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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

What is the converting base formula for logs?
(We don't need to know, but could be useful for checking)

logᵦ x = logₐ x / logₐ β