25
PLC Papers Created For: Trig and pythagoras intervention
PLC Papers
Created For:
Trig and pythagoras intervention
PiXL PLC 2017 Certification
Pythagoras 1 Grade 5
Objective: Know and use Pythagoras's theorem for right-angled triangles
Question 1
ABC is a right angled triangle. AB = 9 cm, BC = 12 cm Calculate the length of AC.
………………………. (3) (Total 3 marks) Question 2
ABC is a right angled triangle. AB = 11 cm, AC = 18 cm Calculate the length of BC. Give your answer correct to 1 decimal place.
………………………. (Total 3 marks) (3)
PiXL PLC 2017 Certification
Question 3
ABCD is a rectangle. AB = 19 m, AD = 13 m Work out the length of the diagonal BD. Give your answer correct to 3 significant figures.
………………………. (4) (Total 4 marks)
Total /10
PiXL PLC 2017 Certification
Trigonometric Ratios 1 Grade 5
Objective: Know and use the trigonometric ratios for right-angled triangles
Question 1
ABC is a right angled triangle. BC = 14 m and the angle ACB is 32o Calculate the length of AB. Give your answer to 1 decimal place.
…..………………. (3) (Total 3 marks) Question 2 ABC is a right angled triangle.
AB = 12 cm, AC = 27 cm Calculate the angle BAC. Give your answer correct to the nearest degree.
…..……………. (Total 3 marks) (3)
PiXL PLC 2017 Certification
Question 3 ABCD is a rectangle.
AD = 12 m and the diagonal BD makes an angle of 28o with AB. Work out the length of the diagonal BD. Give your answer correct to 3 significant figures
………….. …. (4) (Total 4 marks)
Total /10
PiXL PLC 2017 Certification
Cosine Rule 1 Grade 7
Objective: Know and apply the Cosine rule to find unknown lengths and angles
Question 1.
ABC is a triangle.
AB = 12m AC = 10m BC = 15m
Calculate the size of angle BAC. Give your answer correct to one decimal place.
................................°
(4 marks)
PiXL PLC 2017 Certification
Question 2.
ABC is a triangle.
AB = 11.7m
BC = 28.3m
Angle ABC = 67o
Calculate the length of AC. Give your answer correct to three significant figures.
................................
(3 marks)
Question 3.
ABC is a triangle.
AC = 7cm
BC = 10cm
Angle ACB = 73o
Calculate the length of AB. Give your answer correct to three significant figures.
................................
(3 marks)
Total /10
PiXL PLC 2017 Certification
Sine Rule 1 Grade 7
Objective: Know and apply the Sine rule to find unknown lengths and angles
Question 1.
ABC is a triangle AB = 9cm Angle ABC = 21o
Angle ACB = 46o
(a) Calculate the length of AC. Give your answer correct to 3 significant figures.
................................
(3 marks)
(b) Calculate the length of BC. Give your answer correct to 3 significant figures.
................................
(3 marks)
21o 46o
9cm
PiXL PLC 2017 Certification
Question 2.
ABC is a triangle AB = 8.1cm AC = 7.5cm Angle ACB = 30o Calculate the size of angle ABC. Give your answer correct to one decimal place.
................................
(4 marks)
Total /10
PiXL PLC 2017 Certification
Standard trigonometric ratios 1 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 60
(b) Cos 60
(c) Tan 60
(d) Sin 30
(e) Cos 30
(f) Tan 30
(Total 6 marks)
Question 2.
Using the triangle shown, or otherwise, find the exact values of:
(a) Sin 45
(b) Cos 45
(c) Tan 45
(d) Sin 90
(Total 4 marks)
Total /10
1
2 √3
1
1
√2
PiXL PLC 2017 Certification
Pythagoras’ and Trigonometry 2D and 3D 1 Grade 7
Objective: Solve problems using Pythagoras's theorem and trigonometry in general 2-D triangles and 3-D figures
Question 1.
ABC is an isosceles triangle
BC = 24cm
Vertical height = 20cm
Calculate the length of AC. Give your answer correct to one decimal place.
..............................................
(Total 2 marks)
Question 2.
ABCDEFGH is a cuboid
AE = 5cm
AB = 6cm
BC = 9cm
(a) Calculate the length of AG. Give your answer correct to 3 significant figures.
