Plot four points A, B, C and D on the grid to make a rectangle ABCD of length 6 cm and width 4 cm. (2)

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Lesley Lamb
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1 Q1. (a) Here is a centimetre grid. Plot four points A, B, C and D on the grid to make a rectangle ABCD of length 6 cm and width 4 cm. (2) (b) Tick whether each statement is always true, sometimes true or never true. (i) Rectangles with an area of 24 cm have a length of 6 cm. 2 Always true Sometimes true Never true (ii) Rectangles with a perimeter of 20 cm have a length of 12 cm. Always true Sometimes true Never true (iii) Rectangles with length 6 cm and width 4 cm have area 24 cm and perimeter 20 cm. 2 Always true Sometimes true Never true (Total 5 marks) Page 1 of 57

2 Q2. The diagram shows a kite ABCD. Tick a box to show whether each statement is true or false. (a) AB is parallel to CD. True False (b) Angle A = Angle C True False (c) The kite has two lines of symmetry. True False (d) The diagonals are at right angles to each other. True False (Total 4 marks) Page 2 of 57

Q3. A regular octagon is split into triangles A, B, C, D, E and F. (a) Complete this list of pairs of congruent triangles. C and D B and... A and... (2) (b) Triangles A and B make a trapezium as shown.

3 Q3. A regular octagon is split into triangles A, B, C, D, E and F. (a) Complete this list of pairs of congruent triangles. C and D B and... A and... (2) (b) Triangles A and B make a trapezium as shown. Which of the following triangles also make a trapezium? Circle your answers. B and C C and D D and E E and F (2) (c) Shade two triangles in this diagram to make a kite. (Total 5 marks) Page 3 of 57

Q4. The diagram shows five shapes, A, B, C, D and E

......... Answer D...,...,..., A (Total 2 marks) Q5.

4 Q4. The diagram shows five shapes, A, B, C, D and E drawn on a grid. Put the shapes in order of area, starting with the smallest. The smallest and largest are done for you Answer D...,...,..., A (Total 2 marks) Q5. The diagram shows a cube of side 2 cm. (a) How many faces does a cube have? Answer... Page 4 of 57

5 (b) Draw an accurate net of this cube on the grid below. (3) (Total 4 marks) Q6. On the grid, the horizontal line is x units long and the sloping line is y units long. Shapes are drawn on the grid that have dots as their vertices. The perimeter of this shape is 6x + 4y Page 5 of 57

6 Work out the perimeter of the following shapes in terms of x and y (a) Answer... (2) (b) Answer... (2) (Total 4 marks) 2 Q7. The area of a square is 387.5cm. (a) Work out the length of one side of the square. Give all the figures on your calculator display. Answer... cm (2) Page 6 of 57

7 (b) Give your answer to 1 decimal place. Answer... cm (Total 3 marks) Q8. (a) The diagram shows a rectangle drawn on a centimetre grid. Work out the perimeter of the rectangle. Answer... cm Page 7 of 57

Complete the following using greater than or less than or equal to (a) The

8 (b) The perimeter of a square is 12 cm. Draw the square on the grid below. (2) (Total 3 marks) Q9. A and B are two interlocking shapes as shown. Complete the following using greater than or less than or equal to (a) The perimeter of A is... the perimeter of B. (b) The area of A is... the area of B. (Total 2 marks) Page 8 of 57

Q10. Here is a list of words that are connected with circles. centre radius chord diameter circumference tangent Label the four boxes on this diagram, by choosing the correct word from the list.

9 Q10. Here is a list of words that are connected with circles. centre radius chord diameter circumference tangent Label the four boxes on this diagram, by choosing the correct word from the list. (Total 4 marks) Q11. Joanne is making shapes using some of these rods. Not drawn accurately (a) She makes an isosceles triangle using three of the rods. Draw a sketch to show how she could do this. Show the length on each side. (b) She makes a quadrilateral using two 3 cm rods and two 5 cm rods. Write down the names of two possible quadrilaterals that she could make. Answer... and... (2) Page 9 of 57

(c) She tries to make a triangle using one rod of each length. Explain why she cannot do this. (Total 4 marks) Q12. Frank draws two quadrilaterals on a seven-point triangular grid.

10 (c) She tries to make a triangle using one rod of each length. Explain why she cannot do this. (Total 4 marks) Q12. Frank draws two quadrilaterals on a seven-point triangular grid. (a) (i) What special name is given to quadrilateral A? Answer... (ii) What special name is given to quadrilateral B? Answer... (b) By joining 4 dots on the seven-point grid below draw a rectangle. (c) By joining 3 dots on the seven-point grid below draw an equilateral triangle. Page 10 of 57

11 (d) The perimeter of quadrilateral A can be found using the formula Find P when a = 3 and b = 5.2 Answer P =... (2) (e) Frank now draws a quadrilateral and a triangle. Explain why the areas of the two shapes are the same. (2) (Total 8 marks) Page 11 of 57

12 Q13. Which three of the following are nets of a cube? Answer... (Total 2 marks) Q14. The diagram shows quadrilateral A. The angles are labelled w, x, y and z. (a) Measure angle z. Answer... degrees Page 12 of 57

Label the remaining marked angles in the tessellation using either w, x, y or z.

