Wednesday, 24 May Warm-Up Session. Non-Calculator Paper

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1 Wednesday, 24 May 2017 Warm-Up Session Non-Calculator Paper

2 Non-Calculator Paper 80 marks in 90 minutes

3 IF YOU FINISH EARLY CHECK EVERYTHING! You have made a silly mistake somewhere. Redo some questions

4 READ THE QUESTION! Answer the question as asked. Give your answer as requested e.g. 3sf or 2dp it is silly to loose these marks. Round only at the very end especially important when using a calculator. Show your working out. Mistakes require only one line through allow the examiner to give you marks. Diagrams are not drawn accurately.

5 Reciprocal: multiplicative inverse Quick recap Round to decimal places: count the digits after the decimal point Round to significant figures: Count all the digits after the first digit over 0 Solve: Find the value of the letter Estimate: Round to 1sf (usually!) Explain/justify: Give reasons in a sentence Hence: Use what you have done before Co-ordinates: Along the corridor and up the stairs e.g. (3, 4)

6 Number

7 decimal places significant figures decimal places significant figures

8 NEED TO KNOW 4 1 = = = 2 9 3

9 NEED TO KNOW Fractions, Percentages, Decimals! 50 / / / / 100 ½ 50% 0.5 ¼ 25% / 10 10% / 20 5% 0.05

10 You Cannot: FRACTIONS You Can: DENOMINATORS MUST BE THE SAME WHEN WE ADD AND SUBTRACT FRACTIONS!!! 2 3 x

11 NEED TO KNOW Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 Cubes: 1, 8, 27, 64, 125 ½ x ½ = ¼

12 Z Writing Simple Recurring Decimals as Fractions x = x = x = So 99 x = x = 41 99

13 Finding Simple Percentages without a Calculator Percentage Method 1% 100% 100 = 1% 10% 25% 50% 20% 5%

14 Increasing/Decreasing by a % without a calc Find the percentages you need and add/subtract Increase 70 by 35% 35% = 3 x 10% + 5% 10% = = 7 30% = 3 x 7 = 21 5% = 10% 2 = 7 2 = % = = Increase: = Decrease 340 by 85% 85% = 50% + 25% + 10% 50% = = % = 50% 2 = = 85 10% = = 34 85% = = 289 Decrease: = 51

15 Write 96 as a product of prime factors = = 2 5 3

16 INDICES r 3 x r 4 = r 7 x -8 x -3 = x -5 e 8 e 3 = e 5 (2g 4 ) 3 = 8g 12 (g 4 ) 3 = g 12 (2g 2 h 3 ) 3 = 8g 6 h 9

17 INDICES r 0 = = = 8-2 = = (8 1 3) 2 64

18 SURDS 2 x 6 = 12 = Rationalising Surds 4 x 2-3 = 4 (2-3) = (2+ 3)(2-3)

19 Standard form How can we write these numbers in standard form? = = = = =

20 NEED TO KNOW PROPORTION Y = kx Y = k X Y = kx 2 Y = k X 2

21 Find the highest common factor (HCF) and lowest common multiple (LCM) of 44 and 60. Step 1: Use a factor tree to break down the numbers into their prime factors. Step 2: Organise the numbers into a venn diagram LCM = The product of all numbers in the diagram HCF = The product of the numbers in the middle

22 Bearings Measured from North, Clockwise and Three Figures N A B 048

23 Averages and spread Mode Median The mode is the most common or most popular thing The middle value when the numbers are in order Mean Range sum of values number of values greatest value smallest value

24 Algebra

25 NEED TO KNOW 8, 11, 14, 17, 3n + 5 What is the 22nd term? 3(22) + 5 = 71

26 Expand & Factorise 4(d 3) = 4d 12 (x + 3)(x + 2) = x 2 + 5x + 6

27 Solve 5(3x 2) = 50 15x 10 = 50 Expand (+10 to both sides) 15x = to both sides x = 4 Check: 5 x (3 x 4 2) = 50

28 Solve 5x + 2 = 3x + 7 2x = 5 x = 2.5 5x + 2 < 3x + 7 2x < 5 x < 2.5 Check it works! Integer = whole number..

29 n is an integer Inequalities 2 < 2n 6 List all the possible values of n Solution 1 < n 3 Therefore n = 0,1,2,3

30 Solving Quadratics x 2 + 5x + 6 = 0 Factorise first: (x + 2)(x + 3) = 0 Then solve: x + 2 = 0 x + 3 = 0 x = 2 x = 3

31 Simultaneous Equations 6x + 2y = 3 4x 3y = 11 Same sign - Different + Check your answer!

Using a table of values x y = x 2 3 3 2 1 0 1 2 3 6 1 2 3 2 1 6 The points given in the table are plotted Remember (-3) 2

32 Using a table of values x y = x The points given in the table are plotted Remember (-3) 2 = 9 y = (-3) 2 3 y = (-2) 2 3 y = (-1) 2 3 y = (0) 2 3 y = (1) 2 3 y = (2) 2 3 y = (3) 2 3 y x

