Foundation Paper 1 Revision Powerpoint

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

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 out of 40 means 8 / 40 8 / 40 = 4 / 20 = 20 / 100 = 20% 160 out of 200 means 160 / / 200 = 80 / 100 = 80%

Put these decimals in order of size: Ordering Decimals Rewrite each number with extra 0s So order is (smallest to largest) 0.09, 0.71, 0.73, 0.8, 0.801

Draw the graph of: y = 3x - 2 x y 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

(-3,-11) (-2,-8) (-1,-5) (0,-2) (1,1) (2,4) (3, 7) (4, 10) y = 3x – 2

Construct a triangle that has a side 10cm, and angles of 37° and 60° 10cm 0 37° 37° Constructing Triangles: 2 Angles

10cm 37° 37° 0 60° Construct a triangle that has a side 10cm, and angles of 37° and 60°

Construct a triangle that has sides 8cm, 7cm and an angle of 45° 8cm 0 45° Constructing Triangles: 2 Sides

8cm 45° 7cm Construct a triangle that has sides 8cm, 7cm and an angle of 45°

StemLeaves 2 5 means 25

State two things that are wrong with this questionnaire: How many Playstation 3 games did you buy? 0 – 5 5 –

Metric Units of Measurement centimetres grams litre millilitre metre millimetre kilograms

miles stones pints gallons feet inches pounds Imperial Units of Measurement ounces

2 metres 4 x 2 = 8 metres

Fractions, Decimals, Percentages

Tessellations Fit together like a jigsaw without any gaps

Enlargement Enlarge the shape with scale factor 2 Make all the lengths twice as big. Do the horizontal and vertical lines first

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

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 = = 84 cm ²

x 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)

Multiply out the brackets and simplify: ( x - 2 ) ( x + 6) X (Multiply) x- 2 x + 6 x² - 2x + 6x- 12 Answer: x² + 4x - 12

2 + 3 = = 29 = Adding Fractions: SMILEY FACE

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

Top first: 6 5 × 6² = 6 7 (Add the powers) 6 7 = 6³ (DIVIDE: Subtract the powers) 6 4

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 = = £48 Then add on to the amount to get the final answer £320 + £48 = £368

Angles in a quadrilateral add up to – 90 – 62 – 136 = 72⁰ x = 180 – 72 = 108⁰ as it’s on a straight line

Estimate the following calculations a) 86.6 x 34.2 ≈ 90 x 30 = 2700 = b) 74.9 ≈ 70 = 70 x 2 = When we divide by 0.5 this is the same as multiplying by 2 Round each number as simply as possible

Bearing: Angle measured from North, Clockwise 056˚ (Always need 3 figures) This is the angle required 360 – 142 = 218˚ (Answer)

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)

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)

The Perpendicular Bisector of Line AB AB

The Angle Bisector The angle bisector will divide an angle exactly in half.

Time (t minutes) Frequency 10  t <  t <  t <  t <  t < 30 3 Draw a frequency Polygon Plot against midpoints 12, 16, 20, 24, 28

ROTATION 180⁰ about (0, 0) Use your Tracing Paper

Food Mart: 1 yoghurt = 180 ÷ 5 = 36p Jim’s: 1 yoghurt = 105 ÷ 3 = 35p So Jim’s is better value

113⁰ because corresponding (F angle) So x = 180 – 113 = 63⁰ because straight line

127⁰ because alternate (Z angle)

Draw the front & side elevations and the plan of this shape on the cm squared paper Side Front Plan

Solve:7x – 8 = 27 x 27 X  7 7 7 So x = 5 Solving Linear Equations

Angles in triangle add to 180 degrees 3x 2x x x + 30 So 6x + 30 = 180 Use function machines to solve: x = (180 – 30) ÷ 6 = 25˚

Solve:n + 11=3n + 6 n nnn 11 6 n n + 6 So 2n + 6 = 11 5 So 2n = 5 So n = 2.5 Solving Equations with Unknown on Both Sides

So 180 = 2 x 2 x 3 x 3 x 5 = 2 2 x 3 2 x 5 Prime Factor Powers

Angles in Shapes Isosceles Triangle: Two bottom angles are the same. 180 – 44 = 136 x = 136 ÷ 2 = 68°

Also may be asked about the PLAN: Birds eye view

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 = = 42 marks So Niamh who scored 45 marks got higher