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1 PLC Papers Created For: t followed by close scrutiny of the marking scheme followed by reassessing every 3 days to attain at least 8 out o
2 Approximate solutions to equations using iteration 1 Grade 9 Objective: Find approximate solutions to equations using iteration. Question 1. Find the first five iterations of each iterative formulae. Start each one with 1 = 4. a) +1 = b) +1 = c) +1 = (Total 3 marks)
3 Question 2. Starting with 1 = 1.6 find a root of the quadratic equation = 0 to 2 decimal places using the iterative formula +1 = (Total 3 marks)
4 Question 3. a) Show that = 0 can be rearranged into the iterative formula +1 = 3 1. b) Use the iterative formula and a starting value of 1 = 2 to obtain the solution to the equation correct to 2 decimal places. (3) (Total 4 marks) TOTAL /10
5 Approximate solutions to equations using iteration 2 Grade 9 Objective: Find approximate solutions to equations using iteration. Question 1. Find the first four iterations of each iterative formulae. Start each one with 1 = 6. a) +1 = b) +1 = c) +1 = (Total 3 marks) Question 2. Starting with 1 = 5.3 verify that 5.37 is a solution, correct to 2 decimal places, of the quadratic equation = 0 using iteration. (Total 3 marks)
6 Question 3. a) Show that = 4 9 can be rearranged into the equation = 0. b) Use the iterative formula +1 = 4 9 and a starting value of 1 = 0.5 to obtain the solution to the equation correct to 2 decimal places. (3) (Total 4 marks) TOTAL /10
7 Approximate solutions to equations using iteration 3 Grade 9 Objective: Find approximate solutions to equations using iteration, including suffix notation in recursive formula. Question 1. A rectangle has sides ( 2)cm and ( +5)cm and an area of 30cm 2. Starting with 1 =10.5 and using iteration, find the length of each side of the rectangle, correct to 2 decimal places. and (Total 5 marks)
8 Question 2. The graph of = is plotted below. One of the roots is = 4.54 accurate to 2 decimal places. Use iteration together with this graph to obtain the other root accurate to 2 decimal places. Total /10 = (Total 5 marks)
9 Approximate solutions to equations using iteration 4 Grade 9 Objective: Find approximate solutions to equations using iteration, including suffix notation in recursive formula. Question 1. A circle with radius ( +3)cm has an area of 40. Starting with 1 =3.4 and using iteration, find the value of correct to 2 decimal places. You must show all your iterations. = (Total 5 marks)
10 Question 2. Part of the graph of = 2 2sin is shown below. One of the roots is =0. Use iteration together with this graph of to obtain the other root accurate to 2 decimal places. Total /10 = (Total 5 marks)
11 PLC Papers Created For: t followed by close scrutiny of the marking scheme followed by reassessing every 3 days to attain at least 8 out o
12 Approximate solutions to equations using iteration 1 Grade 9 SOLUTIONS Objective: Find approximate solutions to equations using iteration. Question 1. Find the first five iterations of each iterative formulae. Start each one with 1 = 4. a) +1 = = 19, 3 = 64, 4 = 199, 5 = 604, 6 = 1819 (A1) b) +1 = = 2, 3 = 6, 4 = 2, 5 = 14, 6 = 18 (A1) c) +1 = = 1, 3 = 1 2, 4 = 5 4, 5 = 13 8, 6 = (A1) (Total 3 marks) Question 2. Starting with 1 = 1.6 find a root of the quadratic equation = 0 to 2 decimal places using the iterative formula +1 = = = = = 4 to 2dp = 1.58 (C1) (A1) (Total 3 marks)
13 Question 3. a) Show that = 0 can be rearranged into the iterative formula +1 = = 3 1 = = 3 1 b) Use the iterative formula and a starting value of 1 = 2 to obtain the solution to the equation correct to 2 decimal places. 2 = = = = = = = = = = 10 to 2dp = 2.61 (C1) (A1) (3) (Total 4 marks) TOTAL /10
14 Approximate solutions to equations using iteration 2 Grade 9 SOLUTIONS Objective: Find approximate solutions to equations using iteration. Question 1. Find the first four iterations of each iterative formulae. Start each one with 1 = 6. a) +1 = = 26, 3 = 126, 4 = 626, 5 = 3126, (A1) a) +1 = 2 2 = 8, 3 = 9, 4 = 9.5, 5 = 9.75, (A1) b) +1 = = 2, 3 = 14, 3 4 = 42, 17 5 = (A1) (Total 3 marks) Question 2. Starting with 1 = 5.3 verify that 5.37 is a solution, correct to 2 decimal places, of the quadratic equation = 0 using iteration. +1 = = = = = = = 6 to 2dp (C1) (Total 3 marks)
15 Question 3. a) Show that = 4 9 can be rearranged into the equation = 0. = = = 0 b) Use the iterative formula +1 = 4 9 and a starting value of 1 = 0.5 to obtain a solution to the equation correct to 2 decimal places. 2 = 1 3 = 13 4 = = = = = 7 to 2dp = 9.42 (C1) (A1) (3) (Total 4 marks) TOTAL /10
16 Approximate solutions to equations using iteration 3 Grade 9 SOLUTION Objective: Find approximate solutions to equations using iteration, including suffix notation in recursive formula. Question 1. A rectangle has sides ( 2)cm and ( +5)cm and an area of 30cm 2. Starting with 1 =10.5 and using iteration, find the length of each side of the rectangle, correct to 2 decimal places. ( 2)( +5)= = =0 2 =7 +40 = = = = = = = = 6 = to 2dp (C1) 8.73 and (A1) (Total 5 marks)
17 Question 2. The graph of = is plotted below. One of the roots is = 4.54 accurate to 2 decimal places. Use iteration together with this graph to obtain the other root accurate to 2 decimal places. = = 7 3 Suitable 1 used in the range value found = for their values to 2dp (C1) (A1) = (Total 5 marks) Total /10
18 Approximate solutions to equations using iteration 4 Grade 9 SOLUTION Objective: Find approximate solutions to equations using iteration, including suffix notation in recursive formula. Question 1. A circle with radius ( +3)cm has an area of 40. Starting with 1 =3.4 and using iteration, find the value of correct to 2 decimal places. You must show all your iterations. ( +3) 2 =40 ( +3) 2 = = =0 2 =31 6 = = = = = = = = = 7 = 3.37 to 2dp (A1) = (Total 5 marks)
19 Question 2. Part of the graph of = 2 2sin is shown below. One of the roots is =0. Use iteration together with this graph of to obtain the other root accurate to 2 decimal places. = 2sin +1 = 2sin Suitable 1 used in the range 1.2< 1 <1.5 2 value found = for their values to 2dp =1.40 (C1) (A1) = (Total 5 marks) Total /10
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