Transcript Key_Stage_3_Revision_1_

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