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www.mathsrevision.com General Past Papers by Topic 2000 - 2010 Basic Calculations (12) Pythagoras Theorem (11) Straight Line (14) Angles (14) Money & Percentages (44) Trigonometry (12) Linear Patterns (8) Scale Factor (3) Scientific Notation (10) Algebra (12) Symmetry (11) Speed Distance Time (17) Summary of General Next Menu www.mathsrevision.com General Past Papers by Topic 2000 - 2010 Combinations / Logic (14) Proportion & Ratio (8) Length Area Volume (29) Scale Drawing (5) Bearings (4) Variation (3) Negative Numbers (9) Tolerance (1) Probability (7) Statistics Stem Leaf (6) Statistics Mean F Table (4) 24-May-17 Created by Mr. Lafferty Maths Dept. Previous Menu Still need more practice on Basic Calculations Click Here m=0 m<0 m (0,c) m>0 m = undefined Graph of y = mx + c Possible values for gradient m>0 Note : 2y + 4x = 8 rearrange into correct form y = -2x + 4 Parallel lines have same gradient y y1 V 2 H x 2 x1 Straight Line y = mx + c m = gradient m y y1 V 2 H x 2 x1 c = y intercept (0,c) e.g. 17.5% of 300 10% ÷ 10 5% half of 10% 1% ÷ 100 0.5% half of 1% 2% twice 1% 3% 3 times 1% 10%300 ÷ 10 = £30 5% 30 ÷ 2 = £15 2.5% 15 ÷ 2 = £ 7.50 17.5 % Without a calculator With a calculator e.g. 19% of £60 19 x 60 = £11.40 100 £52.50 Percentage out of 100 Finding Percentages % profit or loss I buy a CD for £4 and sell it for £7. What is the percentage profit? Profit made £3 3 x 100 =75% 4 Still need more practice on Money & Percentages Click Here www.mathsrevision.com Complicated Linear Patterns using diagrams and tables Key-Points Write down the 4 main steps 1. Make a table 2. Find the difference 3. Write down part of formula 4. Find the correction factor and then write down the full formula Still need more practice Pattern Click Here Why is this not scientific notation ? 4000 Write out in full a not between 1 and 10 11 x1018 4 x103 1.1 x1019 a x 10n a between 1 and 10 n is positive LARGE numbers Science Scientific Notation = Standard Form Maths SMALL numbers a x 10n a between 1 and 10 n is negative 0.0000006 Write out in full 6 x10-7 5 x10-6 0.5 x10-5 Why is this not scientific notation ? a is less than 1 a<1 Still need more practice on Scientific Notation Click Here Pythagoras Theorem www.mathsrevision.com Finding hypotenuse c c = a +b 2 2 2 c b a Finding shorter side a a = c -b 2 24-May-17 2 2 Compiled by Mr. Lafferty Maths Dept. Finding shorter side b b =c -a 2 2 2 Still need more practice on Pythagoras Theorem Click Here Still need more practice on Angles Click Here Still need more practice on Angles Click Here www.mathsrevision.com Trigonometry Sin x° = Opp Hyp Cos x° = Adj Hyp O A S HC H Tan x° = O T A Opp Adj Trigonometry www.mathsrevision.com Process 1. Write down SOH CAH TOA 2. 3. Identify what you want to find what you know Copy this! Still need more practice on SOHCAHTOA Click Here Scale Factor applies to ANY SHAPES that are mathematically similar. b 7.5 cm a 4 cm 3 cm 8 cm 2cm 10 cm Given the shapes are similar, find the values a and b ? 4 Scale factor = RSF = = 0.4 10 a is 8 x 0.4 = 3.2 10 Scale factor = ESF = = 2.5 4 b is 2 x 2.5 = 5 Still need more practice on Scale Factor Click Here x2 + x + 3 + y + 9 – 2x - 4y = x2 - x – 3y + 12 Note x2 ≠ x 10x 5x 2 – 6xy 3y HCF = 2x divide each term by HCF 2x( - ) Tidying up terms Factorising Algebra Evaluating Expressions a = 2 b = (-3) c = 4 = 2b - 3(a - c)2 = 2(-3) - 3(2 - 4)2 = 2(-3) - 3(-2)2 = -6 – 12 = -18 Removing single bracket BODMAS 9 - 3(8 - y) =9 - 24 + 3y = -15 + 3y www.mathsrevision.com Balancing Method Kirsty goes to the shops every week to buy some potatoes. She always buys the same total weight. One week she buys 2 large bags and 1 small bag. The following week she buys 1 large bag and 3 small bags. If a small bags weighs 4 kgs. How much does a large bag weigh? 4 4 4 How can we go about What instrument solving this using measures balance balance ? 