Pure Year 1 Flashcards

1
Q

When displaying inequalities on graphs, what represents ‘less than or equal to’? Just ‘less than’?

A

Dotted line if just less/more than

Solid line if less/more than or equal to

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2
Q

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

A

y - y₁ = m(x - x₁)

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3
Q

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

A

-1

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4
Q

Describe a perpendicular bisector of a chord

A

It will go through the centre of the circle

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5
Q

Circle theorem: Right-angled triangle

A

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

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6
Q

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

A

Find the equations of the perpendicular bisectors of two different chords
Find the coordinates of intersection of the perpendicular bisectors

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7
Q

What must you include in a mathematical proof?

A

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

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8
Q

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

A

ⁿCᵣ aⁿ⁻ʳbʳ

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9
Q

sin(180° - x) =

A

sin(x)

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10
Q

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

A

sinx: 360°
cosx: 360°
tanx: 180°

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11
Q

Trig: What is the principle value?

A

The angle your calculator gets when you use inverse trig functions

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12
Q

What is the formula for differentiation from first principles?

A

f’(x) = lim h→ ₀ (f(x+h) - f(x))/h

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13
Q

When is a function increasing?

A

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

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14
Q

When is a function decreasing?

A

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

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15
Q

What are the three log laws?

A

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

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16
Q

What is the converting base formula for logs?

We don’t need to know, but could be useful for checking

A

logᵦ x = logₐ x / logₐ β