PLC Papers Created For:
Area of a Triangle 2 Grade 7 Objective: Know and apply the formula A = ½absinC to calculate the area, sides or angles of a triangle Question 1. AB = 8cm BC = 14cm Angle ABC = 106 o Calculate the area of triangle ABC. Give your answer correct to 3 significant figures (3 marks) Question 2. ABC is a triangle with area 27cm 2 AC = 14cm 115 o 14cm Diagram not drawn accurately Angle BAC = 115 o Calculate the length of AB. Give your answer correct to two decimal places. (3 marks)
Question 3. ABC is a triangle AB = 5cm 5cm Diagram not drawn accurately BC = 7cm Angle ABC = 38 o 38 o 7cm Calculate the area of triangle ABC. Give your answer to 1 decimal place. (2 marks) Question 4. RST is a triangle RS = 7m 7m S 35 o 3m Diagram not 3m drawn accurately ST = 3m T Angle RST = 35 o R Calculate the area of triangle RST. Give your answer to 2 decimal places. (2 marks)
Total /10
Combined transformations 2 Grade 6 Objective; Describe the effects of combinations of rotations, reflections and translations (using column vector notation for translations) Question 1 y 10 A 5 15 10 5 5 10 15 x 5 10 a) Reflect shape A in the y axis. Label the reflection with the letter B 8 0 b) Translate shape B through the vector Label the translation with the letter C c) Describe fully the single transformation that will transform shape C onto shape A.
Question 2 y 10 (4) 5 A 15 10 5 5 10 15 x 5 10 a) Rotate shape A through 90 0 clockwise about the origin Label the rotated shape with the letter B 5 1 b) Translate shape B by the vector. Label the translated shape with the letter C c) Describe fully the transformation that will transform shape C onto shape A (6) Total / 10
Congruence and Similarity 2 Grade 6 Objective: Apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures Question 1. Two similar cylinders have heights 6cm and 15cm 6cm 15cm Diagram not drawn accurately (a) If the smaller cylinder has a volume of 100cm 3, find the volume of the larger cylinder. (3 marks) (b) If the curved surface area of the larger cylinder is 175cm 2, find the curved surface area of the smaller cylinder. (3 marks)
Question 2. AB = 6.3cm DE = 2.1cm BC = 15.6cm A D Diagram not drawn accurately Calculate the length of EC. 6.3 cm 2.1cm B E 15.6cm C (2 marks) Question 3. Two similar regular hexagons have an area of 24cm 2 and 84cm 2. The side lengths of the smaller hexagon are 4cm. How long are the sides of the larger hexagon? Give your answer correct to two decimal places. (2 marks) Total /10
Cosine Rule 2 Grade 7 Objective: Know and apply the Cosine rule to find unknown lengths and angles Question 1. ABC is a triangle. AB = 8cm BC = 14cm Angle ABC = 106 o Calculate the length AC. Give your answer correct to one decimal place.... (3 marks)
Question 2. 7cm 5cm ABC is a triangle. AB = 7cm AC = 5cm BC = 8cm 8cm C Calculate the size of angle BAC. Give your answer correct to one decimal place.... (4 marks)
Question 3. 3cm 35 o 7cm ABC is a triangle. AC = 7cm BC = 3cm Angle ACB = 35 o Calculate the length AB. Give your answer correct to one decimal place.... (3 marks) Total /10
Pythagoras and Trigonometry 2D and 3D 2 Grade 7 Objective: Solve problems using Pythagoras's theorem and trigonometry in general 2-D triangles and 3-D figures Question 1. The diagram represents a cuboid ABCDEFGH. Its height is 2.5metres and its width is 4 metres. Angle GHF = 62 o Diagram NOT drawn accurately (a) Calculate the length of the diagonal HF. Give your answer to one decimal place. (b) Calculate the angle CHF. Give your answer to one decimal place... (2)... (2) Question 2. ABC is an isosceles triangle. AC = 18cm Vertical height = 14cm Calculate angle BCA to 1dp. B 14cm (Total 4 marks) Diagram NOT drawn accurately A 18cm C... (2 marks)
Question 3. ABCDE is a square based pyramid. The base has sides 9cm. Diagram NOT drawn accurately The vertical height of the pyramid is 8cm. (a) Calculate the length of AC. Give your answer correct to one decimal place.... (1) (b) Calculate the length of AE. Give your answer correct to one decimal place.... (1) (c) Calculate the size of angle EAC.... (2) Total /10
