Download Foundation GCSE Key Facts 102.08KB 2017-03

FOUNDATION GCSE MATHEMATICS:
STUDENTS MUST MEMORISE THE FOLLOWING:
N
Not to scale:
N
Bearings are measured from north in a clockwise
direction and are written with 3 figures
eg Bearing of B from A is 048o Bearing of A from B is 312o
48
B
312o
o
A
Interior angles of a triangle add up to 180 degrees
Interior angles of a quadrilateral add up to 360 degrees
Interior angles of a pentagon add up to 540 degrees etc
Exterior angles of any shape add up to 360 degrees
a
b
d
c
f
e
g
b
h
Parallel Lines and Transversals
Opposite angles are the same (a & d , b & c , e & h , f & g)
Corresponding angles are the same (a & e , b & f , c & g , d & h)
Alternate angles are the same (c & f , d & e)
and all angles on a straight line are supplementary meaning they
add up to 180 degrees
Perimeter = length around the outside edge of a closed shape
Area of a rectangle = length × width cm2
Area of a triangle = ½ base × height cm2
cm
(area is equivalent to counting how many squares)
(complete the triangle into a rectangle then halve the area)
l1
h
Area of trapezium = (average of length 1 and length 2) × height
l2
Volume of a prism = Area of cross section × length of prism
tangent
radius
chord
i.e.
l1  l 2
 h cm2
2
cm3
Parts of a circle,
circumference and area
diameter
sector
C = πd
“Cherry pie’s delicious,
Apple pies are too!
circumference
Circumference of circle = п × diameter (where п ≈ 3.14)
Area of circle = п × radius2
Pythagoras’ Theorem: for any right-angled triangle: a2 + b2 = c2
Remember: always label the length opposite the right angle: “c”
A = πr2
c
b
a
b
Imperial to metric conversions
2.2 pounds (lbs) ≈ 1 kilogram
5 miles ≈ 8 kilometres
1 gallon ≈ 4.5 litres
1 inch ≈ 2.5 centimetres
1.75 pints ≈ 1 litre
1 foot ≈ 30 centimetres
Metric equivalences
10 millimetres = 1 centimetre
100 centimetres = 1 metre
1000 millimetres = 1 metre
1000 metres = 1 kilometre
1000 milligrams = 1 gram
1000 grams = 1 kilogram
1000 kilograms = 1 (metric) tonne
Compound measures:
Speed =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
Imperial equivalences
12 inches = 1 foot
14 pounds = 1 stone
𝑀𝑎𝑠𝑠
Density = 𝑉𝑜𝑙𝑢𝑚𝑒
𝑇𝑖𝑚𝑒
Naming some common shapes and properties of shapes
2D
3D
Equilateral triangle (all sides same length)
Triangular-based pyramid (tetrahedron)
Isosceles triangle (2 sides same length)
Square-based pyramid
Scalene triangle (all sides different length)
Cone
Square
Cube
Rectangle
Cuboid
Rhombus (like a diamond … diagonals perpendicularly bisect)
Triangular prism (understand the word prism!)
Parallelogram (2 pairs of parallel sides)
Cylinder
Kite (one diagonal perpendicularly bisects the other)
Trapezium (just one pair of parallel sides eg:
)
Equivalent fractions, decimals and percentages:
1
2
 0.5  50%
1
3
 0.3333...  33.333...%
1
8
 0.125  12.5%
1
9
 0.1111...  11.11...%
1
4
 0.25  25%
3
8
2
3
3
4
 0.75  75%
 0.2  20%
2
5
 0.4  40%
3
5
 0.6  60%
 0.6666...  66.666...%
 0.375  37.5%
2
9
1
5
5
8
 0.625  62.5%
7
8
 0.875  87.5%
 0.2222...  22.222...% etc
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 … etc
Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 … etc
Cube numbers: 1, 8, 27, 64, 125 … etc
Triangular numbers: 1, 3, 6, 10, 15, 21, 28, … etc
Equation of a straight line:
or
y = mx + c
…
y=…x+…
(where m is the gradient and c is the y-intercept)
Averages and spread:
f = frequency (this means “how many”)
x = the variable
Mean: Sum of values ÷ number of values
(this involves “making all piles the same size”)
Median: Middle value when written in size order
Mode: Most common value
Range: Largest value – smallest value