GCSE Exams Preparation · Web view2020/05/07 · By calculation, deduce whether triangle ABC is a...
33
Pythagoras (H) - Questions Q1. ABCDEFGH is a cuboid. AB = 7.3 cm CH = 8.1 cm Angle BCA = 48° Find the size of the angle between AH and the plane ABCD. Give your answer correct to 1 decimal place.
Transcript of GCSE Exams Preparation · Web view2020/05/07 · By calculation, deduce whether triangle ABC is a...
Pythagoras (H) - Questions
Q1.
ABCDEFGH is a cuboid.
AB = 7.3 cmCH = 8.1 cm Angle BCA = 48°
Find the size of the angle between AH and the plane ABCD. Give your answer correct to 1 decimal place.
........................................................... °
(Total for question = 4 marks)
Q2.
* The diagram shows a triangle DEF inside a rectangle ABCD.
Show that the area of triangle DEF is 8 cm2. You must show all your working.
(Total for question = 4 marks)
Q3.
ABCDE is a pentagon.
Work out the area of ABCDE.
........................................................... cm2
(Total for question = 5 marks)
Q4.
The diagram shows the positions of three turbines A, B and C.
Diagram NOT accurately drawn
A is 6 km due north of turbine B. C is 4.5 km due west of turbine B.
(a) Calculate the distance AC.
...........................................................km(3)
(b) Calculate the bearing of C from A. Give your answer correct to the nearest degree.
...........................................................°(4)
(Total for Question is 7 marks)
Q5.
The diagram shows a quadrilateral JKLM.
Work out the size of angle KLM. Give your answer correct to 3 significant figures.
........................................................... °
(Total for question = 4 marks)
Q6.
ABC is a right-angled triangle.
Here is Sarah's method to find the length of BC.
(a) What mistake has Sarah made in her method?
.............................................................................................................................................
.............................................................................................................................................
.............................................................................................................................................
(1)
Roy is going to enlarge triangle PQR with centre C and scale factor
He draws triangle XYZ.
(b) Explain why Roy's diagram is not correct.
.............................................................................................................................................
.............................................................................................................................................
.............................................................................................................................................
(1)
(Total for question = 2 marks)
Q7.
The diagram shows triangle ABC.
ADC and DEB are straight lines.
AD = 4.4 cm BC = 8.6 cm E is the midpoint of DB.
Angle CDB = 90° Angle DCB = 40°
Work out the size of angle EAD. Give your answer correct to 1 decimal place. You must show all your working.
........................................................... °
(Total for question = 4 marks)
Q8.
The diagram shows a triangular prism.
The base, ABCD, of the prism is a square of side length 15 cm. Angle ABE and angle CBE are right angles. Angle EAB = 35°
M is the point on DA such that
DM : MA = 2 : 3
Calculate the size of the angle between EM and the base of the prism. Give your answer correct to 1 decimal place.
........................................................... °
(Total for question = 4 marks)
Q9.
The diagram shows a cuboid ABCDEFGH.
AB = 7 cm, AF = 5 cm and FC = 15 cm.
Calculate the volume of the cuboid. Give your answer correct to 3 significant figures.
........................................................... cm3
(Total for question is 4 marks)
Q10.
The diagram shows a square ABCD inside a circle.
The points A, B, C and D lie on the circle.
The radius of the circle is 6 cm.
Work out the total area of the shaded regions. Give your answer correct to 3 significant figures.
........................................................... cm2
(Total for question = 4 marks)
Q11.
Triangle ABC has perimeter 20 cm.
AB = 7 cm.
BC = 4 cm.
By calculation, deduce whether triangle ABC is a right–angled triangle.
(Total for question = 4 marks)
Q12.
This rectangular frame is made from 5 straight pieces of metal.
The weight of the metal is 1.5 kg per metre.
Work out the total weight of the metal in the frame.
........................................................... kg
(Total for question = 5 marks)
Q13.
The diagram represents a metal frame.
The frame is made from four metal bars, AB, AC, BC and BD.
Angle ABC = angle ADB = 90° AB = 5 m BC = 3 m
Work out the total length of the four metal bars of the frame. Give your answer correct to 3 significant figures.
........................................................... m
(Total for question = 5 marks)
Q14.
ADB and AEC are straight lines. DE is parallel to BC.
Angle ABC = 90° AC = 10 cm. BC = 6 cm.
D is the midpoint of AB.
Work out the area of trapezium BCED.
........................................................... cm2
(Total for question = 4 marks)
Q15.
The diagram shows a rectangular framework.
The framework is made from 5 metal rods. The metal rods have a weight of 0.9 kg per metre.