.............................................. (1)
(b) Calculate the size of the angle between AG and the face ABCD.
Give your answer correct to 1 decimal place.
..............................................
(3)
(Total 4 marks)
Diagram NOT drawn
accurately
20cm
24cm
A C
B
Diagram NOT drawn accurately
PiXL PLC 2017 Certification
Question 3.
The diagram shows a square based pyramid.
The square base has sides 18cm.
(a) Calculate the length of the diagonal AB.
Give your answer correct to 1 decimal place.
.............................................. (1)
(b) If ∠VBA = 58o, calculate the vertical height VC.
Give your answer correct to 1 decimal place.
..............................................
(3)
(Total 4 marks)
Total /10
Diagram NOT drawn
accurately
18cm
PiXL PLC 2017 Certification
PLC Papers
Created For:
Trig and pythagoras intervention
PiXL PLC 2017 Certification
Pythagoras 1 Grade 5 Solutions
Objective: Know and use Pythagoras's theorem for right-angled triangles
Question 1
ABC is a right angled triangle. AB = 9 cm, BC = 12 cm Calculate the length of AC. AC2 = 92 + 122 (M2 square, add) = 81 + 144 = 225 AC = 15 (A1)
…………15cm…………. (3) (Total 3 marks) Question 2
ABC is a right angled triangle. AB = 11 cm, AC = 18 cm Calculate the length of BC. Give your answer correct to 1 decimal place. BC2 = 182 - 112 (M2 square, subtract)
= 324 - 121 = 203 BC = 14.2 (A1)
………14.2 cm……. (Total 3 marks) (3)
PiXL PLC 2017 Certification
Question 3
ABCD is a rectangle. AB = 19 m, AD = 13 m Work out the length of the diagonal BD. Give your answer correct to 3 significant figures. BD2 = 192 + 132 (M2 square, add)
= 361 + 169 = 530 BD = 23.0 (A2 correct, correct to 3sf)
……23.0 m…………. (4) (Total 4 marks) Total /10
Total marks / 10
PiXL PLC 2017 Certification
Trigonometry 1 Grade 5 Solutions
Objective: Know and use the trigonometric ratios for right-angled triangles
Question 1
ABC is a right angled triangle. BC = 14 m and the angle ACB is 32o Calculate the length of AB. Give your answer to 1 decimal place.
tan 32 = AB / 14 (M1) AB = 14 tan 32 (M1) = 8.7 (A1)
8.7 m………………. (3) (Total 3 marks) Question 2 ABC is a right angled triangle.
AB = 12 cm, AC = 27 cm Calculate the angle BAC. Give your answer correct to the nearest degree.
cos BAC = 12 / 27 (M1) = 0.444 (M1) BAC = 64 (A1)
64o……………. (Total 3 marks) (3)
PiXL PLC 2017 Certification
Question 3 ABCD is a rectangle.
AD = 12 m and the diagonal BD makes an angle of 28o with AB. Work out the length of the diagonal BD. Give your answer correct to 3 significant figures
sin 28 = 12 / BD (M1) BD = 12 /sin 28 (M1) = 25.56 (A1) (A1)
………25.6 m…. (4) (Total 4 marks)
Total /10
PiXL PLC 2017 Certification
Cosine Rule 1 Grade 7 Solutions
Objective: Know and apply the Cosine rule to find unknown lengths and angles
Question 1.
ABC is a triangle.
AB = 12m AC = 10m BC = 15m
Calculate the size of angle BAC. Give your answer correct to one decimal place.
152 = 102 + 122 – 2 x 10 x 12 x CosA (M1)
225 = 100 + 144 – 240CosA
225 = 244 – 240Cos A
240CosA = 19(M1)
Cos A = 19/240 (M1)
A = Cos-1 (19/240) = 85.5o (A1)
................................°
(4 marks)
PiXL PLC 2017 Certification
Question 2.
ABC is a triangle.
AB = 11.7m
BC = 28.3m
Angle ABC = 67o
Calculate the length of AC. Give your answer correct to three significant figures.
AC2 = 11.72 + 28.32 – 2 x 11.7 x 28.3 x Cos67 (M1)
AC2 = 679.0300321 (M1)
AC = 26.1m (A1)
................................
(3 marks)
Question 3.
ABC is a triangle.
