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Foundation Paper 1 Revision Powerpoint
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Volume of Cuboids Volume of cuboid = length x width x height What is the volume of this cuboid? 10cm 7cm 9cm Volume = 9 x 7 x 10 = 630cm³
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Write the following as percentages a) 8 out of 40 b) 160 out of 200 Fractions to Percentages Change so that the fraction is out of 100 8 out of 40 means 8 / 40 8 / 40 = 4 / 20 = 20 / 100 = 20% 160 out of 200 means 160 / 200 160 / 200 = 80 / 100 = 80%
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Put these decimals in order of size: 0.730.80.801 0.710.09 Ordering Decimals Rewrite each number with extra 0s 0.730 0.800 0.801 0.710 0.090 So order is (smallest to largest) 0.09, 0.71, 0.73, 0.8, 0.801
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Draw the graph of: y = 3x - 2 x-3-201234 y -11 -8 -5 -2 1 4 7 10 Straight Line Graphs Start with positive values 3×0-2 = -2 3×1-2 = 1 3×2-2 = 4 And look for pattern. It goes up in threes
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(-3,-11) (-2,-8) (-1,-5) (0,-2) (1,1) (2,4) (3, 7) (4, 10) y = 3x – 2
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Construct a triangle that has a side 10cm, and angles of 37° and 60° 10cm 0 37° 37° Constructing Triangles: 2 Angles
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10cm 37° 37° 0 60° Construct a triangle that has a side 10cm, and angles of 37° and 60°
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Construct a triangle that has sides 8cm, 7cm and an angle of 45° 8cm 0 45° Constructing Triangles: 2 Sides
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8cm 45° 7cm Construct a triangle that has sides 8cm, 7cm and an angle of 45°
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15322510445 293942172119 0123401234 5 05790579 599599 2929 2424 StemLeaves 2 5 means 25
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State two things that are wrong with this questionnaire: How many Playstation 3 games did you buy? 0 – 5 5 – 10 10 - 15
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Metric Units of Measurement centimetres grams litre millilitre metre millimetre kilograms
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miles stones pints gallons feet inches pounds Imperial Units of Measurement ounces
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2 metres 4 x 2 = 8 metres
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Fractions, Decimals, Percentages
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Tessellations Fit together like a jigsaw without any gaps
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Enlargement Enlarge the shape with scale factor 2 Make all the lengths twice as big. Do the horizontal and vertical lines first
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Area of Triangle Area = 12 x 8 2 = 48cm² Multiply BUT remember to halve your answer Find the area of this triangle REMEMBER your UNITS
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10cm 18cm 6cm Find the area of this trapezium 8cm 6cm 6 x 10 = 60 cm ² 6 x 8 ÷ 2 = 24 cm ² Total Area = 60 + 24 = 84 cm ²
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0 1 2 3 4 5 6 7 8 9 x 1 9 8 7 6 5 4 3 2 y Translation through AB 4 right 2 up Describe the transformation fully from A to B The top number represents horizontal movement (Left or Right) The Bottom number represents vertical movement (Up or Down)
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Multiply out the brackets and simplify: ( x - 2 ) ( x + 6) X (Multiply) x- 2 x + 6 x² - 2x + 6x- 12 Answer: x² + 4x - 12
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2 + 3 = 8 + 21 7 4 28 = 29 = 1 1 28 28 Adding Fractions: SMILEY FACE
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Nadia wants to collect information about the different ways in which teachers travel to school. Design a suitable data collection sheet that Nadia could use to collect the information. How do you travel to school each day? Bus Car Walk Train OTHER TALLYFrequency
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Top first: 6 5 × 6² = 6 7 (Add the powers) 6 7 = 6³ (DIVIDE: Subtract the powers) 6 4
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Increase £320 by 15% Find 10% first by dividing by 10 (take off a 0) 10% of £320 = £32 Then halve this to get 5% 5% of £320 = £16 Then add together to get 15% 15% of £320 = 32 + 16 = £48 Then add on to the amount to get the final answer £320 + £48 = £368
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Angles in a quadrilateral add up to 360 360 – 90 – 62 – 136 = 72⁰ x = 180 – 72 = 108⁰ as it’s on a straight line
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Estimate the following calculations a) 86.6 x 34.2 ≈ 90 x 30 = 2700 = 90 32.2 30 30 b) 74.9 ≈ 70 = 70 x 2 = 140 0.51 0.5 When we divide by 0.5 this is the same as multiplying by 2 Round each number as simply as possible
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Bearing: Angle measured from North, Clockwise 056˚ (Always need 3 figures) This is the angle required 360 – 142 = 218˚ (Answer)
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Factorise x² + 3x x² + 3x = x x + 3 x x is common to both parts so this comes out of the brackets = x (x + 3)
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x coordinates: ½ way between 2 and 12 is 7 (2 + 12) ÷ 2 = 7 y coordinates: ½ way between 3 and 7 is 5 (3 + 7) ÷ 2 = 5 ANSWER: (7, 5)
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The Perpendicular Bisector of Line AB AB
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The Angle Bisector The angle bisector will divide an angle exactly in half.
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Time (t minutes) Frequency 10 t < 14 2 14 t < 18 5 18 t < 22 12 22 t < 26 8 26 t < 30 3 Draw a frequency Polygon Plot against midpoints 12, 16, 20, 24, 28
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ROTATION 180⁰ about (0, 0) Use your Tracing Paper
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Food Mart: 1 yoghurt = 180 ÷ 5 = 36p Jim’s: 1 yoghurt = 105 ÷ 3 = 35p 0 3 6 5 1 8 3 0 0 3 5 3 1 0 1 5 So Jim’s is better value
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113⁰ because corresponding (F angle) So x = 180 – 113 = 63⁰ because straight line
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127⁰ because alternate (Z angle)
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Draw the front & side elevations and the plan of this shape on the cm squared paper Side Front Plan
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Solve:7x – 8 = 27 x 27 X 7 - 8 7 7 7 7 + 8 + 8 27 5 So x = 5 Solving Linear Equations
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Angles in triangle add to 180 degrees 3x 2x x + 30 6x + 30 So 6x + 30 = 180 Use function machines to solve: x = (180 – 30) ÷ 6 = 25˚
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Solve:n + 11=3n + 6 n nnn 11 6 n + 11 3n + 6 So 2n + 6 = 11 5 So 2n = 5 So n = 2.5 Solving Equations with Unknown on Both Sides
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180 90 2 2 45 5 9 3 3 So 180 = 2 x 2 x 3 x 3 x 5 = 2 2 x 3 2 x 5 Prime Factor Powers
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Angles in Shapes Isosceles Triangle: Two bottom angles are the same. 180 – 44 = 136 x = 136 ÷ 2 = 68°
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Also may be asked about the PLAN: Birds eye view
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Belinda Section A 75% = ¾ ¾ of 40 = 40 ÷ 4 x 3 = 30 Section B 60% of 20 10% = 2 so 60% = 12 Belinda total = 30 + 12 = 42 marks So Niamh who scored 45 marks got higher
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