13 (b) Quadrilaterals identical to quadrilateral A are used to make a tessellation. Part of the tessellation is shown below. Label the remaining marked angles in the tessellation using either w, x, y or z. Some of these have been done for you already. (2) (c) Give a reason why the diagram shows that the angles in a quadrilateral add up to 360 (Total 4 marks) Page 13 of 57

14 Q15. (a) Two squares of side 4 cm are removed from a square of side 12 cm as shown. Work out the shaded area. Answer... (3) Page 14 of 57

15 (b) Two squares of side x cm are removed from a square of side 3x cm as shown. Work out the fraction of the large square which remains. Give your answer in its simplest form. You must show your working. Answer... (3) (Total 6 marks) Page 15 of 57

Q16. Shapes tessellate when they fit together with no gaps. Here is a tessellating pattern made from equilateral triangles and regular hexagons.

16 Q16. Shapes tessellate when they fit together with no gaps. Here is a tessellating pattern made from equilateral triangles and regular hexagons. Not drawn accurately (a) Write down the size of each interior angle in the equilateral triangle. Answer... degrees (b) Write down the size of each interior angle in the regular hexagon. Answer... degrees (c) Use your answers to parts (a) and (b) to explain why the two shapes form a tessellating pattern. (3) (Total 5 marks) Page 16 of 57

17 Q17. The diagram shows a triangle. All the sides are equal in length. (a) What is the name given to this special type of triangle? Answer... (b) The diagram shows a shape made up of two of these triangles. (i) What is the mathematical name of this shape? Answer... (ii) Write down the order of rotational symmetry of this shape. (iii) Answer... Draw the lines of symmetry on the shape. (2) (Total 5 marks) Q18. Julie is drawing a quadrilateral with these properties. It has 4 equal sides. Its diagonals intersect at 90. Page 17 of 57

18 She draws a square. (a) Draw a different type of quadrilateral with these properties. (b) What is the name of this quadrilateral? Answer... (Total 2 marks) Q19. (a) Write down the name of this quadrilateral. Answer... Page 18 of 57

19 (b) Three of these statements are true for a kite. Draw arrows from the statements that are true to the picture of the kite. One of them has been done for you. (2) (Total 3 marks) Page 19 of 57

Tick the correct boxes to say whether the following statements are true or false.

20 Q20. The length of a rectangle is 10.8 cm. The perimeter of the rectangle is 28.8 cm. Calculate the width of the rectangle Answer... cm (Total 3 marks) Q21. ABCD is a rectangle. The rectangle has two diagonals AC and BD. Tick the correct boxes to say whether the following statements are true or false. True False (a) (b) (c) (d) The diagonals are equal in length. The diagonals cross at right angles. The diagonals bisect each other. The diagonals are lines of symmetry. (Total 3 marks) Page 20 of 57

21 Q22. (a) The diagram shows a rectangle. Not drawn accurately Work out the area of the rectangle. State the units of your answer. Answer... (3) (b) The diagram shows a rectangle made from two congruent shapes A and B. (i) Write down the mathematical name of shape B. Answer... (ii) Explain how you could work out the area of shape B (2) (Total 6 marks) Page 21 of 57

22 Q23. Here are six shapes on centimetre grids. (a) Which two shapes fit together to make a rectangle? Answer... and... (b) Which two shapes fit together to make a square? Answer... and... (c) Work out the area of shape D. State the units of your answer.... Answer... (2) (Total 4 marks) Page 22 of 57

23 Q24. A rectangle has an area of 40 cm 2 and a perimeter of 26 cm. Find the length and width of the rectangle. You may use the grid to help you Answer Length... cm Width... cm (Total 2 marks) Page 23 of 57

24 Q25. Some shapes are drawn on a 1 centimetre triangular grid. (a) Find the perimeter of shape D. Answer... cm (b) Which two shapes have the same perimeter? Answer... (c) Which two shapes have the same area? Answer... (2) (Total 4 marks) Page 24 of 57

25 Q26. (a) An isosceles triangle has one angle of 80. Write down the possible sizes of the other two angles. Answer... and... degrees or... and... degrees (2) (b) Triangle ABC is a right-angled triangle. BDC is an equilateral triangle. Not drawn accurately Show that triangle ABD is an isosceles triangle. (3) (Total 5 marks) Page 25 of 57

26 M1. (a) Fully correct rectangle (b) (i) Sometimes true for one correct side B2 (ii) Never true (iii) Always true [5] Page 26 of 57

