Pure 1 (non-calc) Flashcards
Describe the gradient of parallel lines
Equal
Describe the gradient of 2 perpendicular lines
They multiply to give -1
When 2 lines intersect, …
… both equations are satisfied.
How do you find the intersection of two lines ?
Simultaneous equations
What are the 3 steps to finding a perpendicular bisector?
- Find midpoint.
- Find gradient of line joining points.
- Find equation of the bisector.
Quote the discriminant.
b^2 - 4ac
What is the quadratic formula?
2a
If D>0 :
Describe roots
2 roots
If D=0 :
Describe roots
1 root / repeated root (bounce)
If D<0 :
Describe roots
No real roots / no solutions.
(Because you can’t square root a negative)
The graph line never touches the x-axis.
What do you use to help you solve quadratic inequalities, and at what point do you use it?
You calculate the discriminant, then draw a graph (there will be a middle section where the line is below the x-axis where the equation is not satisfied, meaning you have to write 3 separate inequalities).
You solve until you have X^2 = on one side. Then draw your graph.
What are the 5 things to include in a graph sketch?
- Axes
- All intercepts
- Equations of lines
- Points of intersection
- Maxima and minima
What is the equation of a circle?
(X-a)^2 + (y-b)^2 = r^2
Where centre is (a,b) and radius r.
CE and ED are chords. Which angle is subtending by the arc between C and D?
Angle E
Circumference & centre circle theorem
The angle at the centre is double the angle at the circumference.
2 angles at the circumference + chord circle theorem:
Angles standing on the same chord are equal.
What must a cyclic quadrilateral do?
Every corner must touch the circumference of the circle.
Cyclic quadrilateral circle theorem
Opposite angles in a cyclic quadrilateral add up to 180 degrees
Semicircle theorem
The angle at the circumference in a semicircle is a right angle.
Tangent circle theorem x2
- The angle between tangent and radius is 90 degrees.
2. Tangents which meet at the same point are equal in length.
Bisector circle theorem
The perpendicular from the centre to a chord bisects the chord
Alternate segment theorem:
The angle between a tangent and a chord is equal to the angle in the alternate segment.
What do the gradients of odd power graphs start and end as?
Positive and positive , or negative and negative
What do the gradients of even power graphs start and end as?
Negative and positive , or positive and negative
How do you rationalise a surd denominator ?
You multiply by the inverse of the denominator.
