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1. (a) Find the value of 3x + 5y when x = –2 and y = 4 ........................…......................................................................................................... Answer .................................................................. (2) (b) Find the value of 3a2 + 5 when a = 4 ........................…......................................................................................................... Answer .................................................................. (2) (c) k is an even number. 1 Jo says that k + 1 is always even. 2 Give an example to show that Jo is wrong. ........................…......................................................................................................... ........................…......................................................................................................... (1) (d) The letters a and b represent prime numbers. Give an example to show that a + b is not always an even number. ........................…......................................................................................................... ........................…......................................................................................................... (1) (Total 6 marks) 2. On the grid below, draw the graph of y = 7 – x for values of x from 0 to 7. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... The Robert Smyth School 1 y 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 x (Total 3 marks) The Robert Smyth School 2 3. On the grid draw the graph of y = 2x + 1 for values of x from 0 to 5. y 12 11 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 x ..................................................................…......................................................................... ..................................................................…......................................................................... ..................................................................…......................................................................... ..................................................................…......................................................................... (Total 3 marks) The Robert Smyth School 3 4. (a) On the grid below, draw the graph of y = 2x – 3 for values of x from –2 to +3. ...................................................................................................................................... ...................................................................................................................................... y 3 2 1 –2 –1 O 1 2 3 x –1 –2 –3 –4 –5 –6 –7 (3) (b) The line y = 2 crosses y = 2x – 3 at P. Write down the coordinates of P. Answer ( .................. , .................. ) (1) (Total 4 marks) The Robert Smyth School 4 5. On the grid below draw the graph of y = 3x – 1 for values of x from 0 to 5. …………..........…............……...................…………….....…………................................ …………..........…............……...................…………….....…………................................ …………..........…............……...................…………….....…………................................ y 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 x –1 (Total 3 marks) The Robert Smyth School 5 The Robert Smyth School 6 6. The line y = –3 crosses the line y = x – 2 at the point P. What are the coordinates of P? You may use the grid below if you wish. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... y 6 5 4 3 2 1 –6 –5 –4 –3 –2 –1 O –1 1 2 3 4 5 6 x –2 –3 –4 –5 –6 Answer (.............................., ..............................) (Total 3 marks) The Robert Smyth School 7 1. (a) 3 × (–2) + 20 –6 seen M1 14 A1 (b) 3 × 16 + 5 M1 (c) 53 Any k which is a multiple of 4 eg 1 1 2 × 4 + 1 (= 3) or A1 B1 1 2 4+1 eg 2 K = 8 (d) Sum of 2 + any other prime nb 1 is not prime: 1 + 2 = 3 B0 B1 [6] 2. 2 plots from: (0,7) (1,6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1) (7, 0) All ± 1 mm B1 for 1 correct plot B2 Straight line (from 0 to 7) through correct plots ± 1 mm B1 [3] 3. Graph passing through (0, 1) 1 correct point plotted or worked B1 Graph with a gradient of 2 3 correct points plotted or worked B1 Graph from (0, 1) to (5, 11) B1 [3] 4. (a) Any correct plot from this list: (–2, –7)(–1, –5)(0, –3)(1, –1) (2, 1)(3, 3) M1 Second correct plot M1 Correct line A1 From –2 to +3 y = 2x y = 2x – 3 both drawn but 2x – 3 not indicated (b) SC1 (2.5, 2) B1 ft ft from their line [4] 5. Graph passing through (0,1) 1 correct point plotted or worked eg (0,–1) (1, 2) (2, 5) (3, 8) (4, 11) (5, 14) B1 Graph with a gradient of 3 2 further correct points plotted or worked B1 Line from (0,–1) to (5, 14) with no errors Freehand line to ½ square accuracy B1 [3] The Robert Smyth School 8 The Robert Smyth School 9 6. y=x–2 B1 Correct line drawn or table with 3 values correct Or – 3 = x – 2 y=–3 B1 Correct line drawn or coordinate at y = – 3 identified or table includes (-1, – 3) Or x = – 1 (–1, –3) B1ft ft their lines not in 1st quadrant Mark method (using either lines or tables or equation) that gives the best score. Do not mix methods. [3] The Robert Smyth School 10