PLC Papers. Created For:

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1 PLC Papers Created For:

2 Convert standard units 2 Grade 3 Objective: Convert standard units (eg time, length, volume, mass) in numerical contexts. Question 1 (a) Convert 3.5 hours into minutes?...mins (1) (b) Convert 380 minutes into hours and minutes. hours mins (1) (c) Convert 1.5 litres to millilitres.ml (1) (d) Convert 2.25 kg to grams..g (1) (Total 4 marks)

3 Question 2 You should know that 1 gallon = 4.5 litres (a) Convert 10 gallons to litres.litres (2) (b) Convert 18 litres to gallons gallons (2) (Total 4 marks) Question 3 (a) Convert 345 cm to metres....m (1) (b) Convert 3470 metres into km.km(1) Total /10

4 Express one quantity as a fraction of another 2 Grade 3 Objective: Express one quantity as a fraction of another where the fraction is less than one or greater than 1. Question 1 What fraction of a circle is: (a) 60 degrees?..(1) (b) 72 degrees?..(1) (c) 18 degrees?..(1) (d) 450 degrees?..(1) (Total 4 marks) Question 2 What fraction of 250, is 100?..

5 Question 3. What fraction of 400 is: (a) 68.(1) (b) 600..(1) Question 4. What fraction of 30 is: (a) 6 miles.(1) (b) 3miles (1) Total /10

6 Use ratio notation 2 Grade 3 Objective: Use ratio notation, including reduction to simplest form. Question 1. Simplify the following ratios: (a) 3:12 (1) (b) 28:7 (1) (c) 12:60 (1) (d) 1 5 : 3 10 (1) (Total 4 marks) Question 2 Share the following into the given ratios. (a) 50 kg into 2:5:3... (2) (b) 45 minutes into 9:6... (2) (Total 4 marks)

7 Question 3 Reduce each of the following ratios to the form n:1 (a) 20:5.(1) (b) 40:8.(1) Total /10

8 Use scale factors, diagrams and maps 2 Grade 3 Objective: Use scale factors, diagrams and maps (including geometrical problems) Question 1 A 2 cm B C 6 cm D Line CD is bigger than line AB. What is the scale factor of the enlargement?.. (Total 1 mark) Question 2 Using scale of 1:25 5 cm on a map is actually how many metres in real life?. Question 3 Using scale of 1:30 7 metres will be drawn as how many cms on a map?

9 Question 4 25m 15m A rectangular field is really 25 metres by 15 metres. On a scale drawing 1: 50 (a) What length will I draw for the field on the map?..(1) (b) What width will I draw for the field on the map? (1) (c) What angle will each corner be? (1) (Total 3 marks)

10 Question 5 These triangles are mathematically similar. (not drawn accurately) The height of the smaller triangle is 3 cms. The height of the bigger triangle is 9 cms What is the scale factor of this enlargement? The angle at the top of the smaller triangle is 25 degrees. What is the angle at the top of the bigger triangle? (1).(1) Total /10

11 PLC Papers Created For:

12 Convert standard units 2 Grade 3 SOLUTIONS Objective: Convert standard units (eg time, length, volume, mass) in numerical contexts. Question 1 (a) Convert 3.5 hours into minutes? 3 hours is 180 mins + 30 mins = 210 mins (A1)...mins (1) (b) Convert 380 minutes into hours and minutes. 6 hours 20 mins (A1) hours mins (1) (c) Convert 1.5 litres to millilitres 1.5 x 1000 = 1500 ml (A1).ml (1) (d) Convert 2.25 kg to grams 2.25 x 2250 g (A1)..g (1) (Total 4 marks) Question 2 You should know that 1 gallon = 4.5 litres (a) Convert 10 gallons to litres 4.5 x 10 (M1) 45 litres (A1).litres (2) (b) Convert 18 litres to gallons 18 / 4.5 (M1) 4 gallons (A1) gallons (2) (Total 4 marks)

13 Question 3 (a) Convert 345 cm to metres 3.45 m (A1)....m (1) (b) Convert 3470 metres into km km (A1).km(1) Total /10

14 (d) 450 degrees? (A1)..(1) Express one quantity as a fraction of another 2 Grade 3 SOLUTIONS Objective: Express one quantity as a fraction of another where the fraction is less than one or greater than 1. Question 1 What fraction of a circle is: (a) 60 degrees? (b) 72 degrees? (c) 18 degrees? 1 6 (A1)..(1) 1 5 (A1)..(1) 1 12 (A1)..(1) (Total 4 marks) Question 2 What fraction of 250, is 100? 100/250 (M1) = 2 5 (A1) (Total 2 mark) Question 3. What fraction of 400 is: (a) (A1).(1) (b) (A1)..(1)

15 Question 4. What fraction of 30 is: (a) 6 miles 1 5 (A1).(1) (b) 3miles 1 10 (A1) (1) Total /10

16 Use ratio notation 2 Grade 3 SOLUTIONS Objective: Use ratio notation, including reduction to simplest form. Question 1. Simplify the following ratios: (a) 3:12 (b) 28:7 1:4 (A1) 4:1 (A1) (1) (1) (c) 12:60 1:5 (A1) (1) (d) 1 5 : 3 10 Question 2 = 2 10 : 3 10 = 2:3 (A1) (1) (Total 4 marks) Share the following into the given ratios. (a) 50 kg into 2:5:3 10 shares, 50 = 5 kg per share (M1) 10 10:25:15 (A1)... (2) (b) 45 minutes into 9:6 15 shares, 45 = 3 mins per share = 27:18 (M1) 15 = 9:6 = 3:2 (A1)... (2) (Total 4 marks)

17 Question 3 Reduce each of the following ratios to the form n:1 (a) 20:5 4:1 (A1).(1) (b) 40:8 5:1 (A1).(1) Total /10

18 Use scale factors, diagrams and maps 2 Grade 3 SOLUTIONS Objective: Use scale factors, diagrams and maps (including geometrical problems) Question 1 A 2 cm B C 6 cm D Line CD is bigger than line AB. What is the scale factor of the enlargement? Scale factor 3 (A1).. (Total 1 mark) Question 2 Using scale of 1:25 5 cm on a map is actually how many metres in real life? 5 x 25 = 125 cm (M1) 1.25 metres (A1). Question 3 Using scale of 1:25 7 metres will be drawn as how many cms on a map? 7 metres is 700 cms (M1) 700/25 = 28 cm on the map (A1)

19 Question 4 25m 15m A rectangular field is really 250 metres by 150 metres. On a scale drawing 1cm: 50m (a) What length will I draw for the field on the map? 250/50 = 5 cm on map (A1)..(1) (b) What width will I draw for the field on the map? 150/50 = 3 cms on map (A1) (1) (c) What angle will each corner be? 90 degrees (A1) (1) (Total 3 marks)

20 Question 5 These triangles are mathematically similar. (not drawn accurately) The height of the smaller triangle is 3 cms. The height of the bigger triangle is 9 cms What is the scale factor of this enlargement? Scale factor 3 (A1) (1) The angle at the top of the smaller triangle is 25 degrees. What is the angle at the top of the bigger triangle? 25 degrees (A1).(1) Total /10