AC = 7cm
BC = 10cm
Angle ACB = 73o
Calculate the length of AB. Give your answer correct to three significant figures.
AB2 = 72 + 102 – 2 x 7 x 10 x Cos73 (M1)
AB2 = 108.0679613 (M1)
AB = 10.4cm (A1)
................................
(3 marks)
Total /10
PiXL PLC 2017 Certification
Sine Rule 1 Grade 7 Solutions
Objective: Know and apply the Sine rule to find unknown lengths and angles
Question 1.
ABC is a triangle AB = 9cm Angle ABC = 21o
Angle ACB = 46o
(a) Calculate the length of AC. Give your answer correct to 3 significant figures. 9Sin46
= ACSin21 (M1)
AC = 9Sin46
x Sin21 (M1)
AC = 4.48cm (A1)
................................
(3 marks)
(b) Calculate the length of BC. Give your answer correct to 3 significant figures. 9Sin46 =
BCSin113 (M1)
BC = 9Sin46
x Sin113 (M1)
BC = 11.5cm (A1)
................................
(3 marks)
21o 46o
9cm
PiXL PLC 2017 Certification
Question 2.
ABC is a triangle AB = 8.1cm AC = 7.5cm Angle ACB = 30o Calculate the size of angle ABC. Give your answer correct to one decimal place. Sinx7.5
= Sin308.1 (M1)
Sinx = Sin308.1 x 7.5 (M1)
Sinx = 0.462962963
x = Sin-1 (0.462962963) (M1)
x = 27.6o (A1)
................................
(4 marks)
Total /10
PiXL PLC 2017 Certification
Standard trigonometric ratios 1 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 60 = ���ℎ�� = √32
(b) Cos 60= ���ℎ�� = 12
(c) Tan 60= ������ = √31
(d) Sin 30= ���ℎ�� = 12
(e) Cos 30= ���ℎ�� = √32
(f) Tan 30= ������ = 1√3
(Total 6 marks)
Question 2.
Using the triangle shown, or otherwise, find the exact values of:
(a) Sin 45= ���ℎ�� = 1√2
(b) Cos 45= ���ℎ�� = 1√2
(c) Tan 45= ������ = 1
(d) Sin 90= ���ℎ�� = 1
(Total 4 marks)
Total /10
1
2 √3
1
1
√2
PiXL PLC 2017 Certification
Pythagoras’ and Trigonometry 2D and 3D 1 Grade 7 Solutions
Objective: Solve problems using Pythagoras's theorem and trigonometry in general 2-D triangles and 3-D figures
Question 1.
ABC is an isosceles triangle
BC = 24cm
Vertical height = 20cm
Calculate the length of AC. Give your answer correct to one decimal place.
242 – 202 (= 176) (M1) 2 √176 = 26.5cm (A1)
..............................................
(Total 2 marks)
Question 2.
ABCDEFGH is a cuboid
AE = 5cm
AB = 6cm
BC = 9cm
(a) Calculate the length of AG. Give your answer correct to 3 significant figures.
AG = √(62 + 92 + 52 ) = �(36 + 81 + 25 ) = √142 = 11.9cm ..............................................
(1)
(b) Calculate the size of the angle between AG and the face ABCD. Give your answer correct to 1 decimal place.
Use of Sin (M1)
Sinθ = 5 ÷ √142 = 0.41959 (M1 ft from (a) )
Θ = 24.8o (A1) (3)
(Total 4 marks)
Diagram NOT drawn
accurately
20cm
24cm
A C
B
Diagram NOT drawn accurately
√142
G
A C
5
θ
PiXL PLC 2017 Certification
Question 3.
The diagram shows a square based pyramid
The square base has sides 18cm
(a) Calculate the length of the diagonal AB.
Give your answer correct to 1 decimal place.
AB = √(182 + 182) AB = 18√2 cm = 25.5 cm
.............................................. (1)
(b) If ∠VBA = 58o, calculate the vertical height VC.
Give your answer correct to 1 decimal place.
Use of tan58o (M1)
tan58o = VC ÷ 9√2 (M1 ft from their 18√2)
VC = 9√2 × tan58 VC = 20.4cm 1M (A1)
..............................................
(3)
(Total 4 marks)
Total /10
Diagram NOT drawn
accurately
18cm
