π β’ Module 10 : Advanced Circle Theorems and Graphs Flashcards
This lesson covers solving equations graphically, cubic and reciprocal graphs, asymptotes, and key circle theorems (angles, tangents, chords, and proofs). It also includes the study of quartiles and percentiles.
What does it mean when a quadratic graph does not touch the x-axis?
The equation has no real solutions (the discriminant is negative)
How do you solve simultaneous linear and quadratic equations graphically?
Plot both equations on the same graph; the points of intersection are the solutions.
What is the general equation of a cubic function?
aπ₯Β³+bπ₯Β²+cπ₯+d
Where a,b,c,d are constants.
What is the angle in a semi-circle theorem?
An angle formed from a diameter in a semi-circle is always 90Β°
What is the tangent-radius theorem?
A radius drawn to a tangent at the point of contact is always perpendicular (90Β°)
What does the alternate segment theorem state?
The angle between a tangent and a chord equals the angle in the opposite segment.
How do you prove the perