Mathematics Revision Guide Common Entrance Level 1 and 2

Menu Level 1 and 2 Topics Click here. This revision list contains revision for both levels. Any topics in red are for level 2 only.

Click here to enter Number Revision Main menu 4 rules number and decimals Arithmetic problems Converting measures: Litres to ml and Grams to kg Reading scales Converting between % fractions decimals Fractions of amounts % problems % profit, profit as a % BIDMAS Writing numbers as product of prime factors using indices + use to find square number Square and Square root Unitary method Distance, Time, Speed. Ratio Proportion Using a calculator Significant figures Decimal places Negative numbers Subtraction and addition of simple fractions x ÷ simple fractions Click here to enter Number Revision Main menu

Click here to enter Algebra Revision ‘Algebra simplifying expressions + - x ÷ Forming algebraic expressions X brackets including x by negative number (level2). Factorising expressions Substitution including negative numbers ( level2) Drawing line graphs using substitution and coordinates Think of number’ inverse method Solving equations Sequences, term to term rule Number patterns investigation Main menu

Click here to enter Shape and Space Revision Equations of lines and coordinates Transformations: reflections rotations, translations. y=x Enlargements Angles Exterior and interior angles of regular polygons Bearings Line Symmetry and Rotational Symmetry Naming shapes Construction Nets of solids Area and perimeter of rectangles and composite shapes Area of triangle Volume of cuboids Volume, link between litres and cm³ (level 2) Circumference of Circles Area of Circles Main menu

Click here to enter Data Handling + Graphs Revision Pie charts Probability and combinations Bar charts range, mode, median, mean Scatter Graphs Conversion Graphs Main menu

Topics Level 1 and 2 Algebra Shape and Space Data Handling + Graphs Number

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2a + 3a + a = 6a 3c – c = 2c 2t -5t = -3t 3p x 4 = 12p t x t = t ² Algebra Main Menu Expressions 2a + 3a + a = 6a 3c – c = 2c 2t -5t = -3t 3p x 4 = 12p t x t = t ² t x t x t = t ³ 2t x 3t = 6t ² 20a ÷ 4 = 5a 15c ÷ 3c = 5

Carol has 2 less than Alan. Carol has m-2 Algebra Main Menu Forming Expressions Alan has m sweets Bob has 3 more than Alan. Bob has m+3 Carol has 2 less than Alan. Carol has m-2 Diana has twice as much as Alan. Diana has 2m Edward has three times as much as Alan. Edward has 3m Altogether they have m + m+3 + m-2 + 2m + 3m = 8m + 1

3( a + b) 2( a + b) 3 lots of (a+b) 2 lots of (a+b) a+b + a+b + a+b Algebra Main Menu Multiplying Brackets 3( a + b) 3 lots of (a+b) a+b + a+b + a+b = 3a + 3b 2( a + b) 2 lots of (a+b) a+b + a+b = 2a + 2b 4 + 3( 2a + 1) 4 plus 3 lots of 2a+1 4 + 2a+1 + 2a+1 + 2a+1 = 4 + 6a + 3 = 6a + 7 2( 3a + 2b) 2 lots of (3a+2b) 3a+2b + 3a+2b = 6a + 4b

= 2(12a + 8b) or 4(6a + 4b) but they still have common factors Algebra Main Menu Factorising 2a + 4b = 2(a + 2b) 6a + 4b = 2(3a + 2b) 9a + 6b = 3(3a + 2b) 24a + 16b = 2(12a + 8b) or 4(6a + 4b) but they still have common factors = 8(3a + 2b) is better 18a + 30 = 6(3a + 5) 10a + 15b = 5(2a + 3b)

Solve 3w = 9 ÷3 ÷3 w = 3 x / 4 =12 x 4 x 4 x = 48 3y + 6 = 18 -6 -6 Algebra Main Menu Equations Find the value of………………Solve these equations…………… Solve 3w = 9 ÷3 ÷3 w = 3 x / 4 =12 means x divided by 4 =12 x 4 x 4 x = 48 3y + 6 = 18 -6 -6 3y = 12 ÷3 ÷3 y = 4

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Adding and Subtracting Main Menu Decimals Adding and Subtracting Sequences Comparing Decimals

0.34 Main Menu 0.3 + 0.04=

0.51 Main Menu 0.34 + 0.17=

Main Menu 0.49 + 0.23 =

0.72 0.49 + 0.23 = Main Menu

0.31 Main Menu 0.25 + 0.06 =

0.85 0.25 + 0.6 = Main Menu

Sequences 1.0 1.2 0.8 Find the next 3 terms Main Menu Sequences Find the next 3 terms A) 0.2, 0.4, 0.6, …. , …. , ….

