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Year 10 Revision Notes

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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

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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, …

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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, …

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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

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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

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2 – Rounding

• To the nearest 1000

Eg. 599 ≈ 1000

2356 ≈ 2000

3981 ≈ 4000

5500 ≈ 6000

212 ≈ 0

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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

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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

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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!

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5 – Negative Numbers

Negative numbers are less than zero!

Negative Positive

-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

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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

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6 - 2D Shapes

A 2D shape is FLAT. You cannot pick them up!!

3 Sides – Triangle

4 Sides - Quadrilateral

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5 Sides – Pentagon

Irregular Regular

(all equal sides AND angles)

108°

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6 Sides – Hexagon

Irregular Regular

120°

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8 Sides – Octagon

Irregular Regular

135°

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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°

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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

7 - Triangles

120°

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Scalene Right-Angled

* No equal sides * One 90° angle* No equal angles * No lines of symmetry **This one can also be* No rotational symmetry Isosceles

120°

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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

8 - Quadrilaterals

120°

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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°

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Trapezium Kite

* 1 pair of parallel sides * 1 line of symmetry

120°

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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.

9 - Perimeter and Area

120°5 cm

3.5 cm 8 cm

2 cm2 cm

4 cm

5 cm

1 cm

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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°

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Area of a Rectangle

Area = length × breadth

** Note that this formula also works for a SQUARE!!

120°

length

breadth

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Area of a Triangle

Area = ½ × base × height

120°

height

base

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Area of a Parallelogram

Area = base × height

** Note that this formula also works for a RHOMBUS!!

120°

height

base

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Area of a Trapezium

Area = ½ × (sum of the parallel sides) × height

120°

height

b

a

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10 - The Circle

Radius

Chord

Dia

met

er

Sector

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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°

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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

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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

11 - 3-d Shapes

120°

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Triangular Prism Cylinder

* 5 faces (2 tri & 3 rect) * 2 faces * 6 Vertices * 0 Vertices * 9 Edges * 2 Edges120°

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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

km3120°

12 - Volume

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Volume of a Cuboid

120°

Length

Breadth

Height

Volume = Length × Breadth × Height

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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

13 - Symmetry

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Rotational Symmetry :

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Reflex Angle

(Between 180° and 360°)

Types of Angle

14 - Angles

Acute Angle

(Less than 90°)

Right Angle

(Exactly 90°)

Obtuse Angle

(Between 90° and 180°)

Straight Angle

(Exactly 180°)

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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

ab

cd

a = c

b = d

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◊ 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!)

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Compass DirectionsNorth (N)

South (S)

East (E)West (W)

North East (NE)

South East (SE)

South West (SW)

North West (NW)

45°

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Co-ordinates help us to describe the position of a point.

15 – Co-ordinates

1 2 3 4 5 6 7 8 9

123456789

x

y

Origin

P

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!!)

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Conversions :

16 – Fractions, Decimals And Percentages

Fraction DecimalPercentag

e

1 1.0 100%

½ 0.5 50%

¼ 0.25 25%

¾ 0.75 75%

1/10 0.1 10%

⅓ 0.33333 33 ⅓%

⅔ 0.66666 66 ⅔%