A ruler is marked in centimetres from 0cm to 15cm. An arrow points exactly halfway between the 8cm mark and the 9cm mark.
(1)
2
Complete these unit conversions.
(a)3.6m = ____ cm(1)
(b)2540mm = ____ cm(1)
3
A rectangular allotment measures 12m by 7m. Calculate the perimeter of the allotment.
(2)
4
A rectangular vegetable patch measures 6m by 4.5m. Turf to cover the patch costs £3.50 per m2.
(a)Calculate the area of the vegetable patch.(1)
(b)Calculate the total cost of the turf needed to cover the whole patch.(2)
5
The diagram shows an L-shaped patio. It is formed from an 8m by 6m rectangle with a 3m by 2m rectangular corner removed from the top-right corner. The two missing side lengths are not labelled on the diagram.
(a)Calculate the area of the patio.(3)
(b)Calculate the perimeter of the patio.(3)
6
Two angles lie on a straight line. One of the angles is 118 degrees. Calculate the size of the other angle.
(2)
7
Three angles meet at a point. Two of the angles are 95 degrees and 140 degrees. Calculate the size of the third angle.
(2)
8
Triangle ABC is isosceles. The angle at the apex, A, is 42 degrees. Calculate the size of each of the two equal base angles.
(3)
9
Look at these three statements about quadrilaterals. For each one, write True or False.
(i)A square is always a rectangle.(1)
(ii)A rhombus is always a square.(1)
(iii)A (non-square) rectangle always has four lines of symmetry.(1)
10
Point A is at (2, 3). Point A is translated 4 units right and 5 units down to point B. Write the coordinates of point B.
(2)
11
Triangle PQR has vertex P at (1, 2). The triangle is reflected in the line x = 3. Find the coordinates of the image of P after the reflection.
(2)
12
How many lines of symmetry does a regular hexagon have?
(1)
13
A net is made from 6 identical squares arranged in a cross (plus-sign) shape. Name the 3D shape that this net folds up to make.
(1)
14
A cuboid box has length 16cm, width 8cm and height 6cm.
(a)Calculate the volume of the box.(2)
(b)The box is filled exactly with cubes of side 2cm, with no gaps. Calculate how many cubes are needed to fill the box completely.(2)
15
A map has a scale of 1 : 25000. The distance between two villages on the map is 6.4cm. Calculate the real distance between the villages, in km.
(3)
16
A train leaves Manchester at 09:47 and arrives in Leeds at 10:23.
(a)Calculate how long the journey from Manchester to Leeds takes, in minutes.(2)
(b)The train then waits at Leeds for 18 minutes before continuing to York, arriving at 11:52. Calculate the length of the journey from Leeds to York, in minutes.(3)
17
A rectangular picture frame has an area of 96 cm2 and a perimeter of 40cm. By trying whole-number pairs of factors of 96, find the length and the width of the frame.
(4)
18
In the diagram, two straight lines cross at a single point, forming four angles. One angle is labelled (2x + 10) degrees and the angle vertically opposite it is labelled (3x - 20) degrees.
(a)Explain why the two labelled angles must be equal in size.(1)
(b)Use this fact to form and solve an equation to find the value of x.(3)
19
An open-top fish tank in the shape of a cuboid is 40cm long, 25cm wide and 30cm high. Water is poured into the tank until it is 18cm deep.
(a)Calculate the volume of water in the tank, in cm3.(2)
(b)1000 cm3 = 1 litre. Calculate the volume of water in litres.(1)
(c)A further 6 litres of water is poured into the tank. Calculate the new depth of the water, in cm.(3)
20
A designer is making a scale model of a rectangular school hall. The real hall measures 24m by 15m. The model is made using a scale of 1 : 60.
(a)Calculate the length and width of the model, in cm.(2)
(b)Calculate the perimeter of the model, in cm.(2)
(c)A ribbon is glued around the edge of the model hall's base, with 5cm extra needed for overlap at the joins. Calculate the total length of ribbon required, in cm.(1)
Mark scheme · KS2.M-R4 Reasoning: Measurement and Geometry
Question 1
B1 8.5cm oe cao
Answer: 8.5cm
Question 2
(a) B1 360cm cao
(a) Answer: 360cm
(b) B1 254cm cao
(b) Answer: 254cm
Question 3
M1 (12+7) x 2 oe, or 12+12+7+7
A1 38m cao
Answer: 38m
Question 4
(a) B1 27 m2 cao
(a) Answer: 27 m2
(b) M1 27 x 3.50 ft from (a)
(b) A1 £94.50 cao
(b) Answer: £94.50
Question 5
(a) M1 8 x 6 = 48 m2 (area of full rectangle)
(a) M1 3 x 2 = 6 m2 (area removed)
(a) A1 42 m2 cao
(a) Answer: 42 m2
(b) M1 finds missing side lengths: 8-3=5m and 6-2=4m
(b) M1 sums all six sides: 8+6+5+2+3+4 oe
(b) A1 28m cao
(b) Answer: 28m
Question 6
M1 180 - 118 oe
A1 62 degrees cao
Answer: 62 degrees
Question 7
M1 360 - 95 - 140 oe
A1 125 degrees cao
Answer: 125 degrees
Question 8
M1 180 - 42 = 138 oe
M1 138 / 2 ft
A1 69 degrees cao
Answer: 69 degrees
Question 9
(i) B1 True, with valid reason (a square has 4 right angles and opposite sides equal)
(i) Answer: True
(ii) B1 False, with valid reason (a rhombus need not have right angles)
(ii) Answer: False
(iii) B1 False, with valid reason (a non-square rectangle has exactly 2 lines of symmetry)
(iii) Answer: False
Question 10
M1 2+4 and 3-5 oe
A1 (6, -2) cao
Answer: (6, -2)
Question 11
M1 finds distance from P to the line x=3 is 2 units (3-1=2)
A1 (5, 2) cao
Answer: (5, 2)
Question 12
B1 6 cao
Answer: 6
Question 13
B1 cube oe cao
Answer: Cube
Question 14
(a) M1 16 x 8 x 6 oe
(a) A1 768 cm3 cao
(a) Answer: 768 cm3
(b) M1 (16/2) x (8/2) x (6/2) oe, or 768 / 8
(b) A1 96 cao
(b) Answer: 96 cubes
Question 15
M1 6.4 x 25000 = 160000 oe
M1 converts 160000cm to km (divides by 100000)
A1 1.6km cao
Answer: 1.6km
Question 16
(a) M1 valid method, e.g. 9:47 to 10:00 = 13 min, 10:00 to 10:23 = 23 min
(a) A1 36 minutes cao
(a) Answer: 36 minutes
(b) M1 10:23 + 18 minutes = 10:41 (departure time from Leeds)
(b) M1 valid method to find duration from 10:41 to 11:52
(b) A1 71 minutes cao
(b) Answer: 71 minutes
Question 17
M1 40 / 2 = 20 (length + width) oe
M1 lists factor pairs of 96 systematically, e.g. 1x96, 2x48, 3x32, 4x24, 6x16, 8x12
M1 identifies the pair that sums to 20 (8 and 12)
A1 length = 12cm, width = 8cm cao (both required)
Answer: Length = 12cm, width = 8cm
Question 18
(a) B1 states that vertically opposite angles (formed when two straight lines cross) are equal