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Angles – Mixed – With Circle Theorems – Higher – GCSE Questions – AQA

Angles – Mixed – With Circle Theorems – Higher – GCSE Questions – AQA These questions are the same format as previous GCSE exams. COPY means they use the exact same numbers as the original GCSE question. Otherwise, they are clone questions using different numbers.

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Angles – Mixed – With Circle Theorems – Higher – GCSE Questions – AQA

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  1. Angles – Mixed – With Circle Theorems – Higher – GCSE Questions – AQA These questions are the same format as previous GCSE exams. COPY means they use the exact same numbers as the original GCSE question. Otherwise, they are clonequestions using different numbers. The worksheets are provided in 2 sizes.

  2. Printing To print handouts from slides - Select the slide from the left. Then click: File > Print > ‘Print Current Slide’ To print multiple slides - Click on a section title to highlight all those slides, or press ‘Ctrl’ at the same time as selecting slides to highlight more than one. Then click: File > Print > ‘Print Selection’ To print double-sided handouts - Highlight both slides before using ‘Print Selection’. Choose ‘Print on Both Sides’ and ‘Flip on Short Edge’.

  3. AQA Higher: June 2018 Paper 3, Q4 AQA Higher: June 2018 Paper 3, Q4 2 1 2 2 2 1 1 1 What is the size of an exterior angle of a regular octagon? Circle your answer. What is the size of an exterior angle of a regular octagon? Circle your answer. What is the size of an exterior angle of a regular octagon? Circle your answer. What is the size of an interior angle of a regular decagon? Circle your answer. What is the size of an exterior angle of a regular octagon? Circle your answer. What is the size of an interior angle of a regular decagon? Circle your answer. What is the size of an interior angle of a regular decagon? Circle your answer. What is the size of an interior angle of a regular decagon? Circle your answer. [1 mark] [1 mark] [1 mark] [1 mark] [1 mark] [1 mark] [1 mark] [1 mark] 140° 140° 140° 22.5° 22.5° 22.5° 22.5° 140° 135° 135° 135° 135° 135° 135° 135° 135° 40° 40° 144° 40° 144° 144° 144° 40° 45° 36° 36° 45° 45° 36° 45° 36° AQA Higher: June 2018 Paper 3, Q4 AQA Higher: June 2018 Paper 3, Q4

  4. AQA Higher: November 2017 Paper 3, Q8 AQA Higher: November 2017 Paper 3, Q8 1 ABCD is a parallelogram. AE = AC 1 ABCD is a parallelogram. AE = AC Not drawn accurately Not drawn accurately E E A A B B 148.5° 148.5° 5 5 C C D D Work out the size of angle . Work out the size of angle . [4 marks] [4 marks] Answer degrees Answer degrees

  5. AQA Higher: November 2017 Paper 1, Q19 AQA Higher: November 2017 Paper 1, Q19 1 The diagram shows a triangle and a trapezium. 1 The diagram shows a triangle and a trapezium. [3 marks] [3 marks] 115° 115° Prove that = Prove that = 65° 65° AQA Higher: November 2017 Paper 1, Q19 AQA Higher: November 2017 Paper 1, Q19 1 The diagram shows a triangle and a trapezium. 1 The diagram shows a triangle and a trapezium. [3 marks] [3 marks] 115° 115° Prove that = Prove that = 65° 65°

  6. AQA Higher: June 2017 Paper 3, Q10 AQA Higher: June 2017 Paper 3, Q10 1 AF, BC and DF are straight lines. 1 AF, BC and DF are straight lines. D D B B A A F F C C E E 1 (a) Josh assumes that BC and DE are parallel. What answer should she get for the size of angle ? 1 (a) Josh assumes that BC and DE are parallel. What answer should she get for the size of angle ? [4 marks] [4 marks] Answer degrees Answer degrees 1 (b) 1 (b) In fact, AB and CD are not parallel angle is 130° What effect does this have on the size of angle ? Tick a box. In fact, AB and CD are not parallel angle is 130° What effect does this have on the size of angle ? Tick a box. is smaller is the same is bigger is the same is smaller is bigger Show working to support your answer. Show working to support your answer. [3 marks] [3 marks]

