Two angles lie on a straight line. One angle is 149 degrees. What is the size of the other angle?
Diagram NOT accurately drawn
A) 21 degrees
B) 31 degrees
C) 41 degrees
D) 51 degrees
(Total for Question 1 is 1 mark)
2
An angle is bigger than a straight line but smaller than a full turn. What type of angle is this?
A) Acute
B) Obtuse
C) Reflex
D) Right angle
(Total for Question 2 is 1 mark)
3
A rectangle has length 13 cm and width 7 cm. What is its perimeter?
A) 20 cm
B) 33 cm
C) 40 cm
D) 91 cm
(Total for Question 3 is 1 mark)
4
A rectangle has length 9 cm and width 7 cm. What is its area?
A) 16 cm2
B) 32 cm2
C) 63 cm2
D) 126 cm2
(Total for Question 4 is 1 mark)
5
Five angles meet at a single point. Four of them are 55 degrees, 80 degrees, 62 degrees and 95 degrees. What is the fifth angle?
Diagram NOT accurately drawn
(Total for Question 5 is 2 marks)
6
In triangle DEF, angle D = 54 degrees and angle E = 79 degrees. Calculate the size of angle F.
Diagram NOT accurately drawn
(Total for Question 6 is 2 marks)
7
A quadrilateral has angles of 78 degrees, 114 degrees and 99 degrees. Calculate the size of the fourth angle.
Diagram NOT accurately drawn
(Total for Question 7 is 2 marks)
8
Marcus draws a regular polygon with 9 equal sides and 9 equal angles.
(a)State the mathematical name of Marcus's polygon.(1)
(b)State the order of rotational symmetry of a regular nonagon.(1)
(Total for Question 8 is 2 marks)
9
Leah draws a quadrilateral that has two pairs of adjacent equal sides and exactly one pair of equal opposite angles, and it is not a rhombus.
(a)Name Leah's quadrilateral.(1)
(b)State the number of lines of symmetry of Leah's quadrilateral.(1)
(Total for Question 9 is 2 marks)
10
Ibrahim draws a parallelogram that is not a rectangle and not a rhombus.
(a)State the number of lines of symmetry of Ibrahim's parallelogram.(1)
(b)State the order of rotational symmetry of Ibrahim's parallelogram.(1)
(Total for Question 10 is 2 marks)
11
A triangular prism has two identical triangular end faces and three rectangular side faces.
(a)State the number of faces of the triangular prism.(1)
(b)State the number of edges of the triangular prism.(1)
(c)State the number of vertices of the triangular prism.(1)
(Total for Question 11 is 3 marks)
12
A 3D shape has 4 faces, 6 edges and 4 vertices, and every one of its faces is an identical triangle. What is this shape?
A) Square-based pyramid
B) Triangular prism
C) Tetrahedron
D) Cube
(Total for Question 12 is 1 mark)
13
The diagram shows a net made from two identical triangles and three rectangles, arranged so the triangles are at opposite ends of a row of rectangles. Which 3D shape does this net fold up to make?
Diagram NOT accurately drawn
A) Cuboid
B) Triangular prism
C) Square-based pyramid
D) Tetrahedron
(Total for Question 13 is 1 mark)
14
The diagram shows a net made from six rectangles: a central column of four rectangles, with one extra rectangle attached to the left of the second rectangle in the column and one extra rectangle attached to the right of the second rectangle in the column.
Diagram NOT accurately drawn
(Total for Question 14 is 1 mark)
15
A triangle has a base of 14 cm and a perpendicular height of 5.5 cm. Calculate the area of the triangle.
(Total for Question 15 is 2 marks)
16
A cuboid has length 6 cm, width 5 cm and height 4 cm. Calculate the volume of the cuboid.
(Total for Question 16 is 2 marks)
17
A point Q has coordinates (-4, 5). In which quadrant of the coordinate grid does Q lie?
A) First
B) Second
C) Third
D) Fourth
(Total for Question 17 is 1 mark)
18
Triangle G has vertices at (2, 3), (2, 6) and (5, 3). Triangle G is reflected in the x-axis to give triangle H.
(a)Write down the coordinates of the image of (2, 3) after this reflection.(1)
(b)Write down the coordinates of the image of (2, 6) after this reflection.(1)
(c)Write down the coordinates of the image of (5, 3) after this reflection.(1)
(Total for Question 18 is 3 marks)
19
Convert each of these lengths.
