Wednesday, 24 May 2017 Warm-Up Session Non-Calculator Paper
Non-Calculator Paper 80 marks in 90 minutes
IF YOU FINISH EARLY CHECK EVERYTHING! You have made a silly mistake somewhere. Redo some questions
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.
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)
Number
0.0453682 0.05 2 decimal places 0.045 2 significant figures 468.493628 468.49 2 decimal places 470 2 significant figures
NEED TO KNOW 4 1 = 4 4 4 2 2 6 6 13 13 1256 = 1 1256 3 6 27 = 2 9 3
NEED TO KNOW Fractions, Percentages, Decimals! 50 / 100 25 / 100 10 / 100 5 / 100 ½ 50% 0.5 ¼ 25% 0.25 1 / 10 10% 0.1 1 / 20 5% 0.05
You Cannot: 2 3 + 3 4 FRACTIONS You Can: 8 12 + 9 12 DENOMINATORS MUST BE THE SAME WHEN WE ADD AND SUBTRACT FRACTIONS!!! 2 3 x 3 4 4 5 2 3
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
Z Writing Simple Recurring Decimals as Fractions x = 0. 41 41 41 41... 100 x = 41. 41 41 41... 99 x = 41. 41 41 41 So 99 x = 41 0. 41 41 41-41. 00 00 00 x = 41 99
Finding Simple Percentages without a Calculator Percentage Method 1% 100% 100 = 1% 10% 25% 50% 20% 5%
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% = 70 10 = 7 30% = 3 x 7 = 21 5% = 10% 2 = 7 2 = 3.50 35% = 21 + 3.50= 24.50 Increase: 70 + 24.50 = 94.50 Decrease 340 by 85% 85% = 50% + 25% + 10% 50% = 340 2 = 170 25% = 50% 2 = 170 2 = 85 10% = 340 10 = 34 85% = 170 + 85 + 34 = 289 Decrease: 340 289 = 51
Write 96 as a product of prime factors 96 3 32 2 16 2 8 2 4 2 2 96 = 2 2 2 2 2 3 = 2 5 3
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
INDICES r 0 = 1 8 1 3 = 3 8 8-1 = 8-2 = 1 8 1 8 2 3 = (8 1 3) 2 64
SURDS 2 x 6 = 12 = 2 3 2 + 6 8 Rationalising Surds 4 x 2-3 = 4 (2-3) = 8-4 3 2+ 3 2-3 (2+ 3)(2-3)
Standard form How can we write these numbers in standard form? 80 000 000 = 8 10 7 230 000 000 = 2.3 10 8 724 000 = 7.24 10 5 0.0007261= 7.261 10-4 0.003152 = 3.152 10-4
NEED TO KNOW PROPORTION Y = kx Y = k X Y = kx 2 Y = k X 2
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. 60 44 LCM = The product of all numbers in the diagram HCF = The product of the numbers in the middle
Bearings Measured from North, Clockwise and Three Figures N A B 048
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
Algebra
NEED TO KNOW 8, 11, 14, 17, 3n + 5 What is the 22nd term? 3(22) + 5 = 71
Expand & Factorise 4(d 3) = 4d 12 (x + 3)(x + 2) = x 2 + 5x + 6
Solve 5(3x 2) = 50 15x 10 = 50 Expand (+10 to both sides) 15x = 60 15 to both sides x = 4 Check: 5 x (3 x 4 2) = 50
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..
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
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
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 = 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 5 4 3 2 1 3 2 1 0 1 2 3 1 2 x
Recognising Graphs Positive Linear Quadratic Cubic Negative
Use (-4, 4) and (-2, -2) 4 + 2 2, 4 + 2 2 (-3,1) 4 2 2, 4 2 2 a
Geometry
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
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
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
Unit conversion
Acute Obtuse Reflex Less than 90 Between 90 and 180 More than 180
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: 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:
Polygons
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
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
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
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
Volume of a prims Area of the cross section x height 10cm 7cm 10cm 5cm Radius = 5cm 4cm 5cm 2cm
Pythagoras 8cm 10cm 3cm x x x 2 = 102 82 x 2 = 36 x = 6cm 4cm x 2 = 32 + 4 2 x 2 = 25 x = 5cm
Z Learn these two triangles 1 2 3 2 45 60 1 1
Constructing a perpendicular bisector
This is the LOCUS of points that are the same distance from A as from B
Bisecting an angle
This is the LOCUS of points that are the same distance from AB as from BC
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
Statistics
Stem and Leaf Diagrams Now we need to put the leaves in numerical order 1 4 3 1 7 9 6 6 8 5 2 1 3 3 4 4 0 2 1 2 8 6 9 5 Key: 1 4 means 14 1 3 4 1 5 6 6 7 8 9 2 0 1 1 2 3 3 4 4 2 5 6 8 9 Key: 1 4 means 14 Median=21
Cumulative Frequency graph. Cumulative frequency Cumulative frequency 200 190 180 170 160 150 140 130 120 110 100 200 90 190 80 180 70 170 60 160 50 150 40 140 30 130 20 120 10 110 0 100 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 90 Age of member 80 70 60 50 40 30 20 10 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Age of member We can now use this to find the following information.. Median Lower quartile Upper quartile Lowest Value Highest Value 37 25 51 This information can now be used to draw a box and whisker diagram.. 0 80 Interquartile range 51-25 26
Probability
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
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
You are as ready today as you can be. Enjoy the test it is a chance to show how much you have learnt.