Question 1 equivalent fractions Question 2 single power of 2 Question 3 bearings from a map

1. Question 1 equivalent fractions Question 2 single power of 2 Question 3 bearings from a map Question 4 perimeter; equilateral triangle in regular hexagon Question 5 area of triangles Question 6 volume from plan and elevations Question 7 multiply out and simplify Question 8 nth term of a sequence Question 9 transformations; rotation; translation; vector Question 10 algebra; expand; factorise; change the subject Question 11 show some algebra Question 12 simultaneous equations Question 13 similar triangles; find lengths of sides Question 14 vectors Question 15 prove triangles congruent Question 16 algebraic identity; simplify algebraic fraction Question 17 draw graph of exponential function Grade boundaries

2. Answer 1 Here is a list of fractions. Which two fractions in the list are equivalent? You must show your working Simplify any which will … 3 marks

3. … when multiplying power numbers add the indices • 2 Write as a single power of 2 • 22 x 23 • (b) 28 ÷ 22 Answer = 25 1 mark Answer = 26 1 mark … when dividing power numbers subtract the indices

4. 3. The diagram shows the map of a bay and four ports P,Q , R and X. • A ship sails due west to X from P. • Write down the three-figure bearing of X from P. 2700 1 mark

5. (b) A boat sails to P from Q. Measure and write down the three figure bearing of P from Q 0650 1 mark (c) A yacht sails to P from R on a bearing of 1100 Work out the three figure bearing of R from P. back bearing is 180 + 110 = 2900 2 marks

6. 9 cm 9 cm 9 cm 4. A regular hexagon is made from 6 equilateral triangles as shown. The perimeter of the hexagon is 54 centimetres. Work out the perimeter of one of the equilateral triangles Perimeter = 27 cm Perimeter = 54cm  one edge is 9 cm 3 marks

7. 5 (a) The diagram shows a right angled triangle. Work out the area of the triangle. State the units of your answer. Area of triangle = ½ base x height 3 marks Area = ½ x 4 x 3 = 6 cm2 1 of the marks is for correct units cm2 The 5 cm measurement is a distractor! Do not use it.

8. 5 (b) Three triangles are shown, A, B and C • Here are four statements • Triangle A has the greatest area. • Triangle B has the greatest area. • Triangle C has the greatest area. • All three triangles have the same area. • Which statement is correct? • Give a reason for your answer. Number 4 2 marks The base = 4cm and the height = 3cm on each triangle

9. 6. A room is in the shape of a cuboid. The diagrams show the plan view, front elevation and side elevation Calculate the volume of the room. Volume = length x width x height 3 marks = 6 x 5 x 3 = 90m3

10. 7 (a) multiply out 6(3p + q) 6(3p+ q) on the grid = 18p + 6q 1 mark 18p 6q (b) multiply out -2(2p + 3q) 1 mark -2(2p+ 3q) on the grid = -4p - 6q -4p -6q (c) multiply out and simplify 6(3p + q) – 2(2p + 3q) = 18p + 6q – 4p – 6q = 18p+ 6q– 4p– 6q = 14p 1 mark

11. 8 (a) Here is a table about squares. Complete the table for n squares 4n 1 mark (b) Here is a sequence of numbers. 5 9 13 17 Write down an expression for the nth term. Goes up in 4s first term 5 is 4 x 1 + 1 nth term is = 4n + 1 2 marks

12. 9 (a) The diagram shows the rotation of shape A to shape B. OX and OY are perpendicular. Work out the angle of rotation. Angle of rotation = 70o 2 marks

13. This means move the shape 4 to the right and 1 down 9. (b) (i) Translate the shaded shape C by the vector 2 marks (ii) Write down the translation vector that would return C back to its original position. 1 mark

14. 10 (a) Expand 2x(x2– 4) (b) Factorise y2 – 4y (c) Make x the subject of the formula y = 3 + x 2xtimes x2= 2x3 2xtimes - 4= - 8x Answer= 2x3 - 8x 2 marks yx y – 4 xy = y( y – 4 ) 1 mark y – 3 =x Take 3 from both sides swap sides x =y – 3 1 mark

15. 11 Show clearly that (n - 2)(n + 3) + (6 - n) = n2 (n - 2)(n + 3) = n2 -2n +3n -6 = n2 + n - 6 adding 6 – n to this answer gives n2 + n – 6 + 6 - n = n2 4 marks

16. 12 There are 70 bags of sugar on a shelf. There are x bags that weigh 1 kg. There are y bags that weigh 2kg. (a) Write down an equation connecting x and y (b) the total weight of the bags is 96kg Use algebra to work out the values of x and y. You must show your working. x + y = 70 1 mark x + y = 70 x + 2y = 96  Subtract from  y = 26 Use y = 26 in  x + 26 = 70  x = 44 Check x=44 and y=26 in  44 + 52 = 96 4 marks

17. 13 The diagram shows three similar triangles (a) Work out the value of x. (b) Work out the value of y. x3 x 2.5 The centre triangle is an enlargement scale factor 3 of the smallest triangle … 2 marks So x = 3cm The largest triangle is an enlargement scale factor 2.5 of the centre triangle … So y = 22.5 cm 3 marks

18. D F C E 14 The diagram shows two vectors Label the points C, D, E and F A O B 1 mark 1 mark 1 mark 1 mark

19. 15. The diagram shows a rhombus ABCD. The diagonals intersect at X. Prove that triangle ABX is congruent to triangle CDX A B Rhombus  all sides equal and diagonals bisect at 900 X Angle AXB = angle CXD = 900 D C AB = CD = equal sides of rhombus AX = CX = bisected diagonal AC  triangle AXB triangle CXD RHS 4 marks

20. 16 (a) You are given the identity x2 – ax + 144  ( x – b)2 Work out the values of a and b. (x - b)2 = x2 – 2bx + b2 so x2 – ax + 144 x2 – 2bx + b2 To be identical 144 = b2 and a = 2b which makes b =  12 and a =  24 3 marks

21. 16 (b) Simplify Factorise the top and the bottom - remember difference of two squares Cancel common factors (x - 2) 3 marks

22. 1 17 (a) Complete the table of values for

23. 15 (b) Draw the graph of for values of x from 0 to 4 2 marks (c) Use your graph to estimate the value of 2 marks

24. Total: out of 70 a rough guide