Exam-Style Problems

Stage 9 - Q1 - 3 marks

20067

Enlarge ABC by factor 2 about O, then by factor \(\frac{1}{2}\) about O. Explain the final result.

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Start

A

B

C

Hint

Track the displacement from the common centre.

Stage 9 - Q2 - 5 marks

20068

Use these cards in order: rotate 90° anticlockwise about O; enlarge by 2 about O; translate by \((2,0)\). Find the final triangle.

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Start

A

B

C

Hint

Keep a coordinate record after each card.

Stage 9 - Q3 - 4 marks

20069

Compare rotate 90° anticlockwise about O then enlarge by 2 about O, with the reverse order. Use ABC.

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Start

A

B

C

Hint

Calculate both sequences and compare matching vertices.

Stage 9 - Q4 - 4 marks

20070

For \(P=(-2,0)\), compare translate by \((2,0)\) then enlarge by 3 about O, with the reverse order.

Hint

The enlargement scales everything that came before it.

Stage 9 - Q5 - 4 marks

20071

A route uses rotate 90° anticlockwise about O, enlarge by 2 about O, then translate by \((2,0)\). Give three cards that undo it.

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Start

Final

A

B

C

A'

B'

C'

Hint

Undo the last card first.

Stage 9 - Q6 - 5 marks

20072

Use these cards in order: rotate 90° anticlockwise about O; enlarge by 3 about O; translate by \((2,0)\). Find the final triangle.

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Start

A

B

C

Hint

Keep a coordinate record after each card.

Stage 9 - Q7 - 4 marks

20073

Compare rotate 90° anticlockwise about O then enlarge by 3 about O, with the reverse order. Use ABC.

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

0

Start

A

B

C

Hint

Calculate both sequences and compare matching vertices.

Stage 9 - Q8 - 4 marks

20074

For \(P=(-2,-1)\), compare translate by \((2,0)\) then enlarge by 2 about O, with the reverse order.

Hint

The enlargement scales everything that came before it.

Stage 9 - Q9 - 4 marks

20075

A route uses rotate 90° anticlockwise about O, enlarge by 3 about O, then translate by \((2,0)\). Give three cards that undo it.

x

y

-10

-8

-6

-4

-2

2

4

6

8

10

0

Start

Final

A

B

C

A'

B'

C'

Hint

Undo the last card first.

Stage 9 - Q10 - 6 marks

20076

Let O be the origin. Start with A\((1,1)\), B\((3,1)\), C\((1,2)\). Reach A′\((0,2)\), B′\((0,6)\), C′\((-2,2)\) using the fewest cards: quarter-turn about O, enlargement by 2 about O, or translation by \((2,0)\). Explain minimality.

x

y

-8

-6

-4

-2

2

4

6

8

0

Start

Target

A

B

C

A'

B'

C'

Hint

Use area, orientation and position to decide which card types are necessary.