  7. AQA Higher: November 2017 Paper 3, Q19 AQA Higher: November 2017 Paper 3, Q19 1 A, B and C are points on a circle. DA is a tangent to the circle. 1 A, B and C are points on a circle. DA is a tangent to the circle. B B A A 44° 44° 88° 88° Not drawn accurately Not drawn accurately 48° 48° D D C C Write down the size of angle . Give a reason for your answer. Write down the size of angle . Give a reason for your answer. [2 marks] [2 marks] Answer degrees Answer degrees Reason Reason AQA Higher: November 2017 Paper 3, Q19 AQA Higher: November 2017 Paper 3, Q19 1 A, B and C are points on a circle. DA is a tangent to the circle. 1 A, B and C are points on a circle. DA is a tangent to the circle. B B A A 44° 44° 88° 88° Not drawn accurately Not drawn accurately 48° 48° D D C C Write down the size of angle . Give a reason for your answer. Write down the size of angle . Give a reason for your answer. [2 marks] [2 marks] Answer degrees Answer degrees Reason Reason

  8. AQA Higher: June 2018 Paper 3, Q22 AQA Higher: June 2018 Paper 3, Q22 1 A, B and C are points on a circle. DCB is a straight line. PAQ is a tangent to the circle. 1 A, B and C are points on a circle. DCB is a straight line. PAQ is a tangent to the circle. Not drawn accurately Not drawn accurately Q Q B B C C D D ° ° 56° 56° A A P P Sam is trying to work out the size of angle . Here is his working. Sam is trying to work out the size of angle . Here is his working. angle ACB = 56° angles in the same segment are equal = 180° – 56° angles at a point on a straight line add up to 180° = 124° angle ACB = 56° angles in the same segment are equal = 180° – 56° angles at a point on a straight line add up to 180° = 124° Make a criticism of his working. Make a criticism of his working. [1 mark] [1 mark]

  9. AQA Higher: June 2017 Paper 2, Q12 AQA Higher: June 2017 Paper 2, Q12 1 A, B, C, D, E and F are points on a circle. 1 A, B, C, D, E and F are points on a circle. D D C C B B Not drawn accurately Not drawn accurately 78° 78° 84° 84° A A 6° 6° 13° 13° F F [1 mark] [1 mark] E E Circle the line that is a diameter of the circle. Circle the line that is a diameter of the circle. DE CE AF BF DE CE AF BF AQA Higher: June 2017 Paper 2, Q12 AQA Higher: June 2017 Paper 2, Q12 1 A, B, C, D, E and F are points on a circle. 1 A, B, C, D, E and F are points on a circle. D D C C B B Not drawn accurately Not drawn accurately 78° 78° 84° 84° A A 6° 6° 13° 13° F F [1 mark] [1 mark] E E Circle the line that is a diameter of the circle. Circle the line that is a diameter of the circle. DE CE AF BF DE CE AF BF

  10. AQA Higher: June 2017 Paper 3, Q19 AQA Higher: June 2017 Paper 3, Q19 1 A, B, C, D and E are points on a circle. AFC and BFE are straight lines. BF = CF 1 A, B, C, D and E are points on a circle. AFC and BFE are straight lines. BF = CF Not drawn accurately Not drawn accurately B B A A F F 42° 42° E E C C D D Work out the size of angle . You must show your working which may be on the diagram. Work out the size of angle . You must show your working which may be on the diagram. [4 marks] [4 marks] Answer Answer

  11. AQA Higher: November 2017 Paper 1, Q24 AQA Higher: November 2017 Paper 1, Q24 1 Here is a cyclic quadrilateral. 1 Here is a cyclic quadrilateral. Not drawn accurately Not drawn accurately + 70° + 70° : = 4 : 11 Work out the size of angle : = 4 : 11 Work out the size of angle [4 marks] [4 marks] Answer degrees Answer degrees

