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Master algebra basics with interactive examples covering BODMAS rule, equation solving, patterns, and sequences. Improve your grades with step-by-step explanations. Visit www.mistrymaths.co.uk for more resources.

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  1. EVERYTHING YOU NEED TO KNOW TO GET A GRADE C ALGEBRA (FOUNDATION) AUTHOR www.mistrymaths.co.uk

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

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

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

  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 = £2.50 £7.50 - £5 Cost for calls after £5 a month charge has been taken off Cost for calls after £5 a month charge has been taken off Cost per minute for calls Minutes of calls = 50

  7. Perimeter is the length around a shape + 6y Solve the equation to work out the value of y 56 + 6y = 68 6y = 12 2 y = 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. 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. - 3b 12a

  11. 3a + 10 6b 12

  12. + 18 - 4 + 14

  13. + 5

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

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

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

  17. + 1 + 1 + 2 + 2 + 1 + 2 4 7 9

  18. 16 +3 +3 +3 +3 Add 3 to the previous term

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

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

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

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

  23. 11 14 17 5, 8, 11, 14, 17 + 2 3n +3 +3 +3 +3 3 x 99 + 2 297 + 2 Nth term 3n + 2 299

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

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

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

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

  28. 3 = 28 2y + 10 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. Too big 33.125 2.5 Too big 2.4 30.624 Too small 2.3 28.267 Too small 2.35 29.428 2.4

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

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

  34. 𝑥 Comment Too small 8 520 Too big 9 738 690.272 Too small 8.8 Too big 713.869 8.95 8.9 Too big 725.87 8.8

  35. -1, 0, 1

  36. 4

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

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

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

  40. Have to make your own table to find the co-ordinates. -1 4 5 -5 y = 2 x 4 - 3 y = 2 x -1 - 3 Plot the coordinates from the table above y = 4.5 3.7 4.5

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

  42. 14 35 8 metres 35 – 27 = 27 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 2pm – 36 minutes Time = 0.6 x 60 = 36 minutes 1:24pm x ÷

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