Section A Plotting Straight Line Graphs Grade D / C

Transcription

1 Name: Teacher Assessment Section A Plotting Straight Line Graphs Grade D / C 1. (a) Complete the table of values for = 3x + x (b) On the grid draw the graph of = 3x + for values of x from 0 to x (c) On the grid draw and label the line x =.5 (Total marks) St Paul s Catholic School 1

2 . (a) Complete the table of values for = 3x + 1 x (b) On the grid draw the graph of = 3x + 1 for values of x from 0 to x (c) Use our graph to solve 5.5 = 3x + l.. Answer x =.. (Total 5 marks) St Paul s Catholic School

3 3. (a) Complete this table of values for = x 1 x (b) On the grid draw the graph of = x 1 for values of x from 1 to O x 3 (c) Find the coordinates of the point where the line = x 1 crosses the line =... Answer (...,...) (Total 5 marks) St Paul s Catholic School 3

4 . (a) (i) Complete the table of values for = x 3 x (ii) On the grid draw the graph of = x 3 for values of x from 1 to x (b) Draw and label the line = 7 on the grid. (Total marks) St Paul s Catholic School

5 5. On the grid draw the line = x + 5 for values of x from 0 to x (Total 3 marks) St Paul s Catholic School 5

6 6. On the grid below draw the graph of = 3x 1 for values of x from 0 to x (Total 3 marks) St Paul s Catholic School 6

7 7. (a) On the grid draw the graph of = 10 x for values of x from 0 to x (3) (b) On the grid draw the line = 7 (Total marks) 8. On the grid below, draw the graph of = 7 x for values of x from 0 to x (Total 3 marks) St Paul s Catholic School 7

8 9. (a) Complete the table of values for the graph of x + = x (b) On the grid, draw the graph of x + = x (c) P is a point on the line x + = David sas, the x coordinate of P is one greater than the coordinate of P. Write down the coordinates of P. Answer (...,...) (Total marks) St Paul s Catholic School 8

9 10. (a) On the grid below draw and label the lines = and = x O x () (b) Success: Write down the coordinates of the point where the lines = and = x + 1 cross. Answer (...,...) (Total 5 marks) Target: St Paul s Catholic School 9

10 Teacher Assessment Section B Quadratic Graphs Grade C 1. (a) Complete the table of values for = x 3. x (b) On the grid below, draw the graph of = x 3 for values of x from 3 to (c) Write down the values of x at the points where the line = crosses our graph. Answer... and... (Total 5 marks) St Paul s Catholic School 10

11 . (a) Complete the table for the graph of = x 3x + 1. x (b) On the grid below, draw the graph of = x 3x + 1 for values of x from 1 to x (c) Use our graph to solve the equation x 3x + 1 = 0. Answer... and... (Total 6 marks) St Paul s Catholic School 11

12 3. (a) Complete this table of values for = ( + x)(3 x) x (b) On the grid, draw the graph of = ( + x)(3 x) for values of x from to O x (Total marks) St Paul s Catholic School 1

13 . (a) Complete the table of values for = x x 1 x (b) On the grid, draw the graph of = x x 1 for values of x from to O 1 3 x 1 3 St Paul s Catholic School 13

14 (c) An approximate solution of the equation x x 1 = 0 is x =. (i) Explain how ou can find this from the graph (ii) Use our graph to write down another solution of this equation. Answer x =... (Total 6 marks) St Paul s Catholic School 1

15 5. (a) Complete the table of values for = x x 1. x (b) On the grid, draw the graph of = x x 1 for values of x from 1 to O x (c) Use our graph to solve the equation x x 1 = 0. Answer... and... (Total 6 marks) Success: Target: St Paul s Catholic School 15

16 Teacher Assessment Section C Using an Appropriate Linear Graph Grade A / A* 1. The grid shows the graph of = x + x O 1 x 6 B drawing an appropriate straight line, solve the equation x + x 5 = x Answer... (Total 3 marks) St Paul s Catholic School 16

