1. EVERYTHING YOU NEED TO KNOW TO GET A GRADE C ALGEBRA (FOUNDATION)

2. a + 2 x b + 3 x c 7 + 2 x 3 + 3 x 5 7 + 6 + 15 BODMAS says you multiply before you add 28 a x b x c Replace the letters with their respective numbers 7 x 3 x 5 105 105 x d = 0Anything multiplied by zero is zero. So, d must equal zero. 0

3. C = 16 + 24 x 10 BODMAS says you multiply before you add C = 16 + 240 256 24 months 12 months in a year 2 C = d + 24 x m 600 = 120 + 24m Solve the equation to work out m 480 = 24m 20 = m 20

4. 5 x 4 20 2 x 4 + 3y = 5 8 + 3y = 5 3y = -3 3 x 4 - -1 12 + 1 13

5. Replace p with 4 and q with -7 5 x 4 + 2 x -7 20 - 14 6 Replace u with 5 and v with 3 5 x 5 – 3 x 3 25 – 9 16

6. 5 £5 + 100 x 5p £5 + 500p £5 + £5 10 £7.50 - £5 = £2.50 Cost for calls after £5 a month charge has been taken off Minutes of calls = Cost for calls after £5 a month charge has been taken off Cost per minute for calls 50

7. Perimeter is the length around a shape + 6y 56 + 6y = 68 Solve the equation to work out the value of y 6y = 12 y = 2 2

8. + 7y Replace p with 4 and q with -7 5 x 4 + 2 x -7 20 - 14 6 Replace u with 5 and v with 3 5 x 5 – 3 x 3 25 – 9 16

9. 7c - 3y

10. 12a - 3b Remember a minus and a minus is only a plus when you multiply, divide or when the signs are together. When you add or subtract you use a number line.

11. 3a 6b + 10 12

12. - 4 + 18 + 14

13. + 5

14. a x a x a x a x a x a When you multiply powers with the same base you can just add the powers b x b x b x b x b x b x b x b x b b x b x b When you divide powers with the same base you can just subtract the powers 1

15. When you multiply powers with the same base you can just add the powers y x y x y x y x y x y x y x y y x y x y x y x y When you divide powers with the same base you can just subtract the powers

16. y x y x y x y x y x y x y x y x y When you multiply powers with the same base you can just add the powers y x y x y x y x y x y x y y x y When you divide powers with the same base you can just subtract the powers When you have powers and brackets you can just multiply the powers Part (iii) A negative number to the power of an even number makes a positive As you multiply a decimal by itself more times the number becomes smaller Part (ii)

17. 4 + 1 + 2 7 9

18. +3 16 Add 3 to the previous term

19. 3n+ 4 5 x 3 - 1 14 14 x 3 - 1 41 1 st term 5 x 1 2 nd term 5 x 2 10 3 rd term 5 x 3 15 4 th term 5 x 4 20 +3

20. 16 x 4 64 Pattern 4 Sequence 1, 4, 7, 10 1 dot4 dots 7 dots 10 dots Sequence goes up in threes 13 +3 +4 +5 +6+7 26

21. x2 8 Multiply the previous term by 2 Add consecutive integers 1, 2, 4, 7 +1 +2+3

22. +17 47 = 15 +15 32 +15 17 47 15

23. 111417 5, 8, 11, 14, 17 +3 3n + 2 3n + 2Nth term 3 x 99 + 2297 + 2 299

24. a = 11 11 b = 15 15 2c = 14 c = 7 7

25. 6 + 11 + 4 = 21 10 + 5 + 6 = 21 7 3 8 3 8 7

26. 15 2y + 3y = 5y 5y = 20 y = 4 4

27. w = 63 63 9 y > 9 Any whole number greater than 9 10

28. 3 2y+ 10 = 28 2y = 18 y = 9 9 Always get rid of the smallest valued letter first when you have letters on both sides. 10z + 2 = 9 10z = 7 0.7

29. 4 6 8z = 16 z = 2 2 3w - 6 = 9 3w = 15 w = 5 5

30. 5 x 8 40 8y- 2= 18 8y = 20 2.5

31. 33.125 Too big 2.4 30.624 Too big 2.3 28.267 Too small 2.35 29.428 Too small 2.4

32. Comment 3 3(3 - 1)(3 + 2) = 30 Too small 4 4(4 - 1)(4 + 2) = 72 Too big 3.5 3.5(3.5 - 1)(3.5 + 2) = 48.125Too big 3.4 3.4(3.4 - 1)(3.4 + 2) = 44.064 Too big 3.3 3.3(3.3 - 1)(3.3 + 2) = 40.227Too big 3.2 3.2(3.2 - 1)(3.2 + 2) = 36.608Too small 3.25 3.25(3.25 - 1)(3.25 + 2) = 38.391 Too small 3.3

33. Comment 2 6 Too small 3 24 Too big 2.5 13.125 Too small 2.7 16.983 Too small 2.8 19.152 Too small 2.9 21.489 Too big 2.85 20.299 Too small 2.9

34. Comment 8 520 Too small 9 738 Too big 8.8 690.272Too small 8.9 713.86 9 Too big 8.95 725.87 Too big 8.8

35. -1, 0, 1

36. 4

37. S - 40 = 3t 3t < 30 t < 10

38. y = 2 x 0 - 1 y = 2 x 2 - 1 3 Plot the coordinates from the table above

39. 2 2 y = -1 x -1 - 2 y = 1 - 2 Plot the coordinates from the table above

40. Have to make your own table to find the co-ordinates. 4 y = 2 x -1 - 3 -5 y = 2 x 4 - 3 5 Plot the coordinates from the table above y = 4.5 3.74.5

41. Option 1 500 – 300 = 200 minutes to pay for 200 x 6p = 1200p = £12 250 – 100 = 150 texts to pay for 150 x 10p = 1500p = £15 Total Cost = £12 + £15= £27 Option 2 500 – 100 = 400 minutes to pay for 400 x 6p = 2400p = £24 Texts are free so no texts to pay for Total Cost= £24 Option 2 ( cheaper) Where the line crosses the y-axis 25 150 350 17.5 = £0.05 5

42. 14 27 35 35 – 27 = 8 metres Yes, he must increase his gap by 8 approximately metres

43. Stop 10 The steeper the line the faster the speed

44. 8 Stationary ( not moving) 16 8

45. 2pm Time = 0.6 hours Time = 0.6 x 60 ÷ x = 36 minutes 2pm – 36 minutes 1:24pm