ESAT Maths

NOTE: this is not a complete set of flashcards, it is only those I need particular practice on

Standard unit of money

£

Unit for rate of pay

£/hr

Unit for unit pricing

£/unit

Synonym for factors

Divisors

Priority of operations

BIDMAS

Convert recurring decimals to fractions

x = 0.1111…

10x = 1.1111…

9x = 1

x = 1/9

Upper and lower bounds (eg. 6.4 to 1 d.p.)

lower bound = 6.35, upper bound = 6.44

Relate ratios to linear functions

2:3 for y:x becomes 3y = 2x (trick = switch)

Simple interest

value * (1 + rn/100)

Compound interest

value * (1 + r/100)^n

Expression

one side of an equation

Equation

has = so equates sides

Formulae

equations with variables

Identities

equations which are true regardless of the value of variables

Name for laws of indices

Four rules

Quadrants

Turning point of completing the square

a(x+b)^2 + c - turning point (-b, c)

Quadratic nth term value of first coefficient

divide the second difference by 2!

Subtended angles

angles between two lines and a point

Angle rules of intersected parallel lines

Angle rules of a kite

Angle rules of an isosceles trapezium

Sum of interior angles

(n - 2)*180°

Congruence criteria for triangles

SSS, SAS (subtended angle), ASA (side between), RHS (right angle, hypothenuse and side)

Similar shapes ratios

sides have factor k, area k^2 and volume k^3

Enlargements need

scale factor + centre of enlargement

Rotations need

centre of rotation + angle + direction

Reflections need

mirror line

Combinations of transformations representations

like composite functions, if S then R = RS

Circle theorem: angle at centre

angle at centre twice than at circumference

Circle theorem: angle in a semicircle

always 90°

Circle theorem: alternate segment

angles in the same segment are equal

Circle theorem: radius and tangent angle

always 90° at intersection

Circle theorem: cyclic quadrilaterals

opposite angles are supplementary (a+c = 180°, b+d = 180°)

Plans and elevations

Volume of sphere

(4/3) · π · r³

Volume of cone

(1/3) · π · r² · h

Volume of square based pyramid

(1/3) · b² · h

Sin, Cos, Tan angles

Two-way tables

Frequency tables

Vertical line charts

Histograms

Cumulative frequency

Modal class

group with highest frequency (f)

Mean for grouped data

(midpoint * frequency)/total frequency = fx/f

Range for grouped data

upper max limit - lower min limit

Median for grouped data

L + w(n/2 - B)/G

L = lower bound of median class, n = total, B = cumulative frequency of previous groups, w = group width, G = frequency of median class

Calculate the median (N=40)

71 + 9(40/2 - 12)/15

= 75.8

Randomness, fairness and equally likely events mean the same thing

True

Relative expected frequency

the frequency expected from observational results

Theoretical probability

the frequency expected from theory

The probabilities of an exhaustive set of outcomes sum to

1

Theoretical possibility space

these are sample space diagrams or Venn diagrams

When to use tree diagrams

for events which are independent, or dependent on the previous outcome