Q1. Here is a flag. Calculate the area of the shaded cross. Q2. The diagram shows a rightangled triangle inside a circle.


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1 Q1. Here is a flag. Calculate the area of the shaded cross. 2 marks Q2. The diagram shows a rightangled triangle inside a circle. The circle has a radius of 5 centimetres. Calculate the area of the triangle. cm 2 1 mark Page 1 of 31
2 Calculate the area of the shaded part of the diagram. 2 marks Q3. This cube has a volume of 64 cubic centimetres. Calculate the height of the cube. cm 1 mark These two cubes are not drawn to scale. 1 mark The ratio of the volumes of the two cubes is 2:3 Page 2 of 31
3 Calculate the volume of the larger cube. 1 mark Q4. Ben makes a letter 'B' out of a piece of wire. It has a straight side and two equal semicircles. Each semicircle has a diameter of 15cm. Page 3 of 31
4 Calculate the total length of the wire. 2 marks Q5. The diagram shows a shaded square inside a larger square. Calculate the area of the larger square. cm 2 1 mark Page 4 of 31
5 Calculate the area of the shaded square. 2 marks Q6. This is a centimetre grid. On the grid draw a triangle which has an area of 7.5cm 2 and which has an obtuse angle. Use a ruler. 2 marks Page 5 of 31
6 Q7. The diagram shows a shaded triangle inside a larger triangle. The area of the shaded triangle is 52 cm 2. The area of the shaded triangle is of the area of the larger triangle. Calculate the area of the larger triangle. 2 marks Q8. Amit has some small cubes. The edge of each cube is 1.5 centimetres. Page 6 of 31
7 He makes a larger cube out of the small cubes. The volume of this larger cube is 216 cm 3. How many small cubes does he use? 2 marks Q9. Twelve rectangles, all the same size, are arranged to make a square, as shown in the diagram. Page 7 of 31
8 Calculate the area of one of the rectangles. 2 marks Q10. The diagram shows 4 identical shaded triangles in a rectangle. The rectangle measures 36 centimetres by 24 centimetres. Calculate the area of one shaded triangle. 2 marks Page 8 of 31
9 Q11. A cuboid has a square base. It is twice as tall as it is wide. Its volume is 250 cubic centimetres. Calculate the width of the cuboid. 2 marks Page 9 of 31
10 Q12. Here is a centimetre grid. Draw two more lines to make a quadrilateral with an area of 18cm Use a ruler. 2 1 mark Page 10 of 31
11 Q13. The diagram shows a square of side length 12 cm. Inside the square are 8 congruent trapeziums and a shaded square. The side length of the shaded square is 6 cm. What is the area of one of the trapeziums? 3 marks Page 11 of 31
12 Q14. The flag of Greenland is a rectangle with a circle drawn inside. Here is the same flag rotated. The sketch gives the information you need to draw the flag. Page 12 of 31
13 Use the correct mathematical equipment to draw accurately the flag of Greenland. Some of the flag is drawn for you. 3 marks Page 13 of 31
14 Q15. The photograph shows a crop circle that was made in Mexico. People flattened crops to make a pattern inside a circle. The photograph has been provided courtesy of Greenpeace Some people are planning to make a crop circle. Here is what they plan to do: They will make a circle of radius 30 m. They will flatten about 60% of the area of the circle. Together, they can flatten 450 m 2 in one hour. Page 14 of 31
15 About how many hours do the people plan to spend making the crop circle? You will need to use this formula: The area of a circle is (radius) 2 3 marks Q16. The grid below is made of rightangled triangles like this: Shade triangles on the grid to make a quadrilateral. Page 15 of 31
16 Your quadrilateral must have an area of 24 cm 2 and a perimeter of 26 cm. 2 marks Q17. Cleo has 24 centimetre cubes. She uses all 24 cubes to make a cuboid with dimensions 6 cm, 2 cm and 2 cm. Write the dimensions of a different cuboid she can make using all 24 cubes. cm, cm and cm 1 mark Page 16 of 31
17 Jon has 20 centimetre cubes. He wants to make a cube with edges that are 3 cm long. How many more centimetre cubes does he need? more 1 mark Q18. Here is a trapezium with a height of 10 centimetres. The parallel sides are 5.5cm long and 10.5cm long. Page 17 of 31
18 Find the area of the trapezium. 2 marks Q19. Every second, 300cm 3 of water comes out of a tap into a cuboid tank. Not actual size The base of the tank is 40cm by 40cm. Page 18 of 31
19 The height is 12cm. How many seconds does it take to fill the tank? 2 marks Page 19 of 31
20 M1. Award TWO marks for the correct answer of 1050 cm² If answer is incorrect, award ONE mark for evidence of an appropriate method, eg: OR OR Calculation need not be performed for the award of ONE mark, but the method shown must be capable of producing the correct answer. Up to 2 [2] M2. (a) 12.5 OR 12½ (b) Award TWO marks for the correct answer in the range of 66 to 66.1 inclusive OR an answer based upon values obtained in 13a. If the answer is incorrect award ONE mark for evidence of an appropriate method, eg ( ) 12.5 The calculation need not be completed for the award of the mark. 1 Up to 2 [3] M3. (a) 4 (b) Award TWO marks for the correct answer of 96. If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg Calculation need not be completed for the award of the mark. 1 Up to 2 [3] Page 20 of 31
21 M4. Award TWO marks for a correct answer of 77 OR any other more accurate representation of the correct answer such as OR an answer based upon π = such as Answers may be rounded to any number of decimal places. If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg Calculation need not be completed for the award of the mark. Up to 2 [2] M5. (a) (b) Award TWO marks for a correct answer of 205 OR a number calculated from the answer given in (a), ie (answer given in (a)) 66 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 196 (4 16.5) OR (answer given in (a)) (4 16.5) OR = (Pythagoras) Calculation need not be completed for the award of the mark. Up to 2 [3] M6. Award TWO marks for any obtuseangled triangle with an area of 7.5cm, eg 2 Page 21 of 31
