gcse facts angles

CHORD

SEGMENTwww.mathsbox.org.uk

TANGENT

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SQUARE

RHOMBUSwww.mathsbox.org.uk

PYRAMID

TRIANGULAR

PRISMwww.mathsbox.org.uk

CUBE NUMBERS

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1, 8, 27, 64, 125, 216…

1x1x1 , 2x2x2, 3x3x3, 4x4x4, 5x5x5…13 23 33 43, , , , 53,…

PRIME NUMBERS

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2, 3, 5, 7, 11, 13, 17, 19..

Express as a product of primes

24 = 2 x 2 x 2 x 3

AREA of ATRIANGLE

½ x base x heightwww.mathsbox.org.uk

AREA of A PARALLELOGRAM

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b x h

h

b

sin x =

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oh

oppositehypotenuse

cos x =

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a

h

adjacenthypotenuse

tan x =

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a

o

adjacentopposite

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FACTORS

The FACTORS of 24 are1, 2, 3, 4, 6, 8, 12 and 24

1×24 2×12 3×8 4×6

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SIGNIFICANT FIGURESThe first significant figure is the first non-zero figure.

25700 = 30000 (1 significant figure)

0.0225700 = 0.023 (2 significant figures)

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MULTIPLES

The MULTIPLES of 24 are24, 48, 72, 96, 120…

1×24 2×24 3×24 4×24 5×24

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SPEED = distance

time

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DENSITY = volumemass

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VOLUME of a CUBOID

l

l × w × h

w

h

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VOLUME of a CYLINDER

h

r

πr2h

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VOLUME of a PRISMArea of cross section × length

length

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ORDER OF OPERATIONSBrackets Indices (powers) Division Multiplication Addition Subtraction

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STANDARD FORM

a × 10nwhere 1 ≤ A < 10 and n is a whole number

34500 = 3.45 × 104

0.00345 = 3.45 × 10-3

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INTERIOR ANGLESThe SUM of the interior angles of a polygon with n sides is

(n-2)×180⁰

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EXTERIOR ANGLESThe SUM of the exterior angles of any polygon

360⁰

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INDICES AND POWERSa × a × a × a = a4

a4 × a3 = a7

(a3)2 = a6

a7 ÷ a3 = a4

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STRAIGHT LINE GRAPHS

y = mx + cgradient y axis intercept

change in xchange in y

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FIBONACCI SEQUENCE

1, 1, 2, 3, 5, 8, 13, 21…

each term is found by adding together the two previous terms

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ARITHMETIC SEQUENCE 4, 7, 10, 13, 16…..( + 3)15, 11, 7, 3, -1 …..(-4)

The same number is added/subtracted to the previous term

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RECIPROCALThe reciprocal of a number is 1 divided by that number.

Reciprocal of 2 = 𝟏𝟏𝟐𝟐

Reciprocal of 0.2 = 𝟏𝟏 ÷ 𝟏𝟏𝟓𝟓

= 5 (0.2 = 𝟏𝟏𝟓𝟓)

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GEOMETRIC SEQUENCE 1, 2, 4, 8, 16…..( × 2)200, 100, 50, 25…..(÷2)

The previous term is multiplied or divided by the same number.

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LENGTH OF A LINE The length of the line joining (x1,y1) and (x2,y2) is

(x2 - x1)2 + (y2 - y1)2

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MID-POINTThe mid point of the line joining (x1,y1) and (x2,y2) is

( )x1+ x2 y1+ y2

2 2,

Corresponding angles

…….are EQUALwww.mathsbox.org.uk

Allied angles

…….add to 180www.mathsbox.org.uk

Alternate angles

…….are EQUALwww.mathsbox.org.uk

Acute

Obtuse

Reflexwww.mathsbox.org.uk

ARC

SECTORwww.mathsbox.org.uk

Vertically Opposite angles

…..are equalwww.mathsbox.org.uk

RECTANGLE

PARALLELOGRAMwww.mathsbox.org.uk

SCALENE TRIANGLE

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EQUILATERAL TRIANGLE

ISOSCELES TRIANGLE

CONE

CYLINDER

SPHERE

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AREA of acircle

π × radius 2www.mathsbox.org.uk

TRAPEZIUM

KITE

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AREA of A TRAPEZIUM

½ (a + b) x hwww.mathsbox.org.uk

a

b

h

AREA of A RECTANGLE

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b x h

h

b

SQUARE NUMBERS1, 4, 9, 16, 25, 36, 49, 64,81, 100, 121, 144, 169…

1x1 , 2x2, 3x3, 4x4, 5x5,……..12 , 22 , 32, 42, 52,………

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a

Pythagorasa2 + b2 = c2

c

b

Longest side

EXACT TRIG VALUES

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0⁰ 30⁰ 45⁰ 60⁰ 90⁰

sin 012

22

32

1

cos 1 32

22

12

0

tan 0 33

1 3

CIRCUMFERENCEof a circle

π × diameterwww.mathsbox.org.uk

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PRESSURE = areaforce

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ERROR INTERVALS

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h = 60 (rounded to the nearest 10)

55 ≤ h < 65

h = 0.3 (rounded to 1 decimal place)

0.25 ≤ h < 0.35