  12. AQA Higher: November 2017 Paper 3, Q8 1 ABCD is a parallelogram. AE = AC Not drawn accurately E A B 148.5° 5 C D Work out the size of angle . [4 marks] Answer degrees

  13. AQA Higher: June 2017 Paper 3, Q10 1 AF, BC and DF are straight lines. D B A F C E 1 (a) Josh assumes that BC and DE are parallel. What answer should she get for the size of angle ? [4 marks] Answer degrees 1 (b) In fact, AB and CD are not parallel angle is 130° What effect does this have on the size of angle ? Tick a box. is bigger is the same is smaller Show working to support your answer. [3 marks]

  14. AQA Higher: June 2018 Paper 3, Q22 1 A, B and C are points on a circle. DCB is a straight line. PAQ is a tangent to the circle. Not drawn accurately Q B C D ° 56° A P Sam is trying to work out the size of angle . Here is his working. angle ACB = 56° angles in the same segment are equal = 180° – 56° angles at a point on a straight line add up to 180° = 124° Make a criticism of his working. [1 mark]

  15. AQA Higher: June 2017 Paper 3, Q19 1 A, B, C, D and E are points on a circle. AFC and BFE are straight lines. BF = CF Not drawn accurately B A F 42° E C D Work out the size of angle . You must show your working which may be on the diagram. [4 marks] Answer

  16. AQA Higher: November 2017 Paper 1, Q24 1 Here is a cyclic quadrilateral. Not drawn accurately + 70° : = 4 : 11 Work out the size of angle [4 marks] Answer degrees

  17. AQA Higher: November 2017 Paper 3, Q8 1 ABCD is a parallelogram. AE = AC Not drawn accurately 31.5° E A B 117° 148.5° 5 31.5° C D Work out the size of angle . [4 marks] AEC = 180 – 148.5 = 31.5 ACE = 31.5 CAE = 180 – (2 × 31.5) = 117 CAE + ABD = 180 (co-interior angles total 180°) ABD = 180 – 117 = 63 6 = 63 = 63 ÷ 6 = 10.5 10.5 Answer degrees

  18. AQA Higher: June 2017 Paper 3, Q10 1 AF, BC and DF are straight lines. D B A F C E 1 (a) Josh assumes that BC and DE are parallel. What answer should she get for the size of angle ? [4 marks] Answer degrees 1 (b) In fact, AB and CD are not parallel angle is 130° What effect does this have on the size of angle ? Tick a box. is bigger is the same is smaller Show working to support your answer. [3 marks] must be smaller must be bigger must be smaller

  19. AQA Higher: June 2018 Paper 3, Q22 1 A, B and C are points on a circle. DCB is a straight line. PAQ is a tangent to the circle. Not drawn accurately Q B C D ° 56° A P Sam is trying to work out the size of angle . Here is his working. angle ACB = 56° angles in the same segment are equal = 180° – 56° angles at a point on a straight line add up to 180° = 124° Make a criticism of his working. [1 mark] Should be ‘Alternate Segment’ stated

  20. AQA Higher: June 2017 Paper 3, Q19 1 A, B, C, D and E are points on a circle. AFC and BFE are straight lines. BF = CF Not drawn accurately B A 42° F 96° 42° 42° E C D Work out the size of angle . You must show your working which may be on the diagram. [4 marks] 180 – (2 × 42°) = 96° 4 + 96 = 180° 4 = 84° = 21° Answer

  21. AQA Higher: November 2017 Paper 1, Q24 1 Here is a cyclic quadrilateral. Not drawn accurately + 70° : = 4 : 11 Work out the size of angle [4 marks] + = 180° 180 ÷ 15 parts = 12° per part = 15 parts (4 × 11°) : (11 × 11°) 44 : 121 + 70 = 114° 180 – 114 = 66° = 44° 66° Answer degrees

  22. Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk

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