Maths Revision. Book 2. Name:.

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1 Maths Revision Book 2 Name:.

2 Number Fractions Calculating with Fractions Addition Subtraction 2 Subtract wholes first Change one whole into thirds Multiplication Division Invert right hand side Merry the monkey eats ⅓ bananas each day. How many bananas will Merry eat in 2 days? 4 4 bananas in day 4 bananas in days bananas in 2 days Fraction Problems How many days will 24 bananas last if Smiley eats 2 of a banana each day? 2 bananas in day 2 bananas in days bananas in 60 days

3 Circles Shapes Polygons radius (r) Angle at the centre Exterior Interior Area of Circle πr ² Circumference 2πr Semi-circles Polygon Formulae: Number of sides(n) 60 Exterior angle Exterior angle 60 Number of sides Angle at the centre Exterior angle Interior angle + Exterior angle 80º Sum of Interior angles 80(n 2) Area ½ πr ² Perimeter 2πr 2 + D Volume Segments radius (r) c a b 72 Volume of a cuboid length x breadth x height Surface area of cuboid 2ab + 2bc + 2ac Find out how many segments make up a full circle: e.g Area of Segment (above) 2π r Volume of a prism cross-sectional area length Surface area of a prism sum of the areas of all faces Perimeter 2π r + 2r Cross-sectional area

4 Graphs Straight Line Graphs Horizontal and Vertical Graphs y y 2 - x y mx + c type graphs 2y x + (which is same as y ½x + ½ ) x - 4 y y 2y x x x - Diagonal Graphs y y x y x - Quadratic Graphs (Level ) x y x y 6 y x² y x - y x - x -4

5 Enlargement: Area and Perimeter If the scale factor is, the perimeter of the enlarged shape will be times longer. the area of the enlarged shape will be 9 times larger ( 2 ) Speed, Distance and Time The formula to calculate speed: Speed Distance Time D S T Work out the speed of a car travelling 80 miles in hours and 20 minutes: B Time in hours. or Speed distance time A 80. ( ) 4 mph Work out the time taken to travel 96 km at a speed of 40 km/h: Q. Triangle F is an enlargement of triangle E using a scale factor of. If triangle F has an area of 72 cm 2, find the area of triangle E. Area of E cm² Time distance speed hours hours 24 minutes Change 4 m/s into km/h 4 metres in second m in hour km/h Change 72 km/h into metres per second: speed distance time m 600 s 20 m/s *Remember: hour seconds

6 Scatter Graphs and Correlation Positive Correlation Negative Correlation No Correlation Example: Molly grows some plants and measures their height and mass. She then plots her results on a scatter graph as shown below. Height and Mass of Plants Mass of Plant (kg).6 Line of best fit height (cm) Question: Use the line of best fit to predict the mass of a 00 cm plant. Answer: Show your working on the graph using dotted lines (see above). If the plant has a height of 00 cm, it will weigh approximately. kg

7 Charge ( ) Conversion Graphs Example: Easycab taxi company charge passengers per mile. How much would they charge a passenger for a 2 mile journey? Answer : mile is miles is distance in miles If a passenger pays 8 for a journey, how far was the journey? Show your working on the graph above. Answer: 6 miles.

8 Algebra Simplification Examples: Substitution Examples: (a) t t t 2 + (i) If p, r 4, s 2, t 6 Substitute: (a) 2r s 2 4 ( 2) (b) (4y ) 2 4y 4y (b) p r 2 4² 6 (c) 4 4 y y y y y y 6 y 6 ab² a²b³ ab² a²b³ a b b. a a b b b 7ab Using Factorisation: 7 (a) Fully factorise 8n + 6 4(2n + 9) (b) A square has a perimeter of 8n + 6 Find the length of one side in terms of n (c) r (6s p) 4(6 2 ) 4( 2 ) 4 ( ) 60 (d) pr 8 t + s _ 6 4 Use factorised expression: 4(2n + 9) Perimeter of a square 4 length of side 4 (2n + 9) Length of one side 2n + 9

9 (ii) If v gh, work out the value of g when v 20 and h 0 v gh 20 g g (square both sides) g 8 Equations Examples: (a) x x 2 (b) y y 0 (c) y 2 (e) 2a + + 2a 6 2 a a 8 (f) 4 2x + x (take x s to side with biggest x) 4 2x + x +2x +2x 4 + x - - x x x y 2 (g) 2x 8 y 4 2x (d) c (or c ) c c 2x 8 2x 24 2 x x 2

10 Brackets (a) 2 (8x + 6y) 6x + 2y (b) (4a + 2) 2a 6 2a Algebra: Writing Expressions On a train, there are m men, twice as many boys as men, less girls than men, and three times as many women as girls. In terms of m: Men Boys Girls Women m 2m (m ) (m ) (a) Write an expression for the total number of people. m + 2m + (m ) + (m ) (c) (2m 4n) 2(m n) 6m 2n 2m + 0n 4m 2n Factorising (a) f + 20 (f + 4) (b) 6a 2 b 24ab 8ab(2a b 2 ) (b) (c) m + 2m + m + m 7m 44 There are a total of 68 people on the train. Write down and solve an equation to find the value of m. 7m m 2 7m m 6 How many women are on the train? (m ) (6 ) women

11 Number Patterns Examples Sequence Rule nth Term 20 th Term 7,,, 9, 2, Add 4 each time (4 times table) ***See example at the bottom of the page*** 40,, 0, 2, 20,.. Subtract each time (based on - table) 4n + 4n n + 4 n , 4, 9, 6, 2, Square numbers n 2 n , 6,, 8, 27, Square then add 2 n n ² , 6, 2, 6,. Add 2 then square (n + 2) 2 (n + 2) 2 (20 + 2) , 4, 8, 6, 2, Doubling 2 n 8 th term: 2 n , 00, 000, Multiply previous term by 0 0 n 8 th term: 0 n ,,, 9, 2,. 4n + ( 4, 8, 2, 6, 20, ) 4n The top sequence is the 4 times table but more for each term, i.e. 4n +

12 Percentages Find % of 60 m Method : % of 60 m m Method 2: 0% Method (Calculator) m Method 4 (Calculator) Buttons on calculator: % 6 0 Pie Charts Angle for Person 0 people surveyed. Angle for person Percentage pie charts: % Bearings You must use figures. 0 of 60 6 m 042, 009, 6 0% 6 m % 8 m Write the bearings and real life distances on the diagrams. 0% 6 08 m % 0% + % m Scales : : 00 to change these do: - cm : cm cm : 00 cm cm : 00 m cm : m

MATHS PAMPHLET Year 7

MATHS PAMPHLET Year 7 TABLE OF CONTENTS A- Course Synopsis B- Practice Questions C- Answer sheets A- Course Synopsis Revision Guide for year 7 Set 3 set will be attempting a calculator and non calculator