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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