Compiled by Mr. Lafferty Maths Dept. Starter Questions Q1. Solve the equation below bo ao Q2. Find all the missing angles 12 5 Q3. Find the mean, median, mode and range of the numbers below 10, 9, 10, 20, 11 Q4. Find 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Statistics Revision Example : Find the mean, median, mode and range for the set of data. 3, 2, 7, 1, 15, 7, 6, 7 www.mathsrevision.com 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Frequency Tables Working Out the Mean Example : This table shows the number of coins in the pockets of some children. No of Coins (x) Freq. (f) (f) x (x) Adding a third column to this table will help us find the total number of coins and the ‘Mean’. 1 5 5 x 1 =5 2 5 5 x 2 = 10 3 1 1 x 3 = 3 www.mathsrevision.com 4 3 3 x 4 = 12 5 2 2 x 5 = 10 Totals 16 40 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Cumulative Frequency Tables Working Out The Median Example : This table shows the number of eggs laid by a clutch of chickens each day over a seven day period. Day Freq. (f) Cum. Freq. Total so far 1 2 2 A third column is added to keep a running total. This makes it easier to get the total number of items. 2 3 5 3 1 6 You have 1 minute to come up with a question you can easily answer from the table. www.mathsrevision.com 4 6 12 5 5 17 6 8 25 7 4 29 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Stem Leaf Graphs Construction of Stem and Leaf A Stem – Leaf graph is another way of displaying information : Ages This stem and leaf graph shows the ages of people waiting in a queue at a post office 2 4 6 8 3 1 4 5 6 7 9 5 3 4 9 How many people in the queue? 20 www.mathsrevision.com 6 1 4 5 How many people in their forties? 6 stem leaves Key : 2 4 means 24 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Stem Leaf Graphs Construction of Stem and Leaf Example : Construct a stem and leaf graphs for the following weights in (kgs) : Weight (kgs) 1 1 3 9 2 4 5 7 2 2 12 13 15 21 23 29 32 40 41 51 54 55 57 12 40 57 54 55 13 15 32 41 21 23 29 51 2 3 4 5 www.mathsrevision.com stem leaves Key : 2 3 means 23 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Solving Real-Life Problems When coming across a problem involving finding a missing side in a right-angled triangle, you should consider using Pythagoras’ Theorem to calculate its length. Example : A steel rod is used to support a tree which is in danger of falling down. What is the length of the rod? 15m 8m rod 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Length of the smaller side To find the length of the smaller side of a right-angled triangle we simply rearrange Pythagoras Theorem. Example : Find the length of side a ? Check answer ! Always smaller than hypotenuse 20cm 12cm a cm 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Calculating Percentages A Mini Cooper cost £15 000 in 2005 At the end 2006 it will have fallen by 20% What will the mini cooper worth at end 2006? End 2006 Fall in value = 20% x £15 000 = 0.2 x £15 000 = £3 000 New value = Old value – Fall in value = £15 000 - £3000 = £12 000 www.mathsrevision.com 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Hire Purchase www.mathsrevision.com Buying Products Interest Free 20% deposit General Buying Products Hoover Cash Price £360 or Interest Free (Deposit + 10 equal monthly payments) www.mathsrevision.com How much is the monthly payments. Deposit = 20% of 360 = 36 x 2 = £72.00 Left to pay = £360 - £72 = £288 Monthly Payment is = £288 ÷ 10 = £28.80 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Complicated Linear Patterns using diagrams and tables General Q. Find the rule (equation) connecting Tables and Chairs Number of Tables (T) 1 2 3 4 5 Number of Chairs (C) 4 6 8 10 12 2 2 2 2 Step 1 : Fill in missing values www.mathsrevision.com Step 2 : Find difference Part of the Formula Step 3 : C = 2T C = 2T + 2 Correction factor Step 4 : “add on 2” 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Complicated Linear Patterns using diagrams and tables General Q. Find the rules given the tables. 2 4 5 1 3 Number of Dots 10 18 22 6 14 Number of Crosses C = 4D + 2 2 4 5 1 3 Number of Stars 11 14 8 Number of Points P = 3S - 1 www.mathsrevision.com 2 4 5 1 3 Number of Balloons 9 17 21 13 Number of People P = 4B + 1 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Finding the equation of a Line General www.mathsrevision.com 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Straight Line General 4 1 2 3 10 11 12 5 6 7 8 9 x y Q. Plot the points below and determine the equation. x 1 2 3 4 5 y 4 6 8 10 12 www.mathsrevision.com 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Straight Line General 4 1 2 3 10 11 12 5 6 7 8 9 x y Q. Given the graph fill in the missing points. Determine the equation of the line. x 1 2 3 4 5 y 6 8 10 12 14 www.mathsrevision.com 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Example : On holiday I exchanged £50 for $75. How many $ will I get for £900. £ $ 50  75 www.mathsrevision.com 1  75 ÷ 50 = 1.5 900  1.5 x 900 = $1350 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Direct Proportion Direct Proportion Example : I am back from holiday and want to exchange $300 back to £’s at the same rate as before. How many £’s will I get back. $ £ www.mathsrevision.com 75  50 1  50 ÷ 75 = 300  x 300 = £200 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. The Circle Example : Find the area and circumference of the circle and the missing angles ao , bo , co , do Tangent line Solution Solution do bo co www.mathsrevision.com 50o ao 10cm ao = 150o bo = co = 65o do = 40o 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Scientific Notation A very quick method for find the scientific notation: Example : Write 2740000 in scientific notation 2.74 Step 1 : move decimal point till it comes between 1st and 2nd digits www.mathsrevision.com Step 2 : now count how many places that you have have moved the point. 6 Step 3 : finally write this number (6) as the power of 10. 2.74 x 106 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Scientific Notation www.mathsrevision.com Quick method for going from scientific notation to number form: Example : Write 5.78 x 104 in full Step 1 : Write down 578 without the point. www.mathsrevision.com Step 2 : Move the point 4 places to the right. 57800 2 zero’s are added for blank spaces. 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Scientific Notation www.mathsrevision.com It is possible to write very small decimal numbers in scientific notation Example : Write 0.0258 in scientific notation 2.58 Step 1 : move decimal point till it is after 1st non zero digit www.mathsrevision.com Step 2 : now count how many places that you have moved the point. 2 Step 3 : finally write this number (2) as the negative power of 10. 2.58 x 10-2 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.

Scientific Notation www.mathsrevision.com Reversing the process scientific notation to a very small decimal number Example 1 : Write 1.7 x 10-3 in full Simply move the point 3 places to the left 0.0017 Example 2 : Write 3.5 x 10-5 in full www.mathsrevision.com Simply move the point 5 places to the left 0.000035 Example 3 : Write 2.39 x 10-4 in full Simply move the point 4 places to the left 0.000239 24-Feb-19 Compiled by Mr. Lafferty Maths Dept.