Pure Year 1 Flashcards
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?
-1
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) =
sin(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
