1. Foundation GCSE Lecture: Targeting that grade C Mr A. Grant

2. REMEMBER You have a calculator, so use it!!!

3. Percentages STEP 1 Divide the amount by 100. STEP 2 Multiply this number by the given percentage A jacket originally costs £130. It is reduced in a sale by 22%. How much does it cost in the sale? 130 ÷ 100 × 22 = £28.60 130 – 28.60 = £101.40 130 – 28.60 = £101.40

4. To find 12% we divide by 100 and multiply by 12 £140 ÷ 100 × 12 = £16.80 Because increase we add on £140 + £16.80 = £156.80

5. Volume of Cuboids Volume of cuboid = length x width x height What is the volume of this cuboid? 10cm 7cm 9cm Volume = 9 x 7 x 10 = 630cm³

6. Volume of Triangular Prisms What is the volume of this prism? 3cm 6cm 10cm V = (6 x 3 x 10) ÷ 2 = 90cm³ = 90cm³

7. Part a) is usually multiply Part b) is usually divide 400 × 2.30 = 920 francs 46 ÷ 2.30 = £20 Exchange Rates Pounds to other currency = MULTIPLY Other currency to pounds = DIVIDE

8. Pythagoras: Finding the Hypotenuse 13cm 17cm Find length x x S S A S because we are finding the hypotenuse 13² + 17² = 458 √458 = 21.4cm(3sf)

9. Pythagoras: Finding another side 15cm x Find length x 21cm S S S S because we are finding a shorter side 21² - 15² = 216 √216 = 14.7cm(3sf)

10. Circumference of Circle Calculate the circumference C = π × d d = 2 × 7.6 = 15.2cm C = 3.14 ×15.2 = 47.8cm

11. Area of Circle Calculate the area Area = π r² A = 3.14 × 7.6² = 181cm² (3sf)

12. Find the total surface area of this triangular prism 8cm 6cm 10cm 18cm Triangle: 6 x 8  2 = 24 Base: 8 x 18 = 144 Slope: 10 x 18 = 180 Back: 6 x 18 = 108 Total Surface Area = 24 + 24 + 144 + 180 + 108 = 480cm² Two Triangles Three different rectangles

13. Which of these fractions are recurring decimals? ¼ 3/53/5 4/94/9 5/65/6 1 ÷ 4 = 0.25 Use Your Calculator 3 ÷ 5 = 0.6 4 ÷ 9 = 0.444444 or 0.4 5 ÷ 6 = 0.833333 or 0.83

14. Estimated Mean Mark (x) Frequency (f) 0 ≤ x < 10 5 10 ≤ x < 20 14 20 ≤ x < 30 22 30 ≤ x < 40 29 40 ≤ x < 50 27 50 ≤ x < 60 19 60 ≤ x < 70 4 Totals Σf =Σfx = f times x (fx) Mid-Group Value (x) 5 15 25 35 45 55 65 25 210 550 1015 1215 1045 260 4320120 Mean = 4320  120 = 36

15. Solve x 2 + 3x = 16 to 1dp using trial & improvement. The solution lies between 2 and 3 x x 2 + 3x x 2 + 3xbig/small 2.5² + (3 x 2.5) = 13.75 2.5 Small 2.6² + (3 x 2.6) = 14.56 2.6 Small 2.7² + (3 x 2.7) = 15.39 2.7 Small 2.8² + (3 x 2.8) = 16.24 2.8 So x = 2.8 (1dp) as it gives a solution closer to 16 than 2.7 Big 16 – 15.39 = 0.6116.24 – 16 = 0.24

16. Metric Units of Measurement centimetres grams litre millilitre metre millimetre kilograms

17. miles stones pints gallons feet inches pounds Imperial Units of Measurement ounces

18. Convert 8m² into cm² There are 100cm in 1 metre Because it is area we multiply by 100 TWICE 8 x 100 x 100 = 80000cm ² If it was cm ³ we would multiply 3 times

19. A piece of wood measure 43m to the nearest metre. What is the greatest and least possible length of the wood? Answers always end in 5 Greatest add 0.5 43.5m 43m Least subtract 0.5 42.5m