17 . The graph of = x x is drawn below O x 3 (a) Write down the solutions of x x = 0. Answer... (b) B drawing an appropriate linear graph, write down the solutions of x x 3 = 0... Answer... (3)(Total 5 marks) St Paul s Catholic School 17

18 3. (a) Complete the table of values for = x x + 3 x (b) On the grid below, draw the graph of = x x + 3 for values of x between 1 and x 1 3 (c) Write down the solutions of x x + 3 = 0 Answer... (d) B drawing an appropriate linear graph, write down the solutions of x 5x + 5 = 0 Answer... (3)(Total 7 marks) St Paul s Catholic School 18

19 . The grid below shows the graph of = x + 3x 10 = x+ 3 x O (a) B drawing an appropriate straight line on the graph solve the equation x + 3x 3 = Answer.. (b) B drawing an appropriate straight line on the graph solve the equation x + x 1 = Answer... (3)(Total 5 marks) St Paul s Catholic School 19

20 5. The diagram shows the graphs = x x 6 and = x O 1 3 x 6 (a) Use the graph of = x x 6 to write down the solutions of the equations (i) x x 6 = 0... Answer... St Paul s Catholic School 0

21 (ii) x x 6 = Answer... (b) Find the quadratic equation whose solutions are the x-coordinates of the points of intersection of = x x 6 and = x + 3 Give our answer in the form x + bx + c = 0 Answer... (c) Find the equation of the straight line that should be drawn on the diagram to solve the equation x x = 0 Answer... (Total 7 marks) St Paul s Catholic School 1

22 6. The graph = x x is drawn below for values of x between 3 and x 6 (a) Using the graph, find the solutions of x x = 0, giving our answers to 1 decimal place.... Answer... (b) B drawing an appropriate linear graph, write down the solutions of x 3x = Answer... (3)(Total marks) St Paul s Catholic School

23 7. A student draws the graph of = x x 1 for x x 1 3 (a) (i) Use the graph to solve the equation x x 1 = x Answer... (3) (ii) Re-write the equation x x 1 = x + 1 in the form of ax + bx + c = Answer... (b) Use the graph, or otherwise, to write down the two solutions to the equation Success: (x 1) (x 1) 1 = 0 Target: Answer... (Total 6 marks) St Paul s Catholic School 3

24 Teacher Assessment Section D Factorising and Solving Quadratics Grade B / A 1. (a) Factorise p + 7p + 1 Answer... (b) Solve the equation p + 7p + 1 = 0. (a) Factorise Answer... (Total 3 marks) Answer... (b) Hence solve the equation = (i) Factorise Answer... (Total 3 marks) Answer... (ii) Hence solve the equation = Answer... St Paul s Catholic School

25 . (i) Factorise x 13x + 36 (Total 3 marks) Answer... (ii) Hence, or otherwise, solve the equation x 13x + 36 = (a) Factorise x + 5x 1 Answer... (Total 3 marks) Answer... (b) Hence solve the equation x + 5x 1 = (a) Factorise x + 3x 0 Answer... (Total 3 marks) Answer... (b) Hence, solve the equation x + 3x 0 = 0 Answer x =... (Total 3 marks) St Paul s Catholic School 5

26 7. Solve the equation 5 = Solve the equation + 5 = 0 Answer... (Total 3 marks) Answer... (Total 3 marks) 9. The diagram shows the graph of an equation of the form = x + bx + c. (Not drawn accuratel) Find the values of b and c. You must show our method Not O 3 5 x Answer b =..., c =... (Total 3 marks) St Paul s Catholic School 6

27 10. (a) Factorise x 7x 15 Answer... (b) The graph of = x 7x 15 is sketched below. (Not to scale) Find the equation of the line of smmetr of this graph No P Q x Mand is x ears old. Her brother is 5 ears older than Mand. The product of their ages is 8. (a) Show that x + 5x 8 = 0 Answer... (3) (Total 5 marks) (b) Solve x + 5x 8 = 0 Do not use a trial and improvement method. Answer x =... (3)(Total marks) St Paul s Catholic School 7