2.6 1.5 2.5 2.4 1.2 3.0 2.2 0.9 2.0 Find the next 3 terms Main Menu 0.5, 1.0, 1.5, …. , …. , ….. 0 , 0.3 , 0.6, …. , …. , …. D) 1.6 , 1.8 , 2.0 , …. , …. , ….

0.25 0.30 0.20 Main Menu E) 0.05 , 0.1 , 0.15 , …. , …. , ….

Which is the largest number? Are you sure? Think of strips and squares Main Menu Which is the largest number? 0.4 or 0.15

Which is the largest? A) 0.25 or 0.3 B) 0.5 or 0.71 C) 0.6 or 0.59 Main Menu Which is the largest? A) 0.25 or 0.3 B) 0.5 or 0.71 C) 0.6 or 0.59 D) 0.75 or 0.125 or 0.075

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Main Menu Percentage Fractions

Main Menu Section 1 Building Percentages 10% 1%

100% is equivalent to one whole 30 35 3.5 45.5 0.4 60 70 7 91 0.8 15 17.5 1.75 22.75 0.2 3 3.5 0.35 4.55 0.04 Finding 10% is a useful starting point to finding percentages of amounts 100% is equivalent to one whole 10% means 10 out of every 100 10 % is one tenth To find 10% find one tenth ÷ by 10 Main Menu Find 10% of 300 350 35 455 4 Find 20% of 300 350 35 455 4 Find 5% of 300 350 35 455 4 Find 1% of 300 350 35 455 4

Start with 10% and build these percentages 2.5+ 1.25 = 3.75 2.4 + 1.2 = 3.6 35 + 3.5 = 38.5 10% 10% 10% 10% 1% 5% 6+6+6 + 3 = 21 0.5% 10% 5% 1% Start with 10% and build these percentages 35% 35% of 60 = 15% of 24 = 15% 11% of 350 = 11% 1.5% of 250 = 1.5% Main Menu

Price after 10% rise £20 + £2 = £22 Price after 5% rise £22 + £1.10 = £23.10 Add this to the initial value. £150 000 + £ 42 000 £ 192 000 Find 28% ( £15 000 X 3 ) – ( £1 500 X 2 ) = £45 000 -3 000 =£42 000 120 – ( 12 + 6 ) = £ 102 30% - 2% Problems Main Menu 1. If the value of a house increases by 28% from £150 000 , find its new value. 2. If a coat is reduced 15% in the sale from £120, find its sale price. 3. If the price of a train ticket increases 10% one year and 5% the next from £20 , find the cost after the two increases.

Percentages expressed as Decimals Main Menu Section 2 Percentages expressed as Decimals Calculator work 0.01 is 1% 0.10 is 10% 0.08 is 8% 0.30 is 30% 0.025 is 2.5% 0.35 is 35% 0.005 is 0.5% 0.175 is 17.5%

Find these percentages 6 160 2.75 39.6 6 3142.5 1.5 3.75 67500 6 6875 7.5 2.5 78750 Using a Calculator Find these percentages Main Menu Hint: Find 1% by dividing by 100. Then multiply by the percentage you need to find. 2% of 300 3% of 250 8% of 2000 10% of 25 11% of 25 15% of 40 33% of 120 0.5% of 300 1.5% of 250 12.5% of 48 5.25% of 65 000 150% of 45 000 175% of 45 000 2.5% of 275 000

Main Menu Section 3 Finding the original value (100%) after a percentage increase or decrease Given 120% To find 1% ÷ 120 Then x 100 Given 80% To find 1% ÷ 80 Then x 100

12000 + 1200 (10%) = 13 200 £12000 Problems to find the initial value after being given the value after an increase or decrease The price of a new car increases by 10%. The price after the increase is £ 13 200 Find the price before the increase. 100%+10% = 110% 110% £ 13 200 Find 1% 13 200 ÷ 110 then x 100 = Check the problem Main Menu

If a car loses 20% of its value and it is worth £ 6 000 £ 6 000 - £1 200 (20%) = £4 800 80% £4 800 4800 ÷ 80 x 100 = If a car loses 20% of its value and it is worth £4 800 , find its original value. What percentage represents £4 800 ? Now calculate the original value. Remember to write down the numbers you use even on the calculator paper. Check the problem Main Menu

Main Menu Fractions of Amounts 47

Measures 1 1000 g = 1 kg How many grams is ½ kg ? Main Menu Measures 1 1000 g = 1 kg How many grams is ½ kg ? How many grams is ¼ kg ? How many grams is ¾ kg ? 48

Measures 2 Main Menu 1 Kg 1000 g 250, 500, 750, 1000, ........, ......... ¼ , ½ , ¾ , 1, ........, ......... 250 g 250 g 250 g 250 g 49

