Pure Year 1 Flashcards
What is the cosine formula- both variations?
a^2 = b^2 + c^2 - 2bc x cos(A) Cos(A) = b^2 + c^2 - a^2 / 2bc
What is the sine formula- both variations?
sin (A) / a = sin (B) / b - angles
a / sin (A) = b / sin (B) - sides
What is pythagoras’ theorem?
a^2 + b^2 = c^2
What is a rational fraction?
A fraction with a surd in the denominator
What is 8^2/3?
4
Bottom number outside
Top number inside
How do you rationalise a surd?
Multiply by either the denominator itself if it is on its own or by itself & the opposite to either + or -
What is the quadratic formula?
x = -b +- root (b^2 - 4ac) / 2a
What is the discriminant and when does it show the number of roots a quadratic has?
b^2 - 4ac = 0 - 1 root (tangent if root repeated)
b^2 - 4ac > 0 - 2 roots
b2 - 4ac < 0 - no roots
How do you find points of intersection?
Equate the 2 equations
How do you write an inequality when the equation is greater than (>) ?
2 separate inequalities with the smaller one as less than ()
Because above the graph- opposite directions of solutions
How do you write an inequality when the equation is less than (
As one inequality because below the graph
What does the reciprocal graph y = 1 / x look like and where are it’s asymptotes?
Line in top right quadrant & bottom left quadrant with asymptotes at x = 0 & y = 0
What does the reciprocal graph y = -2 / x look like and where are it’s asymptotes?
Line in top left quadrant & bottom right quadrant with asymptotes at x = 0 & y = 0
What does the graph y = 2 / x^2 look like & where are it’s asymptotes?
Line in top left quadrant & top right quadrant with asymptotes at x = 0 & y = 0
What does the graph y = -5 / x^2 look like & where are it’s asymptotes?
Line in bottom left quadrant & bottom right quadrant with asymptotes at x = 0 & y = 0
In a function such as (a / b ) what direction does a & b control?
a controls left/right movements
b controls up/down movements
When a graph is translated, are its asymptotes translated with it?
When a graph is translated its asymptotes are translated with it
What does the translation y = -f(x) mean?
Reflection in the x-axis
What does the translation y = f(-x) mean?
Reflection in the y-axis
How do you calculate the gradient of the line between 2 points?
gradient = change in y / change in x gradient = y2 - y1 / x2 - x1
What is the product of the gradients of 2 perpendicular lines?
-1
What is unique about the gradients of 2 lines which are perpendicular to one another?
Their gradients are negative reciprocals of one another
What is unique about the gradients of 2 lines which are parallel to one another?
Their gradients are the same
How do you find the distance between 2 points?
Find the net coordinates by minusing them from one another and then use pythagoras’ theorem
Root {(x2 - x1)^2 + (y2 - y1)^2}