QQQ – Transformations
5
Name __________________
1
2
3
Define ‘image’.
________________________________
________________________________
Reflect the following shape in the given
line of symmetry.
____________________
6
Rotate the following shape 90° clockwise
about the indicated point.
7
The following object has been rotated
90° anticlockwise. Mark with a point the
centre of rotation.
8
A point (3,-2) is reflected in the line
y = -x. What is the resulting point?
Describe the following transformation.
_______________________________
_______________________________
_______________________________
4
A point (3, -2) on a shape is translated by
the vector (−1
). What is the resulting
3
point?
The following object was translated.
__________________
Score ________ / 8
What was the translation vector?
(you can assume each square represents a unit)
________________
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Award ___________
QQQ – Transformations –
ANSWERS
Notes for teacher:
5+ for Bronze Award, 6+ for Silver and 7+ for
Gold. Results can be recorded on a
spreadsheet template found in ‘Tracking and
Assessment’.
1 Define ‘image’.
The shape that results from some
transformation of an object.
2 Reflect the following shape in the given line
of symmetry.
What was the translation vector?
(you can assume each square represents a unit)
(−3
), give a half mark if they wrote (-3, 3).
3
5 A point (3, -2) on a shape is translated by
the vector (−1
). What is the resulting
3
point?
(2, 1)
6 Rotate the following shape 90° clockwise
about the indicated point.
3 Describe the following transformation.
7 The following object has been rotated 90°
anticlockwise. Mark with a point the centre
of rotation.
A reflection in the line y = x
(Note: It is NOT a rotation).
4 The following object was translated.
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8 A point (3,-2) is reflected in the line y = -x.
What is the resulting point?
(2, -3)
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QQQ – Brackets and Equations ANSWERS
1a
Simplify 2𝑥 + 𝑦 − 𝑥
6a
𝒙+𝒚
1b Simplify 2𝑥 × 3𝑥𝑦
2a
𝟔𝒙𝟐 𝒚
Simplify 𝑥 + 𝑥 + 𝑥 2 − 1
𝒙𝟑 + 𝟐𝒙𝟐 − 𝟏
3
5b Solve 6 − 𝑧 = 3
3
7
2b Simplify 2𝑥 2 𝑦
4𝑥𝑦 2
3
4
5a
8
𝒙𝟐 + 𝟑𝒙 − 𝟔
Expand the following brackets (and
simplify)
2𝑥(𝑦 − 𝑥) − 𝑥(2𝑥 − 𝑦)
𝟑𝒙𝒚 − 𝟒𝒙𝟐 𝒐𝒓
𝒛=𝟗
Solve 3𝑥 − 1 = 𝑥 + 3
𝒙=𝟐
6b Solve 3(6 − 𝑧) = 1 − 2(2 − 2𝑧)
2
𝒙
𝟐𝒚
Expand the following brackets (and
simplify).
𝑥(𝑥 + 1) + 2(𝑥 − 3)
𝒛 = 𝟏𝟗
𝒛=𝟑
The children in a family consist of Alice,
Bob and Charles. Bob is three times as
old as Alice and Charles is 2 years older
than Alice. The sum of their ages is 27.
How old is Alice? (Hint: let Alice’s age by
𝑥)
Alice’s age = 5
The sum of two people’s ages is 20 times
the difference of their ages. What is the
ratio (i.e. relative size) of their ages?
𝒙 + 𝒚 = 𝟐𝟎(𝒙 − 𝒚)
𝒔𝒐 𝟏𝟗𝒙 = 𝟐𝟏𝒚
− 𝟒𝒙𝟐 + 𝟑𝒙𝒚
𝒊. 𝒆. 𝒓𝒂𝒕𝒊𝒐 𝒊𝒔 𝟐𝟏: 𝟏𝟗
𝟏𝟗 𝟐𝟏
(𝒐𝒓 𝟏𝟗: 𝟐𝟏 𝒐𝒓
𝒐𝒓
𝟐𝟏 𝟏𝟗
𝒐𝒓 𝟏. 𝟏𝟎𝟓 𝒐𝒓 𝟎. 𝟗𝟎𝟓)
Solve 3𝑧 − 2 = 55
QQQ – Ratio & Map Scales - ANSWERS
1
2
3
4
5
Simplify the ratio 21:28
3:4
What’s the ratio of cats to dogs if
there’s 63 cats and 54 dogs?
7:6 (or 63:54 will do!)
The ratio of value of a gold watch
and a silver watch is 5:3. The silver
watch costs £120. How much does
the gold one cost?
£200
The ratio of boys to girls in a room is
4:5. There’s 270 people in total.
How many boys are there?
120 boys
You measure a distance of 4cm on
the map. The scale is 1:10 000.
What actual distance does this
represent? (choose an appropriate
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6
7
8
unit)
400m or 0.4km
(half mark for 40000cm)
If the scale of a map is 2:100 000,
then an actual distance of 130km
appears how large on a map?
(choose an appropriate unit)
2.6m or 260cm
(half mark for 0.0026km)
Two angles on a line have the ratio
4:5. What is the smaller angle?
80 degrees
1
Puffer fish fill 3 of a tank. Angel fish
1
fill of it. Find the ratio of Puffer
4
fish to Angel fish using whole
numbers.
4:3 (don’t accept 3:4)