Sine Rule 2 Grade 7 Objective: Know and apply the Sine rule to find unknown lengths and angles Question 1. 6cm 7cm 40 0 ABC is a triangle AB = 6cm AC = 7cm Angle ACB = 40 o Calculate the size of angle ABC. Give your answer correct to one decimal place.... (4 marks)
Question 2. 80 0 Total /10 40 0 12m ABC is a triangle AB = 12m Angle ACB = 80 o Angle ABC = 40 o Calculate the length of AC. Give your answer correct to 1 decimal place.... (3 marks)
Question 3. 80 0 Total /10 7cm 60 0 ABC is a triangle BC = 7cm Angle CAB = 60 o Angle ACB = 80 o Calculate the length of AB. Give your answer correct to 3 significant figures.... (3 marks) Total /10
Standard trigonometric ratios 2 Grade 7 Objective: Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45 and 60 degrees. Question 1. A right angled triangle has the dimensions as shown in the diagram. Using the diagram, or otherwise, state the exact values of: (a) Sin y 5 y 3 (b) Cos y (c) Tan y (d) Sin x x 4 (e) Cos x (f) Tan x (Total 6 marks) Question 2. State the values of: (a) Tan 0 (b) Cos 90 (Total 2 marks) Question 3. The relationship Sin 30 = Cos 60, can be found for other values of sin and cos. What must the angles add up to for this relationship to work? (Total 2 marks) Total /10
PLC Papers Created For:
Area of a Triangle 2 Grade 7 Solutions Objective: Know and apply the formula A = ½absinC to calculate the area, sides or angles of a triangle Question 1. AB = 8cm BC = 14cm Angle ABC = 106 o Calculate the area of triangle ABC. Give your answer correct to 3 significant figures 0.5 x a x b x SinC 0.5 x 8 x 14 x Sin106 (M1) 53.83065497 (A1) 53.8cm 2 (A1 ft) (3 marks) Question 2. ABC is a triangle with area 27cm 2 AC = 14cm 115 o 14cm Diagram not drawn accurately Angle BAC = 115 o Calculate the length of AB. Give your answer correct to two decimal places. 0.5 x a x b x SinC 0.5 x 14 x BA x Sin115 = 27 (M1) BA = 27 (0.5 x 14 x Sin115) (M1) 4.26cm (A1) (3 marks)
Question 3. ABC is a triangle AB = 5cm 5cm Diagram not drawn accurately BC = 7cm Angle ABC = 38 o 38 o 7cm Calculate the area of triangle ABC. Give your answer to 1 decimal place. 0.5 x 5 x 7 x Sin38 (M1) 10.8cm 2 (A1) (2 marks) Question 4. RST is a triangle RS = 7m 7m S 35 o 3m Diagram not 3m drawn accurately ST = 3m T Angle RST = 35 o R Calculate the area of triangle RST. Give your answer to 2 decimal places. 0.5 x 3 x 7 x Sin35 (M1) 6.02cm 2 (A1) (2 marks) Total /10
Combined transformations 2 Grade 6 Solutions Objective; Describe the effects of combinations of rotations, reflections and translations (using column vector notation for translations) Question 1 y 10 5 A B C 15 10 5 5 10 15 x 5 10 a) Reflect shape A in the y axis. Label the reflection with the letter B Shape drawn in position shown on the grid 1M b) Translate shape B through the vector 8 0 Label the translation with the letter C Shape drawn in position shown on the grid 1M c) Describe fully the single transformation that will transform shape C onto shape A. Reflection In the line x = 4 ( allow reference to a line on the diagram e.g. the dotted blue line) 1M 1M (4)
Question 2 y 10 A 5 B C 15 10 5 5 10 15 x 5 10 a) Rotate shape A through 90 0 clockwise about the origin Label the rotated shape with the letter B Shape rotated through 90 0 Shape rotated about the correct point 5 1 b) Translate shape B by the vector. Label the translated shape with the letter C 1M 1M Shape translated to position shown in the diagram 1M c) Describe fully the transformation that will transform shape C onto shape A Rotation 1M 90 0 anticlockwise 1M About ( 2, 3 ) 1M (6) Total / 10
Congruence and Similarity 2 Grade 6 Solutions Objective: Apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures Question 1. Two similar cylinders have heights 6cm and 15cm 6cm 15cm Diagram not drawn accurately (a) If the smaller cylinder has a volume of 100cm 3, find the volume of the larger cylinder. Length scale factor = 2.5 (B1) 2.5 3 x 100 (M1) 1562.5cm 3 (A1) (3 marks) (b) If the curved surface area of the larger cylinder is 175cm 2, find the curved surface area of the smaller cylinder. Length scale factor = 2/5 (B1) (2/5) 2 x 175 (M1) 28cm 2 (A1) (3 marks)
