Area – Sine Rule – Higher – GCSE Questions 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. The worksheets are provided in a variety of sizes.

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GCSE GCSE Edexcel Higher: June 2017 Paper 2, Q17 B B O O A A T T OPT is a sector of a circle with centre O and radius 13 cm. A is the point on OT and B is the point on OP such that AOB is an equilateral triangle of side 8cm. Calculate the area of the shaded region as a percentage of the area of the sector OPT. Give your answer correct to 1 decimal place. OPT is a sector of a circle with centre O and radius 13 cm. A is the point on OT and B is the point on OP such that AOB is an equilateral triangle of side 8cm. Calculate the area of the shaded region as a percentage of the area of the sector OPT. Give your answer correct to 1 decimal place. % % (Total for Question 1 is 5 marks) (Total for Question 1 is 5 marks)

GCSE GCSE Edexcel Higher: June 2017 Paper 3, Q15 (x + 3) meters (x + 3) meters 45° 45° A B A B (2x - 1) meters (2x - 1) meters The area of triangle ABC is 6 2 m2. Calculate the value of x. Give your answer correct to 3 significant figures. The area of triangle ABC is 6 2 m2. Calculate the value of x. Give your answer correct to 3 significant figures. (Total for Question 1 is 5 marks) (Total for Question 1 is 5 marks)

GCSE GCSE Edexcel Higher: November 2017 Paper 3, Q17 ABD and BCD are triangles. 1 ABD and BCD are triangles. The area of triangle ABD is 48 m2 Work out the length of CD. Give your answer correct to 1 decimal place. The area of triangle ABD is 48 m2 Work out the length of CD. Give your answer correct to 1 decimal place. m m (Total for Question 1 is 5 marks) (Total for Question 1 is 5 marks)

GCSE Edexcel Higher: June 2017 Paper 2, Q17 B O A T OPT is a sector of a circle with centre O and radius 13 cm. A is the point on OT and B is the point on OP such that AOB is an equilateral triangle of side 8cm. Calculate the area of the shaded region as a percentage of the area of the sector OPT. Give your answer correct to 1 decimal place. % (Total for Question 1 is 5 marks)

GCSE Edexcel Higher: June 2017 Paper 3, Q15 (x + 3) meters 45° A B (2x - 1) meters The area of triangle ABC is 6 2 m2. Calculate the value of x. Give your answer correct to 3 significant figures. (Total for Question 1 is 5 marks)

GCSE Edexcel Higher: November 2017 Paper 3, Q17 ABD and BCD are triangles. A 106° 12 m B D 44° The area of triangle ABD is 48 m2 Work out the length of CD. Give your answer correct to 1 decimal place. 121° C m (Total for Question 1 is 5 marks)

8cm 60° 8cm 8cm 13cm GCSE Sector area = 60 360 x π x 132 = 88.488… cm2 Edexcel Higher: June 2017 Paper 2, Q17 P 1 8cm B Equilateral = 60° interior angle 60° O 8cm 8cm A 13cm T OPT is a sector of a circle with centre O and radius 13 cm. A is the point on OT and B is the point on OP such that AOB is an equilateral triangle of side 8cm. Calculate the area of the shaded region as a percentage of the area of the sector OPT. Give your answer correct to 1 decimal place. Sector area = 60 360 x π x 132 = 88.488… cm2 Triangle area = 1 2 ab SinC = 1 2 x 8 x 8 x Sin 60 = 27.712… cm2 Shaded area = 88.488… - 27.712… = 60.776… Pecentage = 67.271… 88.488… × 100=68.68… 68.7 % (Total for Question 1 is 5 marks)

a C b 𝑥 = 2.63 GCSE 𝐴𝑟𝑒𝑎 = 1 2 𝑎𝑏 𝑆𝑖𝑛 𝐶 Edexcel Higher: June 2017 Paper 3, Q15 C 1 𝐴𝑟𝑒𝑎 = 1 2 𝑎𝑏 𝑆𝑖𝑛 𝐶 (x + 3) meters a C 45° A B (2x - 1) meters b The area of triangle ABC is 6 2 m2. Calculate the value of x. Give your answer correct to 3 significant figures. 𝐴𝑟𝑒𝑎 = 1 2 𝑎𝑏 𝑆𝑖𝑛 𝐶= 1 2 (x + 3)(2x - 1) sin 45 6 2 = 1 2 (x + 3)(2x - 1) sin 45 sin 45 = 1 2 = 2 2 12 2 = (x + 3)(2x - 1) sin 45 𝑥= −𝑏± 𝑏2−4𝑎𝑐 2𝑎 12 2 = (2x2 + 6x - x - 3) 2 2 24 2 = (2x2 + 5x - 3) 2 𝑥= −5± 52−(4×2×−27 ) 2 × 2 24= 2x2 + 5x - 3 𝑥= −5+ 241 4 = 2.6310… 2x2 + 5x – 27 = 0 𝑥= −5− 241 4 = -5.1310… Quadratic Formula A = 2 B = 5 C = -27 𝑥 = 2.63 (Total for Question 1 is 5 marks)

GCSE Edexcel Higher: November 2017 Paper 3, Q17 1 ABD and BCD are triangles. A x 106° 12 m y B D 44° CD The area of triangle ABD is 48 m2 Work out the length of CD. Give your answer correct to 1 decimal place. 121° C Area of ABD = 1 2 𝑎𝑏 𝑆𝑖𝑛 𝐶 = 1 2 × 12 × x × sin 106 = 48 x = 48 1 2 × 12 × sin 106 = 8.3223 m a2 = b2 + c2 – 2bc Cos A y2 = 122 + ANS2 – (2 × 12 × ANS × Cos 106) y2 = 268.317 y = 268.317 = 16.380 m 𝑎 𝑆𝑖𝑛 𝐴 = 𝑏 𝑆𝑖𝑛 𝐵 𝐴𝑁𝑆 𝑆𝑖𝑛 121 = 𝐶𝐷 𝑆𝑖𝑛 44 𝑆𝑖𝑛 44 × 𝐴𝑁𝑆 𝑆𝑖𝑛 121 =𝐶𝐷=13.27 13.3 m (Total for Question 1 is 5 marks)

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