Main Menu Measures 3 100 cm = 1 m How many centimetres is ½ m ? How many centimetres is ¼ m ? How many centimetres is ¾ m ? 50

Main Menu Measures 4 1 m 100 cm 25 cm 25 cm 25 cm 25 cm 25, 50, 75, 100, ........, ......... ¼ , ½ , ¾ , 1, ........, ......... 51

Main Menu Measures 5 1000 m = 1 km How many metres is ½ km ? How many metres is ¼ km ? How many metres is ¾ km ? 52

Main Menu Measures 6 1 km 1000 m 250 m 250 m 250 m 250 m 250, 500, 750, 1000, ........, ......... ¼ , ½ , ¾ , 1, ........, ......... 53

Main Menu Measures 7 15, 30, 45, 60, ........, ......... ¼ , ½ , ¾ , 1, ........, ......... 12 15 min 3 6 54

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Main Menu Multiplication 23 x 32 23 x 30 = 690 23 x 2 = 46 690 +46 736 46 x 23 46 x 20 = 920 46 x 3 = 138 920 +138 1058

Write each of these numbers as a product of prime factors. Main Menu 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37…... Prime Numbers a number produced by multiplying Product Write each of these numbers as a product of prime factors. Examples: 6= 2x3 and 15=3x5 14= 2x7 4= 2x2 12= 2x2x3

Write each of these numbers as a product of prime factors. Main Menu Write each of these numbers as a product of prime factors. 10 9 22 21 33 25 49 = 2x5 = 3x3 = 2x11 = 3x7 = 3x11 = 5x5 = 7x7 20 18 66 42 99 50 98 = 2x2x5 = 2x3x3 = 2x3x11 = 2x3x7 = 3x3x11 = 2x5x5 = 2x7x7

Write each of these numbers as a product of prime factors. 100 90 220 210 330 250 490 2x2x5x5 3x3x2x5 2x11x2x5 3x7x2x5 3x11x2x5 5x5x2x5 7x7x2x5 400 180 72 360 900 Main Menu

Find the prime factors of 60 Main Menu Find the prime factors of 60 Prime Numbers 2, 3, 5, 7, 11 10= 2x5 6= 2x3 60= 2x2x3x5 or 2² x 3 x 5 Find the prime factors of these numbers: 112 30 21 24 100 Find the prime factors of these numbers: 116 25 75 40 90

Recipe for 4 2 kg flour 2 litres water 500g sugar 1 kg strawberries Main Menu Recipe for Splodge! Recipe for 4 2 kg flour 2 litres water 500g sugar 1 kg strawberries 3 bags skittles 200g mushy peas 250g butter Recipe for 8 4kg 4l 1000g or 1kg 2kg 6 400g 500g Recipe for 6 3kg 3l 750g 1.5kg 4.5 300g 375g

Square Numbers or Perfect Squares Cube Numbers Main Menu 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 5 x 5 = 25 6 x 6 = 36 7 x 7 = 49 8 x 8 = 64 9 x 9 = 81 10x 10 =100 1²= 1x1= 1 2²= 2x2= 4 3²= 3x3= 9 4² 5² 6² 7² 8² 9² 10² 1³ = 1x1x1 = 2³ = 2x2x2 = 8 3³ = 3x3x3 = 4³ = 5³ = 5x5x5 =125 6³ = 7³ = 8³ = 9³ = 10³=10x10x10=1000 The area of this square is 400cm². (a) What is the length of one side? (b) What is the perimeter of the square? 1 side = √400 = 20cm perimeter = 20cm x 4 = 80cm

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Circumference = 2 x п x r = п d If r=5 C = 2 п r C = 2 x п x r Circumference of Circles Main Menu r Circumference = 2 x п x r = п d If r=5 C = 2 п r C = 2 x п x r C = 2 x п x 5 C = 31.42 If r=3 C = 2 п r C = 2 x п x r C = 2 x п x 3 C = 18.85 If d=8 C = п d C = п x d C = п x 8 C =25.13

Area = п r² Area of Circles If r=3 If d=8 Area = п r² Area = п r² Main Menu Area of Circles Area = п r² If r=3 Area = п r² Area = п x 3 x3 Area = 28.27 = 28.3 (1dp) If d=8 Area = п r² Area = п x 4 x4 Area = 50.27 = 50.3 (3sf)

Area and Perimeter Perimeter = 2 ( 10 + 2 ) = 24m Area = 2 X 10 = 20m² Main Menu 10m 2m Perimeter = 2 ( 10 + 2 ) = 24m Area = 2 X 10 = 20m²

Main Menu Area of Triangles h height b Find the area of a triangle with base 10cm and height 8 cm. Area = (10 x 8) ÷ 2 Area = 80 ÷ 2 Area = 40 cm² base Area of = ½ ( b x h ) Area of = b x h 2

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