28 1. (i) Factorise x 10x Answer... (ii) Hence, or otherwise, solve the equation ( 3) 10( 3) + 5 = Answer =... (Total marks) 13. Solve the equation = Solve the equation 5 x 1 3x 1 Answer... (Total 5 marks) Answer... St Paul s Catholic School (Total 6 marks) 8

29 15. Solve the equation 1 5x 3 x 1 x (Total 5 marks) 16. Solve this equation 3 x 5 1 x = (Total 7 marks) Success: Target: St Paul s Catholic School 9

30 Teacher Assessment Section E Quadratic Formula Grade A A* 1. Solve the equation x + x 10 = 0. Give our answers to decimal places. You must show our working. Answer... (3). Solve the equation giving our answers to 3 significant figures. x x 5 = Answer... (Total 3 marks) St Paul s Catholic School 30

31 3. Solve the equation x 6x 1 0 Give our answers to two decimal places. You must show our working. Answer (Total 3 marks). Solve the equation x 6x 3 = 0 Give our answers in the form p ± q 3 where p and q are integers Answer (Total marks) Success: Target: St Paul s Catholic School 31

32 Teacher Assessment Section F Completing the Square Grade A A* 1. Find the values of a and b such that x 10x + 18 = (x a) + b Answer a =..., b =... (Total marks). x 8x + 10 = (x a) + b (a) Find the values of a and b. Answer a =...b =... (3) (b) Hence find the minimum value of x 8x + 10 Answer... (Total marks) St Paul s Catholic School 3

33 3. (a) Find the values of a and b such that x + 10x + 0 = (x + a) + b Answer a =..., b =... (b) Hence, or otherwise, write down the minimum value of x + 10x + 0 Answer... (Total 3 marks). x 6x + 13 = (x a) + b (a) Find the values of a and b..... Answer a =... b =... (3) (b) Hence find the minimum value of x 6x Answer... (Total marks) St Paul s Catholic School 33

34 5. (a) Find the values of a and b such that x + 6x 3 = (x + a) + b Answer a =..., b =... (b) Hence, or otherwise, solve the equation x + 6x 3 = 0 giving our answers in surd form Answer... (3) (Total 5 marks) St Paul s Catholic School 3

35 6. (a) Find the values of a and b such that x 6 x 11 ( x a) b... Answer a, b (3) (b) Hence, or otherwise, solve the equation x 6x 11 0 Give our answers in surd form (a) Find the values of a and b such that x + 8x 5 (x + a) + b Answer (Total 5 marks) Answer a =... b =... (b) Hence, or otherwise, solve the equation x + 8x 5 = 0 Give our answers in surd form. Answer... (Total marks) St Paul s Catholic School 35

36 8. (a) Find the values of a and b such that x + 6x 3 = (x + a) + b Answer a =..., b =... (b) Hence, or otherwise, solve the equation x + 6x 3 = 0 giving our answers in surd form Answer... (3) (Total 5 marks) Success: Target: St Paul s Catholic School 36

37 Teacher Assessment Section F Quadratics Problem Solving Grade A A* 1. Mand is x ears old. Her brother is 5 ears older than Mand. The product of their ages is 8. (a) Show that x + 5x 8 = 0 (b) Solve x + 5x 8 = 0 Do not use a trial and improvement method. Answer x =... (3) (Total marks) St Paul s Catholic School 37

38 . A trapezium has parallel sides of length (x + 1) cm and (x + ) cm. The perpendicular distance between the parallel sides is x cm. The area of the trapezium is 10 cm. ( x + 1) cm Not drawn accuratel x cm ( x + ) cm Find the value of x Answer x =... cm (Total 5 marks) St Paul s Catholic School 38

39 3. The diagrams show a rectangle and an L shape All the angles are right angles. All lengths are in centimetres. The shapes are equal in area. Diagrams not to scale x 3 x + 3x x Calculate the value of Answer... cm (Total 6 marks) St Paul s Catholic School 39

40 x. Solve the equation 1 x 1 x 1 5. Solve the equation 1 5x 3 x 1 x Answer... (Total 5 marks) (Total 5 marks) Success: Target: St Paul s Catholic School 0