Rearrange equations and proof/identities – Further Maths

Last updated: 07/03/2020

Summer Start for A-Level Maths Algebra Rearrange equations and proof/identities – Further Maths

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Question 1 of 45

1. Question
Make x the subject of y = 12x
- x = y / 12
- x = 12 / y
- x = y + 12
- x = 12y
Correct

Incorrect
Question 2 of 45

2. Question
Make x the subject of y = x / 3
- x = 3y
- x = y / 3
- x = 3 / y
- x = y – 3
Correct

Incorrect
Question 3 of 45

3. Question
Make x the subject of y = x + 4
- x = y – 4
- x = y + 4
- x = y / 4
- x = 4y
Correct

Incorrect
Question 4 of 45

4. Question
Make x the subject of y = 8 – x
- x = 8 – y
- x = y – 8
- x = 8y
- x = y + 8
Correct

Incorrect
Question 5 of 45

5. Question
Make x the subject of y = 4x + 8
- x = (y – 8) / 4
- x = 4y + 8
- x = 8y + 4
- x = 4 / (y – 8)
Correct

Incorrect
Question 6 of 45

6. Question
Make x the subject of y = (x + 8) / 3
- x = 3y – 8
- x = 3y – 24
- x = 24y – 3
- x = (y + 8) / 3
Correct

Incorrect
Question 7 of 45

7. Question
Make x the subject of y = x / (2 + 11)
- x = 13y
- x = (y + 11) / 2
- x = 2 / (y + 11)
- x = 2y – 11
Correct

Incorrect
Question 8 of 45

8. Question
Make x the subject of y = 10x – 3
- x = (y + 3) / 10
- x = 10y + 3
- x = 10 / (y + 3)
- x = 3y – 10
Correct

Incorrect
Question 9 of 45

9. Question
Make x the subject of y = (x – 6) / 3
- x = 3y + 6
- x = 3y – 6
- x = (y – 6) / 3
- x = 3 / (y – 6)
Correct

Incorrect
Question 10 of 45

10. Question
Make x the subject of y = x / 4 – 4
- x = 4y + 16
- x = 4y + 4
- x = 4y + 10
- x = (y – 4) / 4
Correct

Incorrect
Question 11 of 45

11. Question
Make x the subject of y = (7x + 4) / 6
- x = (6y – 4) / 7
- x = (6y – 7) / 4
- x = (42 – y) / 7
- x = 6y – 4
Correct

Incorrect
Question 12 of 45

12. Question
Make x the subject of y = (8x – 5) / 8
- x = (8y + 5) / 8
- x = (8y + 8) / 5
- x = (8y + 5) / 6
- x = (64 + y) / 8
Correct

Incorrect
Question 13 of 45

13. Question
Make x the subject of 7x + 6y = 6
- x = (6 – 6y) / 7
- x = (7 – 7y) / 6
- x = 6y / 7
- x = (7 – 6y) / 6
Correct

Incorrect
Question 14 of 45

14. Question
Make x the subject of 6x – 5y = 7
- x = (5y + 7) / 6
- x = (5y – 7) / 6
- x = 5y + 13
- x = (5y + 7) / 5
Correct

Incorrect
Question 15 of 45

15. Question
Make x the subject of 7x – 6y = 4
- x = (6y + 4) / 7
- x = (6y – 4) / 7
- x = 28 – 6y
- x = 6y + 28
Correct

Incorrect
Question 16 of 45

16. Question
Make x the subject of (6x + 2y) / 5 = 7
- x = (35 – 2y) / 6
- x = (42 – 2y) / 5
- x = (30 – 7y) / 6
- x = (35 – 6y) / 2
Correct

Incorrect
Question 17 of 45

17. Question
Make x the subject of (8x – 5y) / 5 = 3
- x = (5y + 15) / 8
- x = (8y + 15) / 5
- x = (3y + 40) / 8
- x = (5y + 24) / 5
Correct

Incorrect
Question 18 of 45

18. Question
Make x the subject of (x – 11) $^2$ = y
- x = √y + 11
- x = y / 2 + 11
- x = (y – 11) $^2$
- x = y / 11
Correct