Question 2. AB = 6.3cm DE = 2.1cm BC = 15.6cm Calculate the length of EC. 6.3 cm A 2.1cm D Diagram not drawn accurately B E C 15.6cm Scale factor = 1/3 may be implied in working (B1) EC = 5.2cm (A1) (2 marks) Question 3. Two similar regular hexagons have an area of 24cm 2 and 84cm 2. The side lengths of the smaller hexagon are 4cm. How long are the sides of the larger hexagon? Give your answer correct to two decimal places. Scale factor = 3.5 may be seen in working (B1) Longer sides are 7.48cm (A1) (2 marks) Total /10
Cosine Rule 2 Grade 7 Solutions Objective: Know and apply the Cosine rule to find unknown lengths and angles Question 1. ABC is a triangle. AB = 8cm BC = 14cm Angle ABC = 106 o Calculate the length AC. Give your answer correct to one decimal place. AC 2 = 8 2 + 14 2 2 x 8 x 14 x Cos106 (M1) AC 2 = 260-224Cos106 AC 2 = 321.74 (M1) AC = 17.9cm (M1)... (3 marks)
Question 2. 7cm 5cm ABC is a triangle. AB = 7cm AC = 5cm BC = 8cm 8cm C Calculate the size of angle BAC. Give your answer correct to one decimal place. 8 2 = 7 2 + 5 2 2 x 7 x 5 x CosA (M1) 64 = 74 70Cos A 70CosA = 10 (M1) Cos A = 10/70 (M1) A = Cos -1 (10/70) = 81.8 o (A1)... (4 marks)
Question 3. 3cm 35 o 7cm ABC is a triangle. AC = 7cm BC = 3cm Angle ACB = 35 o Calculate the length AB. Give your answer correct to one decimal place. AB 2 = 7 2 + 3 2 2 x 7 x 3 x Cos35 (M1) AB 2 = 58-42Cos35 AB 2 = 23,5956 (M1) AB = 4.86cm (A1)... (3 marks) Total /10
Pythagoras and Trigonometry 2D and 3D 2 Grade 7 Solutions Objective: Solve problems using Pythagoras's theorem and trigonometry in general 2-D triangles and 3-D figures Question 1. The diagram represents a cuboid ABCDEFGH. Its height is 2.5metres and its width is 4 metres. Angle GHF = 62 o Diagram NOT drawn accurately (a) Calculate the length of the diagonal HF. Give your answer to one decimal place. (b) Calculate the angle CHF. Give your answer to one decimal place cos62 = 4 HF (M1 using cos62) HF = 4 cos62 = 8.5m (A1)... (2) tanchf = 2.5 8.5 (M1 Using tanθ) CHF = tan -1 (2.5 8.5) = 16.4m (A1) FT from (a)... (2) Question 2. ABC is an isosceles triangle AC = 18cm Vertical height = 14cm B 14cm (Total 4 marks) Diagram NOT drawn accurately Calculate the angle BCA to 1dp. A 18cm C TanBCA = 14 9 (M1 use of Tan) Tan -1 (14 9) = 57.3 o... (1 mark)
Question 3. ABCDE is a square based pyramid. Diagram NOT drawn accurately The base has sides 9cm. The vertical height of the pyramid is 8cm. (a) Calculate the length of AC. Give your answer correct to one decimal place. AC = (9 2 + 9 2 ) = 12.7cm (B1)... (1) (b) Calculate the length of AE. Give your answer correct to one decimal place. AE = (8 2 + 6.35 2 ) = 10.2 cm (B1)... (2) (c) Calculate the size of angle EAC. CosEAC = AC AE (M1 use of Cos) EAC = Cos -1 (AC AE) = 51.5 o (A1)... (2) Total /10
Sine Rule 2 Grade 7 Solutions Objective: Know and apply the Sine rule to find unknown lengths and angles Question 1. 6cm 7cm 40 0 ABC is a triangle AB = 6cm AC = 7cm Angle ACB = 40 o Calculate the size of angle ABC. Give your answer correct to one decimal place. Sinx 7 = Sin40 6 Sinx = Sin40 6 (M1) x 7 (M1) Sinx = 0.7499.. x = Sin -1 (0.7499..) (M1) x = 48.6 o (A1)... (4 marks)
Question 2. 80 0 Total /10 40 0 12m ABC is a triangle AB = 12m Angle ACB = 80 o Angle ABC = 40 o Calculate the length of AC. Give your answer correct to 1 decimal place. 12 = AC Sin80 Sin40 (M1) 12 AC = x Sin40 (M1) Sin80 AB = 7.8m (A1)... (3 marks)
Question 3. 80 0 Total /10 7cm 60 0 ABC is a triangle BC = 7cm Angle CAB = 60 o Angle ACB = 80 o Calculate the length of AB. Give your answer correct to 3 significant figures. 7 Sin60 = AB Sin80 (M1) 7 AB = x Sin80 (M1) Sin60 AB = 7.96cm (A1)... (3 marks) Total /10
Standard trigonometric ratios 2 Grade 7 Solutions Objective: Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45 and 60 degrees. Question 1. A right angled triangle has the dimensions as shown in the diagram. Using the diagram, or otherwise, state the exact values of: (a) Sin y = h =0.8 x 5 y 3 (b) Cos y = h =0.6 4 (c) Tan y = = 4 3 (d) Sin x = h =0.6 (e) Cos x = h =0.8 (f) Tan x = =0.75 (Total 6 marks) Question 2. State the values of: (a) Tan 0 =0 (b) Cos 90 =0 (Total 2 marks) Question 3. The relationship Sin 30 = Cos 60, can be found for other values of sin and cos. What must the angles add up to for this relationship to work? 90 (Total 2 marks) Total /10