Flashcards in Pure Year 1 Deck (16)

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1

## When displaying inequalities on graphs, what represents 'less than or equal to'? Just 'less than'?

###
Dotted line if just less/more than

Solid line if less/more than or equal to

2

## What is the equation of a straight line, with gradient m, passing through the point (x₁,y₁)

### y - y₁ = m(x - x₁)

3

## If two lines are perpendicular, what is the product of their gradients equal to?

### -1

4

## Describe a perpendicular bisector of a chord

### It will go through the centre of the circle

5

## Circle theorem: Right-angled triangle

### Every angle at the circumference of a semicircle that is subtended by the diameter is a right angle

6

## How do you find the centre of a circle given any three points?

###
Find the equations of the perpendicular bisectors of two different chords

Find the coordinates of intersection of the perpendicular bisectors

7

## What must you include in a mathematical proof?

###
State any info or assumptions you are using

Show every step of your proof clearly

Make sure you cover all possible cases

Write a statement of proof at the end

8

## What is a general term in the expansion (a + bx)ⁿ given by?

### ⁿCᵣ aⁿ⁻ʳbʳ

9

## sin(180° - x) =

### sin(x)

10

## sinx, cosx and tanx are periodic. How often do they repeat?

###
sinx: 360°

cosx: 360°

tanx: 180°

11

## Trig: What is the principle value?

### The angle your calculator gets when you use inverse trig functions

12

## What is the formula for differentiation from first principles?

### f'(x) = lim h→ ₀ (f(x+h) - f(x))/h

13

## When is a function increasing?

### The function f(x) is increasing in the interval [a,b] of f'(x) ⩾ 0 for all values of x such that a < x < b

14

## When is a function decreasing?

### The function f(x) is decreasing in the interval [a,b] of f'(x) ⩽ 0 for all values of x such that a < x < b

15

## What are the three log laws?

###
logₐ x + logₐ y = logₐ xy

logₐ x - logₐ y = logₐ x/y

logₐ xᵏ = klogₐ x

16