20. Angles in triangle add to 180 degrees 3x 2x x + 30 6x + 30 So 6x + 30 = 180 Use function machines to solve: x = (180 – 30) ÷ 6 = 25˚

21. 2 metres 4 x 2 = 8 metres

22. RATIO is 13 : 12 : 10 STEP 1: 13 + 12 + 10 = 35 STEP 2: £28 ÷ 35 = 80p (Value of 1 part) STEP 3: Becky = 12 x 80p = £9.60 Need to answer the actual question ⅓ of £9.60 = £3.20 so she has £6.40 left

23. 0 1 2 3 4 5 6 7 8 9 x 1 9 8 7 6 5 4 3 2 y Translation through AB 4 right 2 up Describe the transformation fully from A to B The top number represents horizontal movement (Left or Right) The Bottom number represents vertical movement (Up or Down)

24. Nadia wants to collect information about the different ways in which teachers travel to school. Design a suitable data collection sheet that Nadia could use to collect the information. How do you travel to school each day? Bus Car Walk Train OTHER TALLYFrequency

25. RATIO is 13 : 12 : 10 STEP 1: 13 + 12 + 10 = 35 STEP 2: £28 ÷ 35 = 80p (Value of 1 part) STEP 3: Becky = 12 x 80p = £9.60 Need to answer the actual question ⅓ of £9.60 = £3.20 so she has £6.40 left

26. Enlargement Enlarge the shape with scale factor 2 Make all the lengths twice as big. Do the horizontal and vertical lines first

27. Area of Triangle Area = 12 x 8 2 = 48cm² Multiply BUT remember to halve your answer Find the area of this triangle REMEMBER your UNITS

28. 10cm 18cm 6cm Find the area of this trapezium 8cm 6cm 6 x 10 = 60 cm ² 6 x 8 ÷ 2 = 24 cm ² Total Area = 60 + 24 = 84 cm ²

29. Multiply out the brackets and simplify: ( x - 2 ) ( x + 6) X (Multiply) x- 2 x + 6 x² - 2x + 6x- 12 Answer: x² + 4x - 12

30. Top first: 6 5 × 6² = 6 7 (Add the powers) 6 7 = 6³ (DIVIDE: Subtract the powers) 6 4

31. Bearing: Angle measured from North, Clockwise 056˚ (Always need 3 figures) This is the angle required 360 – 142 = 218˚ (Answer)

32. 5 12 19 26 33 5 12 19 26 33 Difference = 7 0 th Term = -2 So nth term formula is: T(n) = 7n - 2 Find the nth term formula of

33. 180 90 2 2 45 5 9 3 3 So 180 = 2 x 2 x 3 x 3 x 5 = 2 2 x 3 2 x 5 Prime Factor Powers

34. Factorise x² + 3x x² + 3x = x x + 3 x x is common to both parts so this comes out of the brackets = x (x + 3)

35. x coordinates: ½ way between 2 and 12 is 7 (2 + 12) ÷ 2 = 7 y coordinates: ½ way between 3 and 7 is 5 (3 + 7) ÷ 2 = 5 ANSWER: (7, 5)

36. Surface Area of Cuboids 9 x 7 = 63cm ² What is the volume of this cuboid? 10cm 7cm 9cm 90 + 90 + 70 + 70 + 63 + 63 = 446cm ² 7 x 10 = 70cm ² 9 x 10 = 90cm ²

37. The Perpendicular Bisector of Line AB AB

38. The Angle Bisector The angle bisector will divide an angle exactly in half.

39. ROTATION 180⁰ about (0, 0) Use your Tracing Paper

40. Food Mart: 1 yoghurt = 180 ÷ 5 = 36p Jim’s: 1 yoghurt = 105 ÷ 3 = 35p So Jim’s is better value

41. 15322510445 293942172119 0123401234 5 05790579 599599 2929 2424 StemLeaves 2 5 means 25

42. State two things that are wrong with this questionnaire: How many Playstation 3 games did you buy? 0 – 5 5 – 10 10 - 15

43. Tessellations Fit together like a jigsaw without any gaps