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EST Grammar and Algebra Essentials

Flashcards covering grammar rules for the EST literacy section and algebra and data formulas for the EST mathematics section. Original study material.

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Subject–verb agreement with 'neither of'

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Subject–verb agreement with 'neither of'

Takes a singular verb: 'Neither of the answers is correct.'

Subject–verb agreement with 'a number of' and 'the number of'

'A number of' takes a plural verb; 'the number of' takes a singular verb

Real conditional (type 1)

if + present simple, will + base verb

Unreal present conditional (type 2)

if + past simple, would + base verb

Unreal past conditional (type 3)

if + past perfect, would have + past participle

Present perfect use

A past action linked to the present, with for, since, already, just, yet

Past perfect use

The earlier of two past actions: 'had finished before he arrived'

Passive voice form

be + past participle: 'The report was written.'

Gerund after these verbs

enjoy, avoid, suggest, finish, mind

Infinitive after these verbs

decide, hope, refuse, manage, plan

Colon use

Introduces a list or explanation after a complete sentence

Semicolon use

Joins two closely related independent clauses

Comma before 'but', 'and', 'so' joining clauses

Use a comma when each side is a full clause

'Its' and 'it's'

'Its' shows possession; 'it's' means 'it is' or 'it has'

Parallel structure

Keep list items in the same form: 'running, swimming and cycling'

Slope of a line through two points

\frac{y _{2} - y _{1}}{x _{2} - x _{1}}

Slope-intercept form

y = m x + b

Quadratic formula

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

Discriminant and roots

b^{2} - 4 a c > 0

two real roots,

= 0

one,

< 0

none

Exponent rules

a^{m} a^{n} = a^{m + n}

and

\frac{a ^{m}}{a ^{n}} = a^{m - n}

Mean, median and mode

Average, middle value of ordered data, most frequent value

Standard deviation unchanged by

Adding a constant to every value

Percentage increase

\frac{increase}{original} \times 100

Horizontal shift of

y = f (x)

right by

h

y = f (x - h)

Probability of independent events A and B both occurring

P (A) \times P (B)

Circle equation centre

(h, k)

(x - h)^{2} + (y - k)^{2} = r^{2}

EST Grammar and Algebra Essentials

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