27 M2. (a) False (b) True (c) False (d) True [4] Page 27 of 57

28 M3. (a) (B and) E (A and) F Page 28 of 57

29 (b) All 3 pairs identified B and C D and E E and F for two identified with none incorrect B2 (c) C and D shaded [5] Page 29 of 57

30 M4. C, B, E Any two in order ie, BEC, ECB, CEB, BCE B2 [2] Page 30 of 57

31 M5. (a) 6 (b) Correct net for 4 squares in a row or column B2 for correct net for open-topped cube ( ±2 mm) SC1 for correct net in correct scale factor B3 [4] Page 31 of 57

32 M6. (a) 10x + 6y For 10x or 6y B2 (b) 8x + 10y For 8x or 10y B2 [4] Page 32 of 57

33 M7. (a) or length 2 = (01969) (b) 19.7 M1 A1 ft [3] Page 33 of 57

34 M8. (a) 20 (b) 3 by 3 square drawn 12 4 (= 3) or 5 by 1 or 4 by 2 rectangle drawn B2 [3] Page 34 of 57

35 M9. (a) Equal to (b) Less than [2] Page 35 of 57

36 M10. Chord Circumference Radius Tangent in correct boxes [4] Page 36 of 57

37 M11. (a) Correct sketch with sides marked Do not accept equilateral triangles (b) Any 2 of rectangle, parallelogram, arrowhead or kite for 1 correct B2 (c) The 3 cm rod and the 5 cm rod would not meet oe eg, < 9 [4] Page 37 of 57

38 M12. (a) (i) Kite (ii) Trapezium (b) (c) Rectangle drawn Equilateral triangle drawn 2 possible sizes (d) P = , M1 A1 Page 38 of 57

39 (e) Method 1 Attempt to compare using equilateral triangles/rhombi Method 2 Using formulae Method 1 eg, 2 bottom halves equal and lines drawn Complete argument Method 2 eg, b h for rhombus or for triangle Method 1 Show that both top halves are of a rhombus or are the same Method 2 Using both formulae and triangle has double the base (or height) oe B2 Complete hexagon on diagram and show each is 1/3 of hexagon [8] Page 39 of 57

40 M13. A B and E 1 eeoo B2 [2] Page 40 of 57

41 M14. (a) 65 ± 2 (b) All angles correctly labelled 4 angles correctly labelled B2 (c) w, x, y and z are angles at a point; sum of angles at a point is 360 ; w, x, y and z are angles in each quadrilateral Any two of the three conditions oe [4] Page 41 of 57

42 M15. (a) 12 2 ( ) oe M1 A1 cm 2 Units mark Page 42 of 57

43 (b) 9x 2 or attempt to use their 112 and 144 Attempt to calculate shaded area (= 7x 2 ) or (3x 3x) ( ) 2(x x) M1 Note: score M1A0 (unshaded) A1 [6] Page 43 of 57

44 M16. (a) 60 (b) 120 (c) = 360 oe For = 180 Hence no gaps B2 dep [5] Page 44 of 57

45 M17. (a) Equilateral (triangle) (b) (i) Rhombus (ii) 2 Accept in words (iii) 2 diagonals drawn 1 eeoo B2 [5] Page 45 of 57

46 M18. (a) Draws any rhombus Accuracy of 3 mm. Angle between sides must not be 90 (b) Rhombus Not square, diamond, oblong ft [2] Page 46 of 57

47 M19. (a) Rhombus (b) Diagonals cross at right angles; One pair of opposite angles equal. 1 eeoo SCI if only two more lines are drawn and one is correct B2 [3] Page 47 of 57

48 M Their Their M1 M1 dep A1 [3] Page 48 of 57

49 M21. True, false, true, false 1 eeoo B3 [3] Page 49 of 57

50 M22. (a) Do not accept M1 A1 cm 2 Units mark Page 50 of 57

51 (b) (i) Trapezium (ii) or Area of rectangle 2 Half the area of both shapes E1 For partial explanation eg, area of rectangle area of A 42 without working E2 [6] Page 51 of 57

52 M23. (a) A and E Either order (b) C and D Either order (c) 8 cm 2 Units mark [4] Page 52 of 57

53 M24. Length 8 and width 5 allow8 by 5 rectangle drawn or rectangle with area 40 or rectangle with perimeter 26 cm B2 [2] Page 53 of 57

54 M25. (a) 8 (b) A&C Page 54 of 57

55 (c) Attempt to find area Lines on diagram making triangles or rhombi; correct number of triangles/rhombi in two or more shapes: 12, 7, 8, 8 or 6,3 ½, 4, 4 M1 D&C A1 [4] Page 55 of 57

56 M26. (a) 80 and and 50 Page 56 of 57

57 (b) BAD = 30 or any angle in Δ BCD = 60 ABD = 30 Isosceles because BAD = ABD oe [5] Page 57 of 57

EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION)

EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION) Rhombus Trapezium Rectangle Rhombus Rhombus Parallelogram Rhombus Trapezium or Rightangle Trapezium 110 250 Base angles in