The shaded shape has an area of 3 hexagons and a perimeter of 14 cm.

Transcription

1 1 Here is a grid of regular hexagons. The shaded shape has an area of 3 hexagons and a perimeter of 14 cm. Draw another shape on the grid which has an area of 4 hexagons and a perimeter of 14 cm. 1 mark 2 The area of this square is 36 cm 2. Page 1 of 20

2 The square is cut into quarters to create 4 identical rectangles. What is the perimeter of one of the small rectangles? 2 marks Page 2 of 20

3 3 What is the area of this shape? 2 marks Page 3 of 20

4 4 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 4 of 20

5 5 The diagram shows a shaded triangle inside a rectangle. What is the area of the shaded triangle? 2 marks Page 5 of 20

6 6 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 mark Page 6 of 20

7 7 Twelve rectangles, all the same size, are arranged to make a square, as shown in the diagram. Calculate the area of one of the rectangles. 2 mark Page 7 of 20

8 8 Here is a T-shape made from 3 identical rectangles. The area of the T-shape is 90cm 2 Work out the value of x 2 marks Page 8 of 20

9 9 The diagram shows a shaded square inside a larger square. Calculate the area of the larger square. 1 mark Calculate the area of the shaded square. 2 mark Page 9 of 20

10 10 Here is a flag. Calculate the area of the shaded cross. 2 marks Page 10 of 20

11 11 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 mark Page 11 of 20

12 12 The diagram shows a rectangle and a shaded circle with radius 20 cm. Calculate the area of the rectangle that is not shaded. Use this formula: The area of a circle is 3.14 (radius) 2 3 marks Page 12 of 20

13 Mark schemes 1 Shape drawn on grid as shown: Accept: shape in any position or orientation. Accept: slight inaccuracies in drawing provided the intention is clear. Accept: alternative unambiguous indications of the correct shape provided the intention is clear. Accept: mathematically correct answers involving fractions of a hexagon. Shape need not be shaded. [1] 2 15 or 6(cm) and 1.5(cm) seen (the dimensions of the rectangle) 2 Page 13 of 20

14 OR Shows or implies a complete correct method, eg: = 8 (error) 8 4 = 2 2 (8 + 2) 6 6 = = 1.2 (error) Do not accept confusion between area and perimeter, ie: side of square is 36 4 = 9 (error) 2 ( ) 1 [2] 3 Award TWO marks for the correct answer of 82 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg (4 10) + (7 6) OR (10 10) (3 6) Answer need not be obtained for the award of the mark. Up to 2 [2] Page 14 of 20

15 4 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 Page 15 of 20

16 ( ) seen or Show the parallel sides of the trapezium are 3(cm) and 6(cm), and the height is 3(cm) eg Diagram marked correctly! Brackets omitted For 1m, condone eg, accept = U1 [3] 5 12 or Shows or implies a complete correct method, eg: = 13 (error) 60 (10 6 2) (6 6 2) [2] Page 16 of 20

17 6 Award TWO marks for the correct answer of 108 cm 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] 7 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] 8 5 cm 2 U1 Page 17 of 20

18 or Answer of 2.5 OR Shows understanding of a correct method even if there are computational errors, eg 90 3 = 36 (error) 12 2 = = 6 1 [2] 9 (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] Page 18 of 20

19 10 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] 11 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] Condone the following that arise from other values of π values between 1371 and 1380 inclusive π Throughout the question do not accept 3 as a value for π 3 Page 19 of 20

20 or 628 seen (area of semi-circle) OR Shows or implies a complete correct method, eg: Rectangle = = 2000 Circle = = 1256 Semi-circle = = 623 (error) ! Partial credit can be awarded for working in metres. Condone the following seen that arise from other values of π values between 620 and 629 inclusive 200π! The squaring must be interpreted correctly, eg: do not accept circle = = or 1256 seen (area of circle) OR! Partial credit can be awarded for working in metres. Condone the following seen that arise from other values of π values between 1240 and 1257 inclusive 400π A value between 743 and 760 inclusive seen (area of whole circle subtracted from rectangle) OR condone π Shows or implies a correct method to find the area of the semi-circle, eg: ! The squaring must be interpreted correctly 1 [3] Page 20 of 20