Mathematics Essentials: Numbers, Shapes, Time, Calendar, Symmetry - Year 10 Revision Notes

1. Year 10 Revision Notes

2. Revision List • Types of Number 11. 3-d Shapes • Rounding 12. Volume • Time 13. Symmetry • The Calendar 14. Angles • Negative Numbers 15. Co-ordinates • 2-d Shapes 16. Fractions/Decimals/Percentages • Triangles • Quadrilaterals • Perimeter and Area • The Circle

3. 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, …

4. 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, …

5. 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

6. 2 – Rounding • To the nearest 10 • Eg. 81 ≈ 80 • 76 ≈ 80 • 85 ≈ 90 • 112 ≈ 110 • 234 ≈ 230 • To the nearest 100 • Eg. 58 ≈ 100 • 11 ≈ 0 • 135 ≈ 100 • 781 ≈ 800 • 1234 ≈ 1200

7. 2 – Rounding • To the nearest 1000 • Eg. 599 ≈ 1000 • 2356 ≈ 2000 • 3981 ≈ 4000 • 5500 ≈ 6000 • 212 ≈ 0

8. 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

9. 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

10. 4 – The Calendar 1stJanuary 7thJuly 2ndFebruary 8thAugust 3rdMarch 9thSeptember 4thApril 10thOctober 5thMay 11thNovember 6thJune 12thDecember 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!

11. 5 – Negative Numbers Negative numbers are less than zero! NegativePositive -11 -10 -9 - 8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 Adding Subtracting

12. 5 – Negative Numbers Two signs together : ++ means Add +- means Subtract -+ means Subtract -- 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. Two of the SAME signs together means ADD but a MIXTURE means MINUS

13. 6 - 2D Shapes A 2D shape is FLAT. You cannot pick them up!! 3 Sides – Triangle 4 Sides - Quadrilateral

14. 5 Sides – Pentagon Irregular Regular (all equal sides AND angles) 108°

15. 6 Sides – Hexagon Irregular Regular 120°

16. 8 Sides – Octagon Irregular Regular 135°

17. 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°

18. 7 - Triangles A triangle is a polygon with 3 sides. Its angles always add to 180° Equilateral Isosceles * 3 equal sides * 2 equal sides * 3 equal 60° angles * 2 equal angles * 3 lines of symmetry * 1 line of symmetry * Rotational symmetry order 3 * No rotational symmetry 120°

19. Scalene Right-Angled * No equal sides * One 90° angle * No equal angles * No lines of symmetry **This one can also be * No rotational symmetryIsosceles 120°

20. 8 - Quadrilaterals A quadrilateral is a polygon with 4 sides. Its angles always add to 360° Square Rhombus (Drunken Square) * 4 equal sides * 4 equal sides * 4 right angles * Opposite angles equal * 4 lines of symmetry * 2 line of symmetry * Rotational symmetry order 4 * Rotational symmetry order 2 120°

21. Rectangle Parallelogram (Drunken Rectangle) * Opposite sides equal * Opposite sides equal * 4 right angles * Opposite angles equal * 2 lines of symmetry * No lines of symmetry * Rotational symmetry order 2 * Rotational symmetry order 2 120°

22. Trapezium Kite * 1 pair of parallel sides * 1 line of symmetry 120°

23. 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 8 cm 3.5 cm 1 cm 4 cm 120° 2 cm 2 cm 5 cm

24. 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 m2 km2 120°

25. Area of a Rectangle Area = length × breadth ** Note that this formula also works for a SQUARE!! breadth length 120°

26. Area of a Triangle Area = ½ × base × height height base 120°

27. Area of a Parallelogram Area = base × height ** Note that this formula also works for a RHOMBUS!! height base 120°

28. Area of a Trapezium Area = ½ × (sum of the parallel sides) × height a height b 120°

29. 10 - The Circle Diameter Radius Sector Chord Circumference

30. 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 Sector - A “pizza slice” of a circle – made by 2 radii 120°

31. 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

32. 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 * 6 rectangular faces * 8 Vertices * 8 Vertices * 12 Edges * 12 Edges 120°

33. Triangular Prism Cylinder * 5 faces (2 tri & 3 rect) * 2 faces * 6 Vertices * 0 Vertices * 9 Edges * 2 Edges 120°

34. 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!! ** Note : Volume can be measured in mm3 cm3 m3 km3 120°

35. Volume of a Cuboid Height Breadth Length 120° Volume = Length × Breadth × Height

36. 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

37. Rotational Symmetry :

38. 14 - Angles Types of Angle Acute Angle (Less than 90°) Right Angle (Exactly 90°) Obtuse Angle (Between 90° and 180°) Straight Angle (Exactly 180°) Reflex Angle (Between 180° and 360°)

39. 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 = d b c a d

40. Alternate Angles are Equal • Corresponding Angles are Equal (Can be remembered as angles in a Z shape!) (Can be remembered as angles in an F shape!)

41. Compass Directions North (N) North East (NE) North West (NW) 45° West (W) East (E) South West (SW) South East (SE) South (S)

42. 15 – Co-ordinates Co-ordinates help us to describe the position of a point. y Point P = (5,4) Because it is 5 across and 4 up Remember : X is a cross so WISE UP! ** Note : the x co-ordinate always comes before the y (just like in the alphabet!!) 9 8 7 6 P 5 4 3 2 1 x 1 2 3 4 5 6 7 8 9 Origin

43. 16 – Fractions, Decimals And Percentages Conversions :