(a)Convert 4.2 kilometres into metres.(1)
(b)Convert 560 centimetres into metres.(1)
(Total for Question 19 is 2 marks)
20
Convert each of these measurements.
(a)Convert 0.75 kilograms into grams.(1)
(b)Convert 3400 millilitres into litres.(1)
(Total for Question 20 is 2 marks)
21
Deepa reads the scale on a measuring jug. The scale is numbered every 100 ml, with 4 equally spaced unlabelled small divisions between each pair of numbered marks. The water level is at the 3rd small division after the 400 ml mark.
(a)State the value of each small division, in millilitres.(1)
(b)Calculate the volume of water in the jug, in millilitres.(1)
(Total for Question 21 is 2 marks)
22
A protractor shows the angle pointer resting exactly one quarter of the way from the 100 degree mark to the 120 degree mark on its scale. What angle is being measured?
(Total for Question 22 is 1 mark)
23
A school sports hall floor is L-shaped, formed by removing a rectangular storage room measuring 7 m by 4 m from a rectangle measuring 16 m by 10 m, as shown in the diagram. Calculate the perimeter of the sports hall floor.
Diagram NOT accurately drawn
(Total for Question 23 is 3 marks)
24
A school stage is L-shaped. The overall shape fits inside a rectangle 11 m by 7 m; a rectangular corner measuring 4 m by 3 m has been removed, as shown in the diagram. Calculate the area of the stage.
Diagram NOT accurately drawn
(Total for Question 24 is 3 marks)
25
A stained-glass window is made from a rectangle with a semicircle on top, as shown in the diagram. The rectangle is 20 cm tall and 14 cm wide, and the semicircle has a diameter of 14 cm. Take π = 22/7.
Diagram NOT accurately drawn
(a)Calculate the perimeter of the window (the two vertical sides, the bottom edge and the curved top; do not include the straight join between the rectangle and the semicircle).(3)
(b)Calculate the total area of the window.(3)
(Total for Question 25 is 6 marks)
26
Priya is filling a cuboid aquarium that measures 60 cm long, 30 cm wide and 25 cm high.
(a)Calculate the volume of the aquarium in cm3.(2)
(b)Given that 1000 cm3 = 1 litre, calculate the capacity of the aquarium in litres.(1)
(c)Priya fills the empty aquarium using a hose at a constant rate of 3 litres per minute. Calculate how many minutes it takes to fill the aquarium completely.(2)
(Total for Question 26 is 5 marks)
Mark scheme · EP.M37 Geometry and Measures Depth Set 2
Question 1
B1 B cao
Answer: B) 31 degrees
Question 2
B1 C cao
Answer: C) Reflex
Question 3
B1 C cao
Answer: C) 40 cm
Question 4
B1 C cao
Answer: C) 63 cm2
Question 5
M1 55 + 80 + 62 + 95 = 292 seen (angles around a point sum to 360 degrees)
A1 68 degrees cao
Answer: 68 degrees
Question 6
M1 180 - 54 - 79 seen
A1 47 degrees cao
Answer: angle F = 47 degrees
Question 7
M1 360 - 78 - 114 - 99 seen (angles in a quadrilateral sum to 360 degrees)
A1 69 degrees cao
Answer: 69 degrees
Question 8
(a) B1 nonagon cao
(a) Answer: nonagon
(b) B1 9 cao
(b) Answer: 9
Question 9
(a) B1 kite cao
(a) Answer: kite
(b) B1 1 cao
(b) Answer: 1
Question 10
(a) B1 0 cao
(a) Answer: 0
(b) B1 2 cao
(b) Answer: 2
Question 11
(a) B1 5 cao
(a) Answer: 5
(b) B1 9 cao
(b) Answer: 9
(c) B1 6 cao
(c) Answer: 6
Question 12
B1 C cao
Answer: C) Tetrahedron
Question 13
B1 B cao
Answer: B) Triangular prism
Question 14
B1 cuboid cao
Answer: cuboid
Question 15
M1 0.5 x 14 x 5.5 seen
A1 38.5 cm2 cao
Answer: 38.5 cm2
Question 16
M1 6 x 5 x 4 seen (or correct substitution into V = l x w x h)