Write down the name of the shape described in each part.
(a)A quadrilateral with all four sides equal in length and all four angles equal to 90 degrees.(1)
(b)A quadrilateral with two pairs of parallel sides, opposite sides equal in length, but no right angles.(1)
(c)A triangle with all three sides of different lengths and all three angles of different sizes.(1)
(d)A polygon with five straight sides and five vertices.(1)
2
For each angle below, write down whether it is acute, right angle, obtuse or reflex.
(a)40 degrees(1)
(b)90 degrees(1)
(c)155 degrees(1)
(d)275 degrees(1)
3
Priya measures the length of her pencil case using a ruler marked in centimetres and millimetres. The case starts at the 2 cm mark and ends at the 19.4 cm mark.
(a)What is the length of the pencil case, in centimetres?(1)
(b)Convert your answer to part a into millimetres.(1)
4
Convert between units of length.
(a)Convert 3.5 m to cm.(1)
(b)Convert 2400 mm to m.(1)
(c)Convert 0.75 km to m.(1)
5
Name the 3D shape that each net below would fold into.
(a)A net made from six identical squares.(1)
(b)A net made from one rectangle and two identical triangles, one attached to each short end of the rectangle.(1)
6
A rectangle ABCD has vertices A(2, 3), B(2, 7) and C(9, 7).
(2)
7
Use angle facts to find the missing angles below.
(a)Two angles lie on a straight line. One of the angles is 118 degrees. Work out the size of the other angle, marked x degrees.(2)
(b)Three angles meet at a point. Two of the angles are 95 degrees and 140 degrees. Work out the size of the third angle, marked y degrees.(2)
8
Use angle facts about triangles to find the missing angles below.
(a)A triangle has angles of 52 degrees and 67 degrees. Work out the size of the third angle, marked z degrees.(2)
(b)An isosceles triangle has an apex angle of 40 degrees. The two base angles are equal, each marked p degrees. Work out the size of each base angle.(2)
9
Answer the questions about the 3D shapes below.
(a)A 3D shape has 6 faces, 12 edges and 8 vertices. Every face is a square. Write down the name of this shape.(1)
(b)A 3D shape has 5 faces, 8 edges and 5 vertices. It has a square base and four triangular faces that meet at a single point. Write down the name of this shape.(1)
(c)A triangular prism has a triangular cross-section. Write down the number of faces it has.(1)
(d)Write down the number of edges a triangular prism has.(1)
(e)Write down the number of vertices a triangular prism has.(1)
10
Answer the questions about translations on a coordinate grid.
(a)Point P has coordinates (3, 4). P is translated 5 squares right and 2 squares down. Write down the coordinates of the image of P.(2)
(b)Point Q is translated from (7, 1) to (2, 6). Describe this translation, giving the number of squares moved left or right and up or down.(2)
11
Answer the questions about reflections on a coordinate grid.
(a)Point R has coordinates (4, 2). R is reflected in the y-axis. Write down the coordinates of the image of R.(2)
(b)Point S has coordinates (-3, 5). S is reflected in the x-axis. Write down the coordinates of the image of S.(2)
12
A rectangular field is 45 m long and 18 m wide.
(a)Work out the area of the field.(2)
(b)Work out the perimeter of the field.(2)
13
A pond is drawn on a centimetre-squared grid. It covers 23 whole squares and 14 part-squares. Each part-square counts as approximately half a whole square.
(2)
14
A cuboid is built using 1 cm cubes. It is 4 cubes long, 3 cubes wide and 2 cubes high.
(a)How many 1 cm cubes are needed to build the cuboid?(2)
(b)Write down the volume of the cuboid, giving the correct unit.(1)
15
A cardboard box measures 12 cm by 7 cm by 5 cm.
(2)
16
Answer the questions about mass and capacity.
(a)Convert 2.3 kg to g.(1)
(b)Convert 650 ml to litres.(1)
(c)A recipe needs 1.2 kg of flour in total. Kwame has already used 800 g of flour. How many more grams of flour does he need?(2)
17
Answer the questions about reading scales.
(a)A kitchen scale dial is numbered every 100 g from 0 g to 1000 g, with 5 equally spaced small divisions between each numbered mark. The pointer stops 3 small divisions past the 400 g mark. What reading does the scale show?(2)
(b)A measuring jug is marked in 50 ml intervals from 0 ml to 500 ml. The water level is exactly halfway between the 250 ml and 300 ml marks. What is the reading?(1)
18
Two straight lines cross at a point, forming four angles. One of the four angles is 65 degrees.
(a)Write down the size of the angle vertically opposite the 65 degree angle, giving a reason.(1)
(b)Work out the size of each of the other two angles.(2)
19
The diagram shows the outline of a school playground shaped like the letter L, drawn on a grid where each square represents 1 metre. Its vertices, taken in order, are at (0, 0), (8, 0), (8, 3), (5, 3), (5, 6) and (0, 6).
(a)Calculate the perimeter of the playground.(3)
(b)Calculate the area of the playground.(3)
20
A rectangular room is 6.5 m long and 4 m wide. Aaliyah wants to cover the whole floor with square tiles that have sides of 50 cm, with no gaps and no overlaps.
