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PLC Papers Created For: Year 11 Topic Practice Paper: Solving Quadratics (Graphically)

Quadratic equations (graphical methods) 1 Grade 6 Objective: Find approximate solutions to quadratic equations using a graph Question 1. a) Complete the table below to work out values for the graph of = 2 +2 8 for values of x from 5 4. Plot the graph using 5 4 and 10 20. b) Use your graph to estimate the solutions of the two roots of 2 +2 8=0 (Total 3 marks)

Question 2. a) Complete the table below to work out values for the graph of =2 2 3 6 for values of x from 2 4 then draw the graph. b) Use your graph to find the y-value when =1.5 (Total 3 marks)

Question 3. a) Using suitable axes draw the graph of = 2 4 2 for 2 5 b) What is the value of when = 0.5 c) For what values of x does 2 4 2= 4 (Total 4 marks) TOTAL /10

Quadratic equations (graphical methods) 2 Grade 6 Objective: Find approximate solutions to quadratic equations using a graph Question 1. a) Complete the table below to work out values for the graph of = 2 3 3 for values of x from 3 5. Plot the graph using 3 5 and 10 15. b) Use your graph to estimate the solutions of the two roots of 2 3 3 = 0 Question 2. (Total 3 marks)

a) Complete the table below to work out values for the graph of = 2 2 4 7 for values of x from 2 4 then draw the graph. b) Use your graph to find the y-value when = 3.5 (Total 3 marks)

Question 3. a) Using suitable axes draw the graph of = 2 5 + 2 for 2 6 b) What is the value of when = 1.5 c) For what values of x does 2 4 2 = 4 (Total 4 marks) TOTAL /10

Quadratic equations (graphical methods) 3 Grade 6 Objective: Find approximate solutions to quadratic equations using a graph Question 1. A ball thrown straight up in the air from a starting point 2 above ground level at a speed of 12 / has a height h at any time that is given by the equation: h = 2 + 12 5 2 a) Draw the graph of the path of the ball for 0 3 b) Use your graph to estimate the time that the ball will hit the ground. c) Use your graph to estimate the highest point the ball reaches. (Total 5 marks)

Question 2. When a driver needs to stop a car, the approximate stopping distance (d) in feet is given by the equation: = 0.05 2 + 2.2 h h h h a) Draw the graph of the stopping distance for 0 50 b) Use your graph to estimate the speed that requires a stopping distance of 150 c) Use your graph to estimate the stopping distance for car travelling at 20 h Total /10 (Total 5 marks)

Quadratic equations (graphical methods) 4 Grade 6 Objective: Find approximate solutions to quadratic equations using a graph Question 1. A scientific study found that a driver s reaction time ( ) to audio stimuli and their reaction time ( ) to visual stimuli (both measured in milliseconds) can be modelled by the following equations: ( ) = 0.0051 2 0.319 + 15 16 70 ( ) = 0.005 2 0.23 + 22 16 70 a) On the same set of axes, draw both graphs for 16 70

b) Estimate the reaction time to audio stimuli for a 45 driver c) Estimate the reaction time to visual stimuli for a 65 driver d) Compare and contrast a driver s reaction audio and visual stimuli throughout their life Total /10 (Total 10 marks)

PLC Papers Created For: Year 11 Topic Practice Paper: Solving Quadratics (Graphically)

Quadratic equations (graphical methods) 1 Grade 6 Solutions Objective: Find approximate solutions to quadratic equations using a graph Question 1. a) Complete the table below to work out values for the graph of = 2 + 2 8 for values of x from 5 4. Plot the graph using 5 4 and 10 20. b) Use your graph to estimate the solutions of the two roots of 2 + 2 8 = 0 4.5 3.5 1.5 2.5 (A1 (Total 3 marks)

Question 2. a) Complete the table below to work out values for the graph of = 2 2 3 6 for values of x from 2 4 then draw the graph. b) Use your graph to find the y-value when = 1.5 6.5 < < 5.5 (Total 3 marks)

Question 3. a) Using suitable axes draw the graph of = 2 4 2 for 2 5 b) What is the value of when = 0.5 0.25 0.25 c) For what values of x does 2 4 2 = 4 0.25 0.75 and 3.25 3.75 (Total 4 marks) TOTAL /10

Quadratic equations (graphical methods) 2 Grade 6 SOLUTIONS Objective: Find approximate solutions to quadratic equations using a graph Question 1. a) Complete the table below to work out values for the graph of = 2 3 5 for values of x from 3 5. Plot the graph using 3 5 and 10 15. b) Use your graph to estimate the solutions of the two roots of 2 3 5 = 0 1.5 < < 0.5 3.5 < < 4.5 (Total 3 marks)

Question 2. a) Complete the table below to work out values for the graph of = 2 2 4 7 for values of x from 2 4 then draw the graph. b) Use your graph to find the y-value when = 3.5 0 < < 1 (Total 3 marks)

Question 3. a) Using suitable axes draw the graph of = 2 5 + 2 for 2 6 b) What is the value of when = 1.5 4 < < 3 c) For what values of x does 2 4 2 = 4 1 < < 0 5 < < 6 (Total 4 marks) TOTAL /10

Quadratic equations (graphical methods) 3 Grade 6 SOLUTIONS Objective: Find approximate solutions to quadratic equations using a graph Question 1. A ball thrown straight up in the air from a starting point 2 above ground level at a speed of 12 / has a height h at any time that is given by the equation: h = 2 + 12 5 2 a) Draw the graph of the path of the ball for 0 3 (A2) b) Use your graph to estimate the time that the ball will hit the ground. 2 < < 3 c) Use your graph to estimate the highest point the ball reaches. 9 < h < 9.5 (Total 5 marks)

Question 2. When a driver needs to stop a car, the approximate stopping distance (d) in feet is given by the equation: = 0.05 2 + 2.2 h h h h a) Draw the graph of the stopping distance for 0 50 (A2) b) Use your graph to estimate the speed that requires a stopping distance of 150 35 < < 40 c) Use your graph to estimate the stopping distance for car travelling at 20 h 62 < < 67 (Total 5 marks) Total /10

Quadratic equations (graphical methods) 4 Grade 6 SOLUTIONS Objective: Find approximate solutions to quadratic equations using a graph Question 1. A scientific study found that a driver s reaction time ( ) to audio stimuli and their reaction time ( ) to visual stimuli (both measured in milliseconds) can be modelled by the following equations: ( ) = 0.0051 2 0.319 + 15 16 70 ( ) = 0.005 2 0.23 + 22 16 70 a) On the same set of axes, draw both graphs for 16 70 (A2) (A4) b) Estimate the reaction time to audio stimuli for a 45 driver 10 < ( ) < 12 c) Estimate the reaction time to visual stimuli for a 65 driver 28 < ( ) < 30

d) Compare and contrast a driver s reaction audio and visual stimuli throughout their life Reaction to audio stimuli is always faster than reaction to visual stimuli for any age. Reactions to both stimuli slow with age once beyond 30 years The fastest response times to visual stimuli are given by people in their early 20s The fastest response times to audio stimuli are given by people about 30 years old. (any two of the above or other justified comment B2) (Total 10 marks) Total /10

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