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Year 10 Revision Notes 1 Revision List 1. Types of Number 11. 3-d Shapes 2. Rounding 12. Volume 3. Time 13. Symmetry 4. The Calendar 14. Angles 5. Negative Numbers 15. Co-ordinates 6. 2-d Shapes 16. Fractions/Decimals/Percentages 7. Triangles 8. Quadrilaterals 9. Perimeter and Area 10. The Circle 2 1 – Types of Number Prime Numbers – A prime number can ONLY be divided by itself AND 1. eg. 2, 3, 5, 7, 11, 13, 17, 19, … Note : ALL prime numbers (except 2) are ODD numbers! Square Numbers – A square number is the answer you get when you multiply a whole number by itself. eg. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, … 3 1 – Types of Number Cube Numbers – A cube number is the answer you get when you multiply a whole number by itself twice. eg. 1, 8, 27, 64, 125, … 4 1 – Types of Number Multiples – The multiples of a number are the answers to its times table. eg. Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, … Multiples of 10 = 10, 20, 30, 40, 50, … Factors – The factors of a number are the whole numbers that divide exactly into it. eg. Factors of 10 = 1, 10, 2, 5 Factors of 40 = 1, 40, 2, 20, 4, 10, 5, 8 5 2 – Rounding • To the nearest 10 • To the nearest 100 Eg. Eg. 81 ≈ 80 58 ≈ 100 76 ≈ 80 11 ≈ 0 85 ≈ 90 135 ≈ 100 112 ≈ 110 781 ≈ 800 234 ≈ 230 1234 ≈ 1200 6 2 – Rounding • To the nearest 1000 Eg. 599 ≈ 1000 2356 ≈ 2000 3981 ≈ 4000 5500 ≈ 6000 212 ≈ 0 7 3 – Time 12 Hour Clock The 12 Hour clock works from 1 to 12 and back again! The way to show the difference between morning and evening is to use am and pm. am – means before noon (and after midnight) pm – means after noon Eg. 8.30 am = half past eight in the morning 9.45 pm = a quarter to ten at night 1.20 pm = twenty past one in the afternoon 8 3 – Time 24 Hour Clock The 24 Hour clock runs all the way to 24!! It can only be shown on a digital clock. You never use am or pm with 24 hour clock – you will lose marks if you write 13.00pm!! Eg. 1 pm = 13:00 2 pm = 14:00 5.15 pm = 17:15 7.45 am = 07:45 Midnight = 00:00 9 4 – The Calendar 1st January 7th July 2nd February 8th August 3rd March 9th September 4th April 10th October 5th May 11th November 6th June 12th December 30 days has September, April, June and November All the rest have 31, except for February alone It has 28 days clear and 29 on each leap year! 10 5 – Negative Numbers Negative numbers are less than zero! -11 -10 -9 - 8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 Negative Positive Adding Subtracting 11 5 – Negative Numbers Two signs together : ++ means Add +- means Subtract Two of the SAME signs together means ADD -+ means Subtract but a MIXTURE means MINUS -- means Add Multiplying and Dividing Two numbers with the SAME signs, multiplied or divided by each other will give a POSITIVE answer. Two numbers with DIFERENT signs multiplied or divided by each together will give a NEGATIVE answer. 12 6 - 2D Shapes A 2D shape is FLAT. You cannot pick them up!! 3 Sides – Triangle 4 Sides - Quadrilateral 13 5 Sides – Pentagon 108° Irregular Regular (all equal sides AND angles) 14 6 Sides – Hexagon 120° Irregular Regular 15 8 Sides – Octagon 135° Irregular Regular 16 7 Sides – Heptagon (Regular = angle of 128.6°) 9 Sides – Nonagon (Regular = angle of 140°) 10 Sides – Decagon (Regular = angle of 144°) 12 Sides – Dodecagon (Regular = angle of 150°) 120° 17 7 - Triangles A triangle is a polygon with 3 sides. Its angles always add to 180° Equilateral Isosceles 120° * 3 equal sides * 3 equal 60° angles * 3 lines of symmetry * Rotational symmetry order 3 * 2 equal sides * 2 equal angles * 1 line of symmetry * No rotational symmetry 18 Scalene Right-Angled * No equal sides * No equal angles * No lines of symmetry * No rotational symmetry * One 90° angle **This one can also be 120° Isosceles 19 8 - Quadrilaterals A quadrilateral is a polygon with 4 sides. Its angles always add to 360° Square * 4 equal sides * 4 right angles * 4 lines of symmetry * Rotational symmetry order 4 Rhombus (Drunken Square) 120° * 4 equal sides * Opposite angles equal * 2 line of symmetry * Rotational symmetry order 2 20 Rectangle * Opposite sides equal * 4 right angles * 2 lines of symmetry * Rotational symmetry order 2 Parallelogram (Drunken Rectangle) * * * * Opposite sides equal Opposite angles equal No lines of symmetry 120° Rotational symmetry order 2 21 Trapezium * 1 pair of parallel sides Kite * 1 line of symmetry 120° 22 9 - Perimeter and Area Perimeter – The distance around the OUTSIDE of a shape! To find the perimeter of a shape, we just add up ALL the sides! Eg. Eg. 5 cm 3.5 cm 120° 5 cm 8 cm 1 cm 4 cm 2 cm 2 cm 23 Area - the amount of space INSIDE a shape! To find the area of an irregular shape, you can often just count the squares inside it!! To find the area of a regular shape – you must choose the appropriate formula!! ** Note : Area can be measured in mm2 cm2 m2120° km2 24 Area of a Rectangle breadth length 120° Area = length × breadth ** Note that this formula also works for a SQUARE!! 25 Area of a Triangle height base 120° Area = ½ × base × height 26 Area of a Parallelogram height base 120° Area = base × height ** Note that this formula also works for a RHOMBUS!! 27 Area of a Trapezium a height b 120° Area = ½ × (sum of the parallel sides) × height 28 10 - The Circle Radius Sector 29 Radius - A line drawn from the centre of a circle to its edge (r) Diameter - A line drawn from edge to edge of a circle, through its centre (D) { D = 2r} Chord - A line drawn from edge to edge of a circle NOT through its centre 120° Sector - A “pizza slice” of a circle – made by 2 radii 30 Circumference - the distance around the OUTSIDE of a circle! C = 2 × π × radius Area - the formula for the area of a circle is a bit more complicated than for other shapes, but you just need to learn it off!! Area = π × radius 2 31 11 - 3-d Shapes A 3-d shape is one that is solid – it is possible to pick it up! Cube Cuboid * 6 square faces * 8 Vertices * 12 Edges * 6 rectangular faces * 8120° Vertices * 12 Edges 32 Triangular Prism * 5 faces (2 tri & 3 rect) * 6 Vertices * 9 Edges Cylinder * 2 faces * 0 Vertices * 2 120° Edges 33 12 - Volume Volume - the amount of space INSIDE a 3-d shape! To find the volume of an irregular shape, you can often just count the little cubes inside it!! mm3 ** Note : Volume can be measured in cm3 m3 120° km3 34 Volume of a Cuboid Height Breadth Length 120° Volume = Length × Breadth × Height 35 13 - Symmetry Line Symmetry : A line of symmetry cuts a shape EXACTLY in 2, so that one side is the mirror image of the other! Rectangle Isosceles Triangle Square Parallelogram 36 Rotational Symmetry : 37 14 - Angles Types of Angle Acute Angle Right Angle (Less than 90°) (Exactly 90°) Obtuse Angle Straight Angle (Between 90° and 180°) (Exactly 180°) Reflex Angle (Between 180° and 360°) 38 Angle Facts ◊ Angles in a Triangle add to 180° ◊ Angles in a Quadrilateral add to 360° ◊ Angles on a Straight Line add to 180° ◊ Angles around a Point add up to 360° ◊ Vertically Opposite Angles are EQUAL a=c b a c d b=d 39 ◊ Alternate Angles are Equal (Can be remembered as angles in a Z shape!) ◊ Corresponding Angles are Equal (Can be remembered as angles in an F shape!) 40 Compass Directions North (N) North East (NE) North West (NW) West (W) South West (SW) 45° South (S) East (E) South East (SE) 41 15 – Co-ordinates Co-ordinates help us to describe the position of a point. y 9 8 7 6 5 4 3 2 1 Point P = (5,4) Because it is 5 across and 4 up P 1 2 3 4 5 6 7 8 9 Origin Remember : x X is a cross so WISE UP! ** Note : the x co-ordinate always comes before the y (just like in the alphabet!!) 42 16 – Fractions, Decimals And Percentages Conversions : Fraction 1 ½ ¼ ¾ 1/10 ⅓ ⅔ Decimal 1.0 0.5 0.25 0.75 0.1 0.33333 0.66666 Percentage 100% 50% 25% 75% 10% 33 ⅓% 66 ⅔% 43