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Flashcards in Pure Year 1 Deck (16)
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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


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

y - y₁ = m(x - x₁)


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



Describe a perpendicular bisector of a chord

It will go through the centre of the circle


Circle theorem: Right-angled triangle

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


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


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


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

ⁿCᵣ aⁿ⁻ʳbʳ


sin(180° - x) =



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

sinx: 360°
cosx: 360°
tanx: 180°


Trig: What is the principle value?

The angle your calculator gets when you use inverse trig functions


What is the formula for differentiation from first principles?

f'(x) = lim h→ ₀ (f(x+h) - f(x))/h


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


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


What are the three log laws?

logₐ x + logₐ y = logₐ xy
logₐ x - logₐ y = logₐ x/y
logₐ xᵏ = klogₐ x


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