1. What does Radius ^ 2 mean in Cambridge pseudocode?
A. Radius multiplied by itself ✓
B. Radius multiplied by 2
The ^ operator raises a number to a power. Radius ^ 2 is Radius * Radius. It is not Radius * 2.
2. Which line correctly works out the area of a circle?
A. Answer ← Pi * Radius * 2
B. Answer ← Pi * Radius ^ 2 ✓
The area of a circle is Pi multiplied by the radius squared. Radius ^ 2 squares the radius. Radius * 2 only doubles it.
3. If Side is 4, what is the value of Side ^ 3?
A. 64 ✓
B. 12
Side ^ 3 means 4 * 4 * 4 = 64. Multiplying 4 by 3 gives 12, which is wrong.
4. Which expression gives the square of Length?
A. Length ^ 2 ✓
B. Length ^ 3
A square means a power of 2. A power of 3 gives a cube.
5. In Answer ← Pi * Radius ^ 2, which part is worked out first?
A. Pi * Radius
B. Radius ^ 2 ✓
The power is worked out before multiplication. Radius is squared first, then the result is multiplied by Pi.

Match the Pairs

Side ^ 3 → Side raised to the power 3, so Side * Side * Side (a cube)
Area ← Pi * Radius ^ 2 → Squares Radius first, then multiplies the result by Pi
Square a number by raising it to the power 2 → Square ← Number ^ 2
Power is worked out before multiplication, so only Radius is squared → Answer ← 3 * Radius ^ 2
Area ← Pi * Radius * 2 → Radius * 2 doubles the radius instead of squaring it. The power operator ^ is needed, so it should be Pi * Radius ^ 2.
Answer ← Pi * (Radius ^ 2 → The bracket is opened but never closed, which is a syntax error. It should be Pi * Radius ^ 2 or Pi * (Radius ^ 2).

Key Term

^
The power operator. Radius ^ 2 raises Radius to the power 2, meaning Radius * Radius. It is worked out before multiplication, so Pi * Radius ^ 2 squares Radius first.

Fill in the Blanks

1. Answer ← Pi * Radius ^ 2
Hint: Type the operator that raises a number to a power.
2. Area ← Side ^ 2
Hint: Type the power that squares a number.
3. Volume ← Side ^ 3
Hint: Type the power that cubes a number.
4. Answer ← Pi * Radius ^ 2
Hint: Type the variable that stores the area of the circle.
5. Side ← 4 Area ← Side ^ 2 OUTPUT Area
Hint: Type the variable that holds the squared value so it can be displayed.

Spot the Error

Question 1
A Square ← 5 ** 2
B Cube ← 5 ^ 3
C OUTPUT Square, Cube
Line A — Cambridge pseudocode uses ^ for powers, not **. The line should be Square ← 5 ^ 2.
Question 2
A Area ← (3.14 * 4) ^ 2
B OUTPUT Area
C OUTPUT Area * 2
Line A — The brackets make the multiplication happen first, so 12.56 is squared. Without them, only 4 is squared before multiplying by 3.14: Area ← 3.14 * 4 ^ 2.
Question 3
A DECLARE Side : INTEGER
B INPUT Side
C Cube ← Side * 3
D OUTPUT Cube
Line C — Side * 3 only triples the side. To cube it you raise it to the power 3: Cube ← Side ^ 3.
Question 4
A CONSTANT Pi ← 3.14
B Radius ← 3
C Area ← Pi * 2 ^ Radius
D OUTPUT Area
Line C — The base and the power are swapped. This raises 2 to the power Radius. It should be Pi * Radius ^ 2, which squares Radius.
Question 5
A Radius ← 2
B Area = 3.14 * Radius ^ 2
C OUTPUT Area
Line B — Assignment must use the ← operator, not =. The line should be Area ← 3.14 * Radius ^ 2.

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