Work out the total weight of the framework. Give your answer, in kg, correct to 3 significant figures.
........................................................... kg
(Total for question = 4 marks)
Q16.
ABC and ABD are two right-angled triangles.
Angle BAC = angle ADB = 90°
AB = 13 cm DB = 5 cm
Work out the length of CB.
........................................................... cm
(Total for question is 3 marks)
Q17.
ABC is a right-angled triangle.AC = 6 cmAB = 13 cm
(a) Work out the length of BC. Give your answer correct to 3 significant figures.
..............................................................................................................................................(3)
PQR is a right-angled triangle.PR = 17 cmPQ = 25 cm
(b) Work out the size of angle RPQ. Give your answer correct to 1 decimal place.
..............................................................................................................................................(3)
(Total for Question is 6 marks)
Q18.
The diagram shows a quadrilateral ABCD.
Diagram NOT accurately drawn
AB = 16 cm.AD = 12 cm.Angle BCD = 40°.
Angle ADB = angle CBD = 90°.
Calculate the length of CD.Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . . cm
(Total for Question is 5 marks)
Q19.
ABCD is a square with a side length of 4xM is the midpoint of DC.N is the point on AD where ND = x
BMN is a right-angled triangle.
Find an expression, in terms of x, for the area of triangle BMN. Give your expression in its simplest form.
..............................................................................................................................................(Total for Question is 4 marks)
Q20.
ABCD is a trapezium.
AD = 10 cmAB = 9 cmDC = 3 cm Angle ABC = angle BCD = 90°
Calculate the length of AC. Give your answer correct to 3 significant figures.
..............................................................................................................................................(Total for Question is 5 marks)
Q21.
Here is a right–angled triangle.
Four of these triangles are joined to enclose the square ABCD as shown below.
Show that the area of the square ABCD is x2 + y2
(Total for question = 3 marks)
Q22.
Calculate the length of AB. Give your answer correct to 1 decimal place.
..............................................................................................................................................(Total for Question is 3 marks)
Q23.
The diagram shows the marking on a school playing field.
Diagram NOT accurately drawn
The diagram shows a rectangle and its diagonals.
Work out the total length of the four sides of the rectangle and its diagonals.
. . . . . . . . . . . . . . . . . . . . . . m
(Total for Question is 5 marks)
Q24.
DEF is a right-angled triangle.
Work out the length of DF. Give your answer correct to 2 decimal places.
...........................................................cm
(Total for question = 3 marks)
Q25.Here is a right-angled triangle.
Work out the length of AC.
Give your answer correct to 1 decimal place.
........................................................... cm
(Total for Question is 3 marks)
Q26.
* Here is part of a field.
This part of the field is in the shape of a trapezium. A farmer wants to put a fence all the way around the edge of this part of the field.
The farmer has 50m of fence.
Does he have enough fence? You must show all your working.
(Total for question = 5 marks)
Q27.
The diagram shows the positions of a tower and a tree.
The tree is 2.1 km South of the tower and 4.5 km East of the tower.
(a) Work out the distance between the tower and the tree. Give your answer correct to one decimal place.
...........................................................km(3)
(b) Work out the bearing of the tree from the tower. Give your answer correct to the nearest degree.
...........................................................°(4)
(Total for Question is 7 marks)
Q28.
In the diagram,
triangles ABD and BCD are right-angled triangles AB = 5 cm AD = 10 cm CD = 4 cm Angle ADB = 30°
Work out the value of x. Give your answer correct to 2 decimal places.
...........................................................cm
(Total for question = 4 marks)
Q29.
(a) Calculate the length of AB.
Give your answer correct to one decimal place.
........................................................... cm
(3)
(b) Calculate the length of DE.
Give your answer correct to three significant figures.
........................................................... m
(3)
(Total for question = 6 marks)
Q30.
ABCD is a trapezium.
Work out the size of angle CDA. Give your answer correct to 1 decimal place.
........................................................... °
(Total for question = 5 marks)
Q31.
In the diagram,
ABC, ACD and APD are right-angled triangles. AB = 4 cm. BC = 3 cm. CD = 2 cm.
Work out the length of DP.
..............................................................................................................................................(Total for Question is 5 marks)
Q32.
The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5
Work out the area of the triangle.
........................................................... cm2
(Total for question = 4 marks)
Q33.
ABC is a right-angled triangle. A, B and C are points on the circumference of a circle centre O. AB = 5 cm BC = 8 cm
AOC is a diameter of the circle.
Calculate the circumference of the circle. Give your answer correct to 3 significant figures.
........................................................... cm
(Total for question = 4 marks)