24-May-17 Created by Mr Lafferty Maths Dept 4 www.mathsrevision.com Balancing Method Take a small bag away from each side. Take a big bag away from each side. We can see that a big bag is equal to 4 + 4 = 8 kg 24-May-17 Created by Mr Lafferty Maths Dept 4 4 4 4 Balancing Method What symbol should we use for the scales ? www.mathsrevision.com Lets solve it using maths. Let P be the weigh of a big bag. P P 4 We know that a small bag = 4 2P + 4 = P + 12 -4 -4 2P = P + 8 -P -P Subtract 4 from each side Subtract P from each side P=8 24-May-17 Created by Mr Lafferty Maths Dept P 4 4 4 Still need more practice on Factorising & Multiplying Out Brackets Click Here Still need more practice on Solving Equations Click Here Careful with time units you must work in decimal time and convert back at the end. Time Distance Speed www.mathsrevision.com Mixed Problems D=S T D S= D T S T T= D S Simple way to remember the 3 formulae ! 24-May-17 Created by Mr. Lafferty Maths Dept. Still need more practice on Speed Distance Time Click Here Book Title Book Title Book Title Total Cost B r L A =LxB A = h πr2 h A =Bxh a A = ½bh V = πr2h V = Area x H Volume = Area x Height Simple Volume Area & Volume of a Prism Composite Volume L made up of basic areas h V = L x BxH V = Area x H h Composite Areas B A = L x B + ½bh L B Simple Areas b A = ½(a + b) h h H h H B made up of basic volumes L V = (LxBxH) + (½BhL) V = Area x H Calculate the area of the base 24 cm 30 cm Still need more practice on Length Area Volume Click Here Land Still need more practice on Scientific Notation Click Here www.mathsrevision.com Probability We can normally attach a value to the probability of an event happening. To work out a probability number of outcomes P(A) = Total number of possible outcomes Probability is ALWAYS in the range 0 to 1 24-May-17 Created by Mr Lafferty Maths Dept Probability Number Likelihood Line www.mathsrevision.com 1 0 2 0.1 Impossible 3 0.2 4 0.3 5 0.4 6 0.5 0.6 7 0.7 8 0.8 Evens P= Q. What is the chance of picking a number that is even ?P(E) = Q. What is the chance of picking the number 1 ? Created by Mr Lafferty Maths Dept 1 Certain Q. What is the chance of picking a number between 1 – 8 ? 24-May-17 0.9 P(1) = 8 =1 8 4 = 0.5 8 1 = 0.125 8 Stem Leaf Graphs www.mathsrevision.com Construction of Stem and Leaf A Stem – Leaf graph is another way of displaying information : Ages This stem and leaf graph shows 2 4 6 8 the ages of people waiting in a 3 0 1 3 queue at a post office 4 4 4 5 6 7 9 5 0 3 4 9 How many people in the queue? 20 6 1 4 5 6 How many people in their forties? 6 leaves stem n = 20 Key : 2 4 means 24 24-May-17 Created by Mr. Lafferty Maths Dept. Frequency Tables www.mathsrevision.com Working Out the Mean Example : This table shows the number No of of coins in the pockets of some children. Coins (c) Adding a third column to this table will help us find the total number of coins and the ‘Mean’. Mean Number of coins = 24-May-17 Freq. (f) fxC 1 5 5 x 1 =5 2 5 5 x 2 = 10 3 1 1x3=3 4 3 3 x 4 = 12 5 2 2 x 5 = 10 Totals 16 40 40 = 2.5 coins 16 Created by Mr. Lafferty Maths Dept. Still need more practice on Proportion Click Here Still need more practice on Ratio Click Here www.mathsrevision.com Scaled Drawings using Bearings Make an accurate drawing of the plane journey N N N N 24-May-17 120o 45o 8km 120o 12km 45o 8km 12km 1cm represents 2km Created by Mr. Lafferty Maths Dept. Direct Variation Harder Direct Variation S4 www.mathsrevision.com Q. The cost (C) of producing a football magazine varies as the square root of the number of pages (P). Given 36 pages cost 48p to produce. Find a formula connecting C and P. Since C is directly proportional to “square root of” P the formula is of the form C C =k P √P 24-May-17 C = 40 P=2 48 = k 36 k = 48 ÷ 6 = 8 C =8 P Direct Variation Harder Direct Variation www.mathsrevision.com S4 Q. How much will 100 pages cost. C C = 8 100 √P C = 8 100 = 8 10 = 80p 24-May-17 Created by Mr. Lafferty Maths Dept. Still need more practice on Variation Click Here Tolerance www.mathsrevision.com S4 Tolerance is written as (50±2)mm He might be prepared to accept any bolt as long as it lies between 48mm and 52mm This means he will accept a bolt which is within 2mm of the 50mm he asked for. This is referred to as the TOLERANCE for the measurement. 24-May-17