(3)
21
Ffion needs to fence a garden shaped like the letter L. Taking the vertices in order, and measuring in metres, they are at (0, 0), (9, 0), (9, 4), (6, 4), (6, 7) and (0, 7). Fencing costs £8.50 per metre.
(4)
Mark scheme · KS2.M-GEOM2 Geometry and Measures Depth
Question 1
(a) B1 square cao
(a) Answer: Square
(b) B1 parallelogram cao
(b) Answer: Parallelogram
(c) B1 scalene triangle cao
(c) Answer: Scalene triangle
(d) B1 pentagon cao
(d) Answer: Pentagon
Question 2
(a) B1 acute cao
(a) Answer: Acute
(b) B1 right angle cao
(b) Answer: Right angle
(c) B1 obtuse cao
(c) Answer: Obtuse
(d) B1 reflex cao
(d) Answer: Reflex
Question 3
(a) B1 17.4 cm cao
(a) Answer: 17.4 cm
(b) B1 174 mm cao (ft from part a)
(b) Answer: 174 mm
Question 4
(a) B1 350 cm cao
(a) Answer: 350 cm
(b) B1 2.4 m cao
(b) Answer: 2.4 m
(c) B1 750 m cao
(c) Answer: 750 m
Question 5
(a) B1 cube cao
(a) Answer: Cube
(b) B1 triangular prism cao
(b) Answer: Triangular prism
Question 6
M1 recognises D must share the x-coordinate of C and the y-coordinate of A, or equivalent method
A1 (9, 3) cao
Answer: D = (9, 3)
Question 7
(a) M1 180 - 118 seen or implied
(a) A1 x = 62 degrees cao
(a) Answer: x = 62 degrees
(b) M1 360 - 95 - 140 seen or implied
(b) A1 y = 125 degrees cao
(b) Answer: y = 125 degrees
Question 8
(a) M1 180 - 52 - 67 seen or implied
(a) A1 z = 61 degrees cao
(a) Answer: z = 61 degrees
(b) M1 180 - 40 (= 140) seen or implied
(b) A1 p = 70 degrees each cao
(b) Answer: p = 70 degrees each
Question 9
(a) B1 cube cao
(a) Answer: Cube
(b) B1 square-based pyramid cao
(b) Answer: Square-based pyramid
(c) B1 5 cao
(c) Answer: 5
(d) B1 9 cao
(d) Answer: 9
(e) B1 6 cao
(e) Answer: 6
Question 10
(a) M1 3 + 5 and 4 - 2 seen or implied
(a) A1 (8, 2) cao
(a) Answer: (8, 2)
(b) M1 7 - 2 = 5 and 6 - 1 = 5 seen or implied
(b) A1 5 left and 5 up oe cao
(b) Answer: 5 left and 5 up
Question 11
(a) M1 correct process shown, the x-coordinate changes sign and the y-coordinate stays the same
(a) A1 (-4, 2) cao
(a) Answer: (-4, 2)
(b) M1 correct process shown, the y-coordinate changes sign and the x-coordinate stays the same
(b) A1 (-3, -5) cao
(b) Answer: (-3, -5)
Question 12
(a) M1 45 x 18 set up
(a) A1 810 m2 cao
(a) Answer: 810 m2
(b) M1 2 x (45 + 18) set up
(b) A1 126 m cao
(b) Answer: 126 m
Question 13
M1 14 / 2 (= 7) seen or implied
A1 30 cm2 cao
Answer: 30 cm2
Question 14
(a) M1 4 x 3 x 2 set up
(a) A1 24 cao
(a) Answer: 24
(b) B1 24 cm3 cao (ft from part a)
(b) Answer: 24 cm3
Question 15
M1 12 x 7 x 5 set up
A1 420 cm3 cao
Answer: 420 cm3
Question 16
(a) B1 2300 g cao
(a) Answer: 2300 g
(b) B1 0.65 l cao
(b) Answer: 0.65 l
(c) M1 1.2 kg converted to 1200 g
(c) A1 400 g cao
(c) Answer: 400 g
Question 17
(a) M1 each small division found as 100 / 5 = 20 g
(a) A1 460 g cao
(a) Answer: 460 g
(b) B1 275 ml cao
(b) Answer: 275 ml
Question 18
(a) B1 65 degrees, with reason that vertically opposite angles are equal
(a) Answer: 65 degrees
(b) M1 180 - 65 seen or implied
(b) A1 115 degrees each cao
(b) Answer: 115 degrees each
Question 19
(a) M1 all six side lengths correctly identified using the coordinates: 8, 3, 3, 3, 5 and 6
(a) M1 8 + 3 + 3 + 3 + 5 + 6 set up, dependent on the previous method mark
(a) A1 28 m cao
(a) Answer: 28 m
(b) M1 area of the full bounding rectangle found, 8 x 6 = 48
(b) M1 area of the missing corner square found, 3 x 3 = 9, dependent on the previous method mark
(b) A1 39 m2 cao
(b) Answer: 39 m2
Question 20
M1 tiles along the length found, 6.5 / 0.5 = 13
M1 tiles along the width found, 4 / 0.5 = 8, dependent on the previous method mark
A1 104 cao
Answer: 104 tiles
Question 21
M1 all six side lengths correctly identified using the coordinates: 9, 4, 3, 3, 6 and 7
A1 perimeter = 32 m cao
dM1 32 x 8.50 set up, dependent on the perimeter mark