33 Recognising Graphs Positive Linear Quadratic Cubic Negative

34 Use (-4, 4) and (-2, -2) , (-3,1) 4 2 2, a

35 Geometry

36 h b Area of Rectangle = b x h b h Area of Triangle = bh 2 a perpendicular height base perpendicular height b Area of a parallelogram = bh Area of a trapezium = 1 2 a + b h

37 The circumference of a circle The area of a circle C = πd or C = 2πr A = πr 2 3 cm C = πd = π 3 2 cm A = πr 2 = π 2 2 = 4π cm 2 = 3π cm 6 m C = πd = π 12 = 12π m 10 m A = πr 2 = π 5 2 = 25π m 2

38 Unit conversion When converting to a smaller unit, multiply. When converting to a larger unit, divide. m x 100 cm km x 1000 m g x 1000 mg m 100 cm km 1000 m g 1000 mg cm x 10 mm kg x 1000 g l x 1000 ml cm 10 mm kg 1000 g l 1000 ml

39 Unit conversion

40 Acute Obtuse Reflex Less than 90 Between 90 and 180 More than 180

41 Angles on a straight line Straight line = 180⁰ Angles around a point Angles around a point = 360⁰ Angles in a Quadrilateral Angles in a quadrilateral (4-sided shape) add up to 360⁰ Angles in a Triangle Angles in a triangle add up to 180⁰

Special Triangles: Equilateral Triangle All the angles in an Equilateral Triangle are equal (60 ) Special Triangles: Right-Angled Triangle One angle is 90 degrees Example: Example: Special Triangles:

42 Special Triangles: Equilateral Triangle All the angles in an Equilateral Triangle are equal (60 ) Special Triangles: Right-Angled Triangle One angle is 90 degrees Example: Example: Special Triangles: Isosceles Triangle The two angles at the base are equal (the base is always the line without a stroke!) Example: Special Triangles: Scalene Triangle All angles and side lengths are different Example:

43 Polygons

45 Transformations 1. Reflection (2 marks) State reflection and line of symmetry 2. Rotation (3 marks) State rotation, centre of rotation, Degrees of rotation, Direction clockwise/ anti clockwise 3. Enlargement (3 marks) State enlargement, centre of enlargement, scale factor 4. Translation (2 marks) State translation and vector e.g. 2 4

46 Scale Factors Example S.F. of 2 SIMILAR SHAPES are to the power of the dimensions 3cm x 2 6cm 6cm 2 x 2 2 Length x (SF) 1 Area x (SF) 2 Volume x (SF) 3 24cm 2

47 Prisms Prisms are 3 dimensional shapes that have a constant cross-sectional area Cuboid Triangular-based prism Rectangular-based prism Pentagonal-based prism Cylinder Hexagonal-based prism Octagonal-based prism Circular-based prism

48 Volume of prisms Volume = Area of cross-section x length 5cm 10cm 4cm Cross section=trapezium 7cm Area of trapezium = (7+5)x4 = 24cm 2 2 Volume = 24x10=240cm 3

49 Volume of a prims Area of the cross section x height 10cm 7cm 10cm 5cm Radius = 5cm 4cm 5cm 2cm

50 Pythagoras 8cm 10cm 3cm x x x 2 = x 2 = 36 x = 6cm 4cm x 2 = x 2 = 25 x = 5cm

51 Z Learn these two triangles

52 Constructing a perpendicular bisector

53 This is the LOCUS of points that are the same distance from A as from B

54 Bisecting an angle

55 This is the LOCUS of points that are the same distance from AB as from BC

56 Z Parallel Line Angles Corresponding angles are equal Alternate angles are equal Interior angles add up to 180 a a b b a b a = b a = b a + b = 180 Look for an F-shape Look for a Z-shape Look for a C- or U-shape

57 Statistics

58 Stem and Leaf Diagrams Now we need to put the leaves in numerical order Key: 1 4 means Key: 1 4 means 14 Median=21

59 Cumulative Frequency graph. Cumulative frequency Cumulative frequency Age of member Age of member We can now use this to find the following information.. Median Lower quartile Upper quartile Lowest Value Highest Value This information can now be used to draw a box and whisker diagram Interquartile range

60 Probability

61 Probability Probability of the target event happening = Number of target outcomes Total number of possible outcomes Theoretical Probability = The expected probability if an experiment is fair Expected Frequency = Theoretical probability x number of trials Mutually exclusive = outcomes Exhaustive outcomes = Two outcomes that cannot occur at the same time All the possible outcomes of an event P(outcome) + P(complementary outcome) = 1

62 1 30 minutes, easy marks only! 2 30 minutes, harder but doable questions TAKE A BREAK!!!! 3 go back over the (approx) 60 marks you ve attempted 4 guess the rest! A blank page scores 0

65 You are as ready today as you can be. Enjoy the test it is a chance to show how much you have learnt.

CAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE

CAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE TIER TOPIC HEADING SUB HEADING Both Number Integers Ordering numbers Both Number Integers Rounding numbers Both Number Integers Adding and subtracting whole