22 If the answer is incorrect, award ONE mark for any triangle with an area of 7.5cm (irrespective of angles) Accept any obtuseangled triangle with appropriate base and height each correct to within 2mm The triangle need not have vertices on the grid intersections. Accept a triangle not drawn with a ruler, provided the vertices are correctly placed. Up to 2 2 [2] M7. Award TWO marks for the correct answer of 117. If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 52 4 = 13 AND 9 13 OR = AND Calculation need not be completed for the award of the mark. Up to 2 [2] M8. Award TWO marks for the correct answer of 64 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 216 = = 4 number of cubes = OR = number of cubes = Calculation need not be completed for the award of the mark. Up to 2 [2] Page 22 of 31
23 M9. Award TWO marks for the correct answer of 75 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg width = (50 40) 2 length (50 5) 3 area = OR (50 40 ) 12 Calculation need not be completed for the award of the mark. Up to 2 [2] M10. Award TWO marks for the correct answer of 108cm 2 If the answer is incorrect award ONE mark for evidence of an appropriate method, eg 36 2 = = 12 area = ½ Calculation need not be completed for the award of the mark. No mark is awarded for the result of calculating only. Up to 2 [2] M11. Award TWO marks for the correct answer of 5cm If the answer is incorrect award ONE mark for evidence of an appropriate method, eg 2n n n = 250 so n n n = 125 The calculation need not be completed for the award of the 3 mark, but n n n = 125 OR n = 125 must be reached. Up to 2 [2] Page 23 of 31
24 M12. Two more lines drawn which intersect at a fourth vertex located anywhere on the dotted line shown on the diagrams below, eg OR OR Accept slight inaccuracies in drawing provided the intention is clear. [1] Page 24 of 31
25 M13. or equivalent 3 or Shows or implies a complete correct method with not more than one computational error The most common correct methods: Find the total area of the trapezia and divide by 8 eg ( ) = 94 (error) 94 8 = Do not accept squaring evaluated as 2 eg ( ) 8 = (24 12) 8 Find the dimensions of a trapezium and use the formula or component parts eg (3 + 6) (3 3) 2 or The only error is to work with 4 congruent trapezia (not 8), but correctly finds the area of one of them eg (144 36) 4 = = 9, 9 3 = 27 Do not accept for 2m, 27 seen with no method 2 or Shows or implies a correct method to find the total area of the trapezia eg ( ) seen or Show the parallel sides of the trapezium are 3(cm) and 6(cm), and the height is 3(cm) Page 25 of 31
26 eg Diagram marked correctly! Brackets omitted For 1m, condone eg, accept = U1 [3] M14. Completes the drawing according to the following conditions, with a tolerance of 3 mm in each case the circle has a diameter of 8 cm the highest point at which the circle crosses the central vertical line is 3 cm from the top of the answer box the lowest point at which the circle crosses the central vertical line is 7 cm from the bottom of the answer box or 3 Any two of the three conditions given above are correct 2 or Any one of the three conditions given above is correct Accept flag constructed upside down! Shading incorrect or omitted, or additional lines drawn Condone, provided the response is unambiguous! Compasses not used For pupils who meet one or more of the conditions without using compasses, deduct ONE mark 1 [3] Page 26 of 31
27 M U1 or Shows or implies at least two of these three steps correctly: eg: 1. A correct method for evaluating the area of the circle in which the squaring is interpreted correctly 2. A correct method for finding 60% of a quantity 3. Division by 450 Shows the value 3.7(...) or 3.8 [1, 2 and 3 but rounding omitted] Shows the value 1696.(...) or 1697 [1 and 2] π [1 and 2] [2 and 3] = (error) = 0.25(...) [2 and 3] 2827.(...) 450 [1 and 3] Do not accept Ambiguous implication for method eg, to imply 1 and 3 2 or Shows or implies one of the three steps above correctly, eg: Shows the value 2827.(...) or 2828 [1] [[1[] π [1] 60% of (error) = 113.(...) [2] = (error) = 0.2(...) [3] 1 [3] Page 27 of 31
28 M16. Shows a correct quadrilateral, eg OR 2 U1 or Shows a quadrilateral with an area of 24 cm 2 but not a perimeter of 26 cm, eg OR! Shading omitted Accept provided the quadrilateral drawn is unambiguous! Lines not ruled or accurate Accept slight inaccuracies in drawing provided the pupil's intention is clear 1 [2] Page 28 of 31
29 M17. (a) Gives three integers other than 2, 2, 6 (in any order) whose product is 24, eg: 1, 1, 24 1, 24, 1 1, 2, 12 1, 3, 8 1, 4, 6 (b) 7 2, 3, 4! Noninteger(s) used As this shows understanding of volume, condone provided the three values given have a product of 24 eg, accept 1.5, 2, [2] M18. 80! Measures 2 or Shows or implies a complete correct method, eg: ( ) ( 10 5) ( ) 10 (10 5.5) + ( 10 5) = (error) 1 [2] M or! For 2m, condone 63.99( ) (some calculator displays will show this as their final answer) 2 Shows the value (volume of the tank) Page 29 of 31
30 OR Shows or implies a complete correct method, eg: ( ) 300 = 58 (error)! For 1m, condone 63.9 as evidence of an appropriate method (calculator display incorrectly rounded) 1 [2] Page 30 of 31
31 Page 31 of 31
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