Incorrect
Question 19 of 45

19. Question
Make x the subject of (x + 14) $^2$ = y
- x = √y – 14
- x = y / 14
- x = (y + 14) $^2$
- x = √y + 14
Correct

Incorrect
Question 20 of 45

20. Question
Make x the subject of √(x – 14y) = 9
- x = 14y + 81
- x = 14y – 81
- x = y + 81
- x = 81 – 14y
Correct

Incorrect
Question 21 of 45

21. Question
Make x the subject of √(x + 5y) = 7
- x = 49 – 5y
- x = 14 – 5y
- x = 49 + 5y
- x = 49 – 7y
Correct

Incorrect
Question 22 of 45

22. Question
Make x the subject of y = √((x – 5) / 4)
- $x = 4y^2 + 5$
- x = √((y – 5) / 4)
- x = √((y + 5) / 4)
- x = 16y + 25
Correct

Incorrect
Question 23 of 45

23. Question
Make x the subject of y = √((x + 13) / 8)
- $x = 8y^2 - 13$
- $x = 8y - 13$
- $x = \sqrt((y -13) / 8)$
- $x = \sqrt((y -8) / 13)$
Correct

Incorrect
Question 24 of 45

24. Question
Make x the subject of 3x $^2$ – 4y = 14
- x = √((4y + 14) / 3)
- x = 588 – 4y
- x = √(14) – 4y / 3
- x = √((4y – 14) / 3)
Correct

Incorrect
Question 25 of 45

25. Question
Make x the subject of 5x $^2$ + 8y = 6
- x = √((8y – 6) / 5)
- x = √((8y – 5) / 6)
- x = 8y + 180
- x = √(6) + 8y / 5
Correct

Incorrect
Question 26 of 45

26. Question
Make x the subject of 14x – y = xy + 9
- x = (y + 9) / (14 – y)
- x = (y – 9) / (y – 14)
- x = (14 – y) / (y – 9)
- x = (14 – y) / (y + 9)
Correct

Incorrect
Question 27 of 45

27. Question
Make x the subject of 12x + y = xy – 13
- x = (y + 13) / (y – 12)
- x = (y – 13) / (y + 12)
- x = (y – 12) / (y + 13)
- x = (y + 12) / (y – 13)
Correct

Incorrect
Question 28 of 45

28. Question
Make x the subject of (4y + 2x) / xy = 8
- x = 4y / (8y – 2)
- x = 12y – 2
- x = (4y + 16) / 8y
- x = 4y / (8y + 2)
Correct

Incorrect
Question 29 of 45

29. Question
Make x the subject of (4y – 5x) / xy = 9
- x = 4y / (9y + 5)
- x = 13y + 5
- x = 4y / (9y – 5)
- x = (4y – 45) / 9y
Correct

Incorrect
Question 30 of 45

30. Question
Make x the subject of (13y – 7x) / xy = 12
- x = 13y / (12y + 7)
- x = (13y – 84) / 12y
- x = 13y / (12y – 7)
- x = 25y + 7
Correct

Incorrect
Question 31 of 45

31. Question
Show that 3(x – 6) + 9(x – 2) ≡ 12(x – 3)
- 3x – 18 + 9x – 18 ≡ 12x – 36 ≡ 12(x – 3)
- 3x – 18 + 10x – 20 ≡ 13x – 38 ≡ 12(x – 3)
- 2x – 12 + 9x – 18 ≡ 11x – 30 ≡ 12(x – 3)
- 4x – 24 + 9x – 18 ≡ 13x – 42 ≡ 12(x – 3)
Correct

Incorrect
Question 32 of 45

32. Question
Show that 9(x – 6) + 6(x – 1) ≡ 15(x – 4)
- 9x – 54 + 6x – 6 ≡ 15x – 60 ≡ 15(x – 4)
- 9x – 54 + 7x – 7 ≡ 16x – 61 ≡ 15(x – 4)
- 8x – 48 + 6x – 6 ≡ 14x – 54 ≡ 15(x – 4)
- 9x – 54 + 6x – 5 ≡ 15x – 59 ≡ 15(x – 4)
Correct

Incorrect
Question 33 of 45

33. Question
Show that 4(x – 5) + 2(x – 2) ≡ 6(x – 4)
- 4x – 20 + 2x – 4 ≡ 6x – 24 ≡ 6(x – 4)
- 4x – 20 + 2x – 2 ≡ 5x – 22 ≡ 6(x – 4)
- 3x – 15 + 2x – 4 ≡ 5x – 19 ≡ 6(x – 4)
- 5x – 25 + 2x – 4 ≡ 7x – 29 ≡ 6(x – 4)
Correct

Incorrect
Question 34 of 45

34. Question
Show that 4(x – 5) – 2(x – 8) ≡ 2(x – 2)
- 4x – 20 – 2x + 16 ≡ 2x – 4 ≡ 2(x – 2)
- 5x – 25 – 2x + 16 ≡ 2x + 9≡ 2(x – 2)
- 5x – 25 – 2x + 16 ≡ 3x – 9 ≡ 2(x – 2)
- 3x – 15 – 2x + 16 ≡ x – 1 ≡ 2(x – 2)
Correct

Incorrect
Question 35 of 45

35. Question
Show that 8(x – 7) – 3(x – 2) ≡ 5(x – 10)
- 8x – 56 – 3x + 6 ≡ 5x – 50 ≡ 5(x – 10)
- 9x – 63 – 3x + 6 ≡ 6x + 57 ≡ 5(x – 10)
- 9x – 63 – 3x + 6 ≡ 6x – 57 ≡ 5(x – 10)
- 8x – 56 – 2x + 4 ≡ 6x – 52 ≡ 5(x – 10)
Correct

Incorrect
Question 36 of 45

36. Question
Show that 8(x – 1) – 5(x – 4) ≡ 3 (x + 4)
- 8x – 8 – 5x + 20 ≡ 3x + 12 ≡ 3(x + 4)
- 7x – 7 – 5x + 20 ≡ 2x + 13 ≡ 3(x + 4)
- 9x – 9 – 5x + 20 ≡ 4x + 13 ≡ 3(x + 4)
- 8x – 8 – 6x + 24 ≡ 2x + 16 ≡ 3(x + 4)
Correct

Incorrect
Question 37 of 45

37. Question
Show that 5(x + 3) – 3(x + 7) ≡ 2(x – 3)
- 5x + 15 – 3x – 21 ≡ 2x – 6 ≡ 2(x – 3)
- 5x – 15 – 4x + 28 ≡ x + 13 ≡ 2(x – 3)
- 4x – 12 – 3x + 21 ≡ x + 9 ≡ 2(x – 3)
- 5x – 15 – 4x + 28 ≡ x – 13 ≡ 2(x – 3)
Correct

Incorrect
Question 38 of 45

38. Question
Show that 6(x + 6) – 4(x + 4) ≡ 2(x + 10)
- 6x + 36 – 4x – 16 ≡ 2x + 20 ≡ 2(x+10)
- 6x – 36 – 5x + 20 ≡ x + 16 ≡ 2(x+10)
- 6x – 36 – 3x + 12 ≡ 2x + 16 ≡ 2(x+10)
- 5x – 30 – 4x + 16 ≡ x – 14 ≡ 2(x+10)
Correct

Incorrect
Question 39 of 45

39. Question
Show that 6(x + 9) – 3(x + 7) ≡ 3(x + 11)
- 6x + 54 – 3x – 21 ≡ 3x + 33 ≡ 3(x + 11)
- 5x – 45 – 3x + 21 ≡ 2x – 24 ≡ 3(x + 11)
- 6x – 54 – 4x + 28 ≡ 2x + 26 ≡ 3(x + 11)
- 7x – 63 – 3x + 21 ≡ 2x + 42 ≡ 3(x + 11)
Correct

Incorrect
Question 40 of 45

40. Question
Prove that (x + 12) $^2$ – (x + 2) $^2$ is divisible by 20
- (x + 12)(x + 12) – (x + 2)(x + 2)x² + 12x + 12x + 12² – x² – 2x -2x -2², 20x + 14020(x + 7)
- (12x + 2)(12x + 2) – (12x – 2)(12x – 2)144x² + 48x + 4 – 144x² + 48x + 4104 x 4(26x)
- (12x + 2)(12x + 2) + (12x – 2)(12x – 2)144x + 43x + 4 – 144x² + 48x + 414 x 7(26x)
- (x + 12)(x + 12) – (x + 2)(x + 2)x² + 12x + 12x + 12² – x² + 2x + 2x + 2², 28x + 14828(x + 5)
Correct

Incorrect
Question 41 of 45

41. Question
Prove that (x + 9) $^2$ – (x + 5) $^2$ is divisible by 8
- (x + 9)(x + 9) – (x + 5)(x + 5)x² + 9x + 9x + 9² – x² – 5x – 5x – 5², 8x + 568(x + 7)
- (9x + 5)(9x + 5) – (9x – 5)(9x – 5)81x² + 25 – 81x² – 2550
- (x + 9)(x + 9) – (x + 5)(x + 5)x² + 9x + 9x + 9² – x² + 5x + 5x + 5², 28x + 10628(x + 4)
- (9x + 5)(9x + 5) – (9x – 5)(9x – 5)81x² + 90x + 25 – 81x² + 90x + 25230x, 10(23x)
Correct

Incorrect
Question 42 of 45

42. Question
Prove that (x + 5) $^2$ – (x + 3) $^2$ is divisible by 4
- (x + 5)(x + 5) – (x + 3)(x + 3)x² + 5x + 5x + 5² – x² – 3x – 3x – 3², 4x + 164(x + 4)
- x² + 25 – x² – 9², 16
- (5x + 3)(5x + 3) – (5x – 3)(5x – 3)25x² + 9 – 25x² – 9, 18
- (5x + 3)(5x + 3) – (5x – 3)(5x – 3)25x² + 30x + 9 – 25x² + 30x + 978 x 6(13x)
Correct

Incorrect
Question 43 of 45

43. Question
Prove that (8x + 7) $^2$ – (8x – 7) $^2$ is divisible by 56
- (8x + 7)(8x + 7) – (8x – 7)(8x – 7)64x² + 112x + 49 – 64x² + 112x – 49224x 56(4x)
- (10x + 7)(10x + 7) – (8x – 7)(8x – 7)6x² + 112x + 49 + 4x² + 112x – 49224
- (8x)(8x)64x² + 12x + 49 + 64x² + 112x – 49224 + 56(4x)
- (8x – 7)(8x – 7)64x² + 112x + 49 – 64x² + 112x – 49224 x 56(4x)
Correct

Incorrect
Question 44 of 45

44. Question
Prove that (8x + 3) $^2$ – (8x – 3) $^2$ is divisible by 3
- (8x + 3)(8x + 3) – (8x – 3)(8x – 3)64x² + 48x + 9 – 64x² + 48x – 996x 3(32x)
- (8x – 3)(8x – 3)64x² + 9 – 64x² + 48x – 96x 7(32x)
- (8x + 2)(8x + 2) – (8x – 3)(8x – 3)64x² + 10 – 64x²
- 48x + 9 – 64x² + 38x – 9x 3(32x)
Correct

Incorrect
Question 45 of 45

45. Question
Prove that (9x + 6) $^2$ – (9x – 6) $^2$ is divisible by 18
- (9x + 6)(9x + 6) – (9x – 6)(9x – 6)81x² + 108x + 36 – 81x² + 108x – 36216x 18(12x)
- (9x + 6)(9x + 6) – (9x – 6)(9x – 6)56x² + 134x + 36 – 81x² + 348x – 36216x 8(45x)
- (9x + 5)(9x + 5) + (10x – 6)(10x – 6)81x² + 10x + 36 – 81x² + 108x – 36x 18(12x)
- (10x + 6)(10x + 6) – (9x + 6)(9x + 6)81x² + 10x + 36 – 83x² + 18x – 36216x 12(2x)
Correct

Incorrect