Solve equations with iterative methods – Further Maths

Last updated: 07/03/2020

Summer Start for A-Level Maths Algebra Solve equations with iterative methods – Further Maths

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Question 1 of 45

1. Question
Show that x $^3$ = 2 has a solution between 1 and 2
- When x = 1, you get 1 which is too small and when x = 2, you get 8 which is too big.
- When x = 1, you get 1 which is too small and when x = 2, you get 27 which is too big.
- When x = 1, you get 1 which is too small and when x = 2, you get 1 which is too big.
- When x = 1, you get 8 which is too small and when x = 2, you get 8 which is too big.
Correct

Incorrect
Question 2 of 45

2. Question
Show that x $^3$ = 13 has a solution between 2 and 3
- When x = 2, you get 8 which is too small and when x = 3, you get 27 which is too big.
- When x = 2, you get 8 which is too small and when x = 3, you get 64 which is too big.
- When x = 2, you get 8 which is too small and when x = 3, you get 27 which is too big.
- When x = 2, you get 4 which is too small and when x = 3, you get 9 which is too big.
- When x = 2, you get 27 which is too small and when x = 3, you get 8 which is too big.
Correct

Incorrect
Question 3 of 45

3. Question
Show that x $^3$ = -34 has a solution between -4 and -3
- When x = -4, you get -64 which is too small and when x = -3, you get -27 which is too big.
- When x = -4, you get -27 which is too small and when x = -3, you get -64 which is too big.
- When x = -4, you get 64 which is too small and when x = -3, you get 27 which is too big.
- When x = -4, you get -125 which is too small and when x = -3, you get -27 which is too big.
Correct

Incorrect
Question 4 of 45

4. Question
Show that x $^3$ = -65 has a solution between -5 and -4
- When x = -5, you get -125 which is too small and when x = -4, you get -64 which is too big.
- When x = -5, you get -25 which is too small and when x = -4, you get -64 which is too big.
- When x = -5, you get -64 which is too small and when x = -4, you get -64 which is too big.
- When x = -5, you get -125 which is too small and when x = -4, you get -125 which is too big.
Correct

Incorrect
Question 5 of 45

5. Question
Show that x $^3$ – 5x = 63 has a solution between 4 and 5
- When x = 4, you get 44 which is too small and when x = 5, you get 100 which is too big.
- When x = 4, you get 16 which is too small and when x = 5, you get 25 which is too big.
- When x = 4, you get 100 which is too small and when x = 5, you get 100 which is too big.
- When x = 4, you get 44 which is too small and when x = 5, you get 44 which is too big.
Correct

Incorrect
Question 6 of 45

6. Question
Show that x $^3$ – x = 76 has a solution between 4 and 5
- When x = 4, you get 60 which is too small and when x = 5, you get 120 which is too big.
- When x = 4, you get -60 which is too small and when x = 5, you get -120 which is too big.
- When x = 4, you get 24 which is too small and when x = 5, you get 120 which is too big.
- When x = 4, you get 120 which is too small and when x = 5, you get 120 which is too big.
Correct

Incorrect
Question 7 of 45

7. Question
Show that x $^3$ = -15 has a solution between -3 and -2
- When x = -3, you get -27 which is too small and when x = -2, you get -8 which is too big.
- When x = -3, you get -27 which is too small and when x = -2, you get -1 which is too big.
- When x = -3, you get -8 which is too small and when x = -2, you get -27 which is too big.
- When x = -3, you get -27 which is too small and when x = -2, you get -27 which is too big.
Correct

Incorrect
Question 8 of 45

8. Question
Show that x $^3$ + x = -35 has a solution between -4 and -3
- When x = -4, you get -68 which is too small and when x = -3, you get -30 which is too big.
- When x = 4, you get -68 which is too small and when x = 3, you get -30 which is too big.
- When x = -4, you get 68 which is too small and when x = -3, you get 30 which is too big.
- When x = -4, you get -30 which is too small and when x = -3, you get -30 which is too big.
Correct

Incorrect
Question 9 of 45

9. Question
Show that x $^3$ + 5x = -66 has a solution between -4 and -3
- When x = -4, you get -84 which is too small and when x = -3, you get -42 which is too big.
- When x = -4, you get 84 which is too small and when x = -3, you get 42 which is too big.
- When x = -4, you get -42 which is too small and when x = -3, you get -42 which is too big.
- When x = -4, you get -84 which is too small and when x = -3, you get -84 which is too big.
Correct

Incorrect
Question 10 of 45

10. Question
Show that x $^3$ + 3x $^2$ = 40 has a solution between 2 and 3
- When x = 2, you get 20 which is too small and when x = 3, you get 54 which is too big.
- When x = 2, you get -20 which is too small and when x = 3, you get -54 which is too big.
- When x = 2, you get 25 which is too small and when x = 3, you get 50 which is too big.
- When x = 2, you get 10 which is too small and when x = 3, you get 25 which is too big.
Correct

Incorrect
Question 11 of 45

11. Question
Show that x $^3$ + x $^2$ + 3x = 36 has a solution between 2 and 3
- When x = 2, you get 18 which is too small and when x = 3, you get 45 which is too big.
- When x = 2, you get 18 which is too small and when x = 3, you get 92 which is too big.
- When x = 2, you get 45 which is too small and when x = 3, you get 45 which is too big.
- When x = 2, you get 18 which is too small and when x = 3, you get 18 which is too big.
Correct

Incorrect
Question 12 of 45

12. Question
Show that x $^3$ + 3x $^2$ + 3x = 70 has a solution between 3 and 4
- When x = 3, you get 63 which is too small and when x = 4, you get 124 which is too big.
- When x = 3, you get 26 which is too small and when x = 4, you get 124 which is too big.
- When x = 3, you get 63 which is too small and when x = 4, you get 63 which is too big.
- When x = 3, you get 63 which is too small and when x = 4, you get 124 which is too small.
Correct

Incorrect
Question 13 of 45

13. Question
Show that x $^3$ – 4x $^2$ + 4x = -64 has a solution between -3 and -2
- When x = -3, you get -75 which is too small and when x = -2, you get -32 which is too big.
- When x = -3, you get 75 which is too small and when x = -2, you get 32 which is too big.
- When x = -3, you get -75 which is too small and when x = -2, you get -75 which is too big.
- When x = -3, you get -32 which is too small and when x = -2, you get -32 which is too big.
Correct

Incorrect
Question 14 of 45

14. Question
Show that x $^3$ – 4x $^2$ – 2x = -49 has a solution between -3 and -2
- When x = -3, you get -57 which is too small and when x = -2, you get -20 which is too big.
- When x = -3, you get 57 which is too small and when x = -2, you get 20 which is too big.
- When x = -3, you get -57 which is too small and when x = -2, you get -57 which is too big.
- When x = -3, you get -20 which is too small and when x = -2, you get -20 which is too big.
Correct

Incorrect
Question 15 of 45

15. Question
Show that x[late]^3[/latex] + 3x $^2$ + 2x = -10 has a solution between -4 and -3
- When x = -4, you get -24 which is too small and when x = -3, you get -6 which is too big.
- When x = -4, you get 24 which is too small and when x = -3, you get 6 which is too big.
- When x = -4, you get -24 which is too small and when x = -3, you get -24 which is too big.
- When x = -4, you get -6 which is too small and when x = -3, you get -6 which is too big.
Correct

Incorrect
Question 16 of 45

16. Question
x $^3$ = 63 has a solution between 3 and 4, find the solution to 1DP
- x ≈ 4.0
- x ≈ 4.2
- x ≈ 4.1
- x ≈ 3.9
Correct

Incorrect
Question 17 of 45

17. Question
x $^3$ = 10 has a solution between 2 and 3, find the solution to 1DP
- x ≈ 2.2
- x ≈ 2.4
- x ≈ 2.3
- x ≈ 2.1
Correct

Incorrect
Question 18 of 45

18. Question
x $^3$ = -56 has a solution between -4 and -3, find the solution to 1DP
- x ≈ -3.8
- x ≈ -3.9
- x ≈ -3.7
- x ≈ -3.0
Correct

Incorrect
Question 19 of 45

19. Question
x $^3$ = -24 has a solution between -3 and -2, find the solution to 1DP
- x ≈ -2.9
- x ≈ -2.0
- x ≈ -2.7
- x ≈ -2.1
Correct

Incorrect
Question 20 of 45

20. Question
x $^3$ = 35 has a solution between 3 and 4, find the solution to 1DP
- x ≈ 3.3
- x ≈ 3.2
- x ≈ 3.4
- x ≈ 3.1
Correct

Incorrect
Question 21 of 45

21. Question
x $^3$ + x = 58 has a solution between 3 and 4, find the solution to 1DP
- x ≈ 3.8
- x ≈ 4.0
- x ≈ 3.7
- x ≈ 3.9
Correct

Incorrect
Question 22 of 45

22. Question
x $^3$ – 3x = -14 has a solution between -3 and -2, find the solution to 1DP
- x ≈ -2.8
- x ≈ -2.6
- x ≈ -2.0
- x ≈ -2.7
Correct

Incorrect
Question 23 of 45

23. Question
x $^3$ + x = -36 has a solution between -4 and -3, find the solution to 1DP
- x ≈ -3.2
- x ≈ -3.0
- x ≈ -3.1
- x ≈ -3.3
Correct

Incorrect
Question 24 of 45

24. Question
x $^3$ + 3x = -61 has a solution between -4 and -3, find the solution to 1DP
- x ≈ -3.7
- x ≈ -3.8
- x ≈ -3.6
- x ≈ -3.9
Correct

Incorrect
Question 25 of 45

25. Question
x $^3$ + 2x = 14 has a solution between 2 and 3, find the solution to 1DP
- x ≈ 2.1
- x ≈ 2.9
- x ≈ 2.2
- x ≈ 2.0
Correct

Incorrect
Question 26 of 45

26. Question
x $^3$ + x $^2$ + 2x = 59 has a solution between 3 and 4, find the solution to 1DP
- x ≈ 3.4
- x ≈ 3.6
- x ≈ 3.5
- x ≈ 3.3
Correct

Incorrect
Question 27 of 45

27. Question
x $^3$ + 2x $^2$ + 2x = 72 has a solution between 3 and 4, find the solution to 1DP
- x ≈ 3.5
- x ≈ 3.6
- x ≈ 3.3
- x ≈ 3.4
Correct

Incorrect
Question 28 of 45

28. Question
x $^3$ – x $^2$ = -72 has a solution between -4 and -3, find the solution to 1DP
- x ≈ -3.9
- x ≈ -3.1
- x ≈ -3.7
- x ≈ -3.8
Correct

Incorrect
Question 29 of 45

29. Question
x $^3$ – 4x $^2$ – 3x = -79 has a solution between -4 and -3, find the solution to 1DP
- x ≈ -3.5
- x ≈ -3.3
- x ≈ -3.4
- x ≈ -3.6
Correct

Incorrect
Question 30 of 45

30. Question
x $^3$ – 2x $^2$ + x = -49 has a solution between -4 and -3, find the solution to 1DP
- x ≈ -3.0
- x ≈ -3.9
- x ≈ -3.8
- x ≈ -3.2
Correct

Incorrect
Question 31 of 45

31. Question
x $^3$ = 43 has a solution between 3 and 4, find the solution to 2DP
- x ≈ 3.50
- x ≈ 3.51
- x ≈ 3.52
- x ≈ 3.53
Correct

Incorrect
Question 32 of 45

32. Question
x $^3$ = 38 has a solution between 3 and 4, find the solution to 2DP
- x ≈ 3.36
- x ≈ 3.34
- x ≈ 3.38
- x ≈ 3.37
Correct

Incorrect
Question 33 of 45

33. Question
x $^3$ = 78 has a solution between 4 and 5, find the solution to 2DP
- x ≈ 4.27
- x ≈ 4.25
- x ≈ 4.29
- x ≈ 4.26
Correct

Incorrect
Question 34 of 45

34. Question
x $^3$ = 55 has a solution between 3 and 4, find the solution to 2DP
- x ≈ 3.80
- x ≈ 3.81
- x ≈ 3.83
- x ≈ 3.79
Correct

Incorrect
Question 35 of 45

35. Question
x $^3$ – 5x = 76 has a solution between 4 and 5 ,find the solution to 2DP
- x ≈ 4.63
- x ≈ 4.65
- x ≈ 4.64
- x ≈ 4.61
Correct

Incorrect
Question 36 of 45

36. Question
x $^3$ + 4x = 3 has a solution between 0 and 1, find the solution to 2DP
- x ≈ 0.67
- x ≈ 0.65
- x ≈ 0.68
- x ≈ 0.69
Correct

Incorrect
Question 37 of 45

37. Question
x $^3$ = 58 has a solution between 3 and 4, find the solution to 2DP
- x ≈ 3.87
- x ≈ 3.85
- x ≈ 3.88
- x ≈ 3.89
Correct

Incorrect
Question 38 of 45

38. Question
x $^3$ – 5x = 31 has a solution between 3 and 4, find the solution to 2DP
- x ≈ 3.67
- x ≈ 3.66
- x ≈ 3.65
- x ≈ 3.68
Correct

Incorrect
Question 39 of 45

39. Question
x $^3$ = 48 has a solution between 3 and 4, find the solution to 2DP
- x ≈ 3.63
- x ≈ 3.62
- x ≈ 3.61
- x ≈ 3.65
Correct

Incorrect
Question 40 of 45

40. Question
x $^3$ + 3x $^2$ + 4x = 4 has a solution between 0 and 1, find the solution to 2DP
- x ≈ 0.63
- x ≈ 0.62
- x ≈ 0.64
- x ≈ 0.65
Correct

Incorrect
Question 41 of 45

41. Question
x $^3$ – x $^2$ + 3x = 8 has a solution between 1 and 2, find the solution to 2DP
- x ≈ 1.80
- x ≈ 1.81
- x ≈ 1.83
- x ≈ 1.82
Correct

Incorrect
Question 42 of 45

42. Question
x $^3$ + 4x $^2$ – x = 45 has a solution between 2 and 3, find the solution to 2DP
- x ≈ 2.67
- x ≈ 2.66
- x ≈ 2.68
- x ≈ 2.69
Correct

Incorrect
Question 43 of 45

43. Question
x $^3$ – 4x $^2$ + 2x = 16 has a solution between 4 and 5, find the solution to 2DP
- x ≈ 4.38
- x ≈ 4.40
- x ≈ 4.36
- x ≈ 4.39
Correct

Incorrect
Question 44 of 45

44. Question
x $^3$ + x $^2$ + 2x = 55 has a solution between 3 and 4, find the solution to 2DP
- x ≈ 3.34
- x ≈ 3.32
- x ≈ 3.36
- x ≈ 3.33
Correct

Incorrect
Question 45 of 45

45. Question
x $^3$ + 3x $^2$ – 2x = 30 has a solution between 2 and 3, find the solution to 2DP
- x ≈ 2.52
- x ≈ 2.53
- x ≈ 2.51
- x ≈ 2.54
Correct

Incorrect