MATHEMATICS
Geometry and measures
AQA 8300 | Premium Learning Edition
What this pack does
Geometry and measures is one of the six broad AQA GCSE Mathematics areas. This pack teaches the
methods that sit inside geometry and measures, shows how to recognise each question type and then builds
from short practice to mixed exam-style problems.
LEARN SEE IT
Plain-English teaching in short sections. Worked questions with every step explained.
TRY IT FIX IT
Questions immediately after each lesson. Answer sheet explains the method, not just the
result.
Independent resource
Original revision material aligned to the current AQA topic structure. ClearGrade is not affiliated with or
endorsed by AQA. Questions are independently written and are not reproduced past-paper questions.
ClearGrade GCSE | Premium Learning Edition Mathematics | 1
, Before you start
Geometry and measures is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that
sit inside geometry and measures, shows how to recognise each question type and then builds from short practice to
mixed exam-style problems.
By the end of this pack, you should be able to:
• explain and apply angles and polygons
• explain and apply perimeter and area
• explain and apply circles
• explain and apply surface area and volume
• explain and apply transformations
• explain and apply congruence and similarity
• explain and apply pythagoras
• explain and apply trigonometry
• explain and apply bearings and scale drawings
• explain and apply circle theorems
• explain and apply vectors
How to use the pack
1. Read one lesson. 2. Cover the page and explain it from memory. 3. Study the worked example. 4. Attempt
the three “Your turn” questions without looking back. 5. Mark them using the explained answers at the back. 6.
Re-do every question you got wrong.
ClearGrade GCSE | Premium Learning Edition Mathematics | 2
, LESSON 1
Angles and polygons
The idea in plain English
Angle facts and polygon sums should be supported by reasons.
What you need to know
• Straight line=180 degrees; around a point=360 degrees; triangle=180 degrees.
• Interior sum of n-gon=(n-2)x180 degrees.
• Regular exterior angle=360/n.
WORKED EXAMPLE
Question: Find one interior angle of a regular octagon.
Step 1: Interior sum=(8-2)x180=1080 degrees.
Step 2: A regular octagon has 8 equal interior angles.
Step 3: 1080/8=135 degrees.
Step 4: Answer=135 degrees.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
YOUR TURN
1. Straight-line partner of73? [1-2 marks]
2. Interior sum hexagon? [2-3 marks]
3. Exterior angle regular15-gon? [3-4 marks]
LESSON 2
Perimeter and area
The idea in plain English
Perimeter is total boundary length; area measures surface covered. Choose the correct formula and units.
What you need to know
• Triangle area=0.5bh.
• Parallelogram area=bh.
• Trapezium area=0.5(a+b)h.
ClearGrade GCSE | Premium Learning Edition Mathematics | 3
Geometry and measures
AQA 8300 | Premium Learning Edition
What this pack does
Geometry and measures is one of the six broad AQA GCSE Mathematics areas. This pack teaches the
methods that sit inside geometry and measures, shows how to recognise each question type and then builds
from short practice to mixed exam-style problems.
LEARN SEE IT
Plain-English teaching in short sections. Worked questions with every step explained.
TRY IT FIX IT
Questions immediately after each lesson. Answer sheet explains the method, not just the
result.
Independent resource
Original revision material aligned to the current AQA topic structure. ClearGrade is not affiliated with or
endorsed by AQA. Questions are independently written and are not reproduced past-paper questions.
ClearGrade GCSE | Premium Learning Edition Mathematics | 1
, Before you start
Geometry and measures is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that
sit inside geometry and measures, shows how to recognise each question type and then builds from short practice to
mixed exam-style problems.
By the end of this pack, you should be able to:
• explain and apply angles and polygons
• explain and apply perimeter and area
• explain and apply circles
• explain and apply surface area and volume
• explain and apply transformations
• explain and apply congruence and similarity
• explain and apply pythagoras
• explain and apply trigonometry
• explain and apply bearings and scale drawings
• explain and apply circle theorems
• explain and apply vectors
How to use the pack
1. Read one lesson. 2. Cover the page and explain it from memory. 3. Study the worked example. 4. Attempt
the three “Your turn” questions without looking back. 5. Mark them using the explained answers at the back. 6.
Re-do every question you got wrong.
ClearGrade GCSE | Premium Learning Edition Mathematics | 2
, LESSON 1
Angles and polygons
The idea in plain English
Angle facts and polygon sums should be supported by reasons.
What you need to know
• Straight line=180 degrees; around a point=360 degrees; triangle=180 degrees.
• Interior sum of n-gon=(n-2)x180 degrees.
• Regular exterior angle=360/n.
WORKED EXAMPLE
Question: Find one interior angle of a regular octagon.
Step 1: Interior sum=(8-2)x180=1080 degrees.
Step 2: A regular octagon has 8 equal interior angles.
Step 3: 1080/8=135 degrees.
Step 4: Answer=135 degrees.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
YOUR TURN
1. Straight-line partner of73? [1-2 marks]
2. Interior sum hexagon? [2-3 marks]
3. Exterior angle regular15-gon? [3-4 marks]
LESSON 2
Perimeter and area
The idea in plain English
Perimeter is total boundary length; area measures surface covered. Choose the correct formula and units.
What you need to know
• Triangle area=0.5bh.
• Parallelogram area=bh.
• Trapezium area=0.5(a+b)h.
ClearGrade GCSE | Premium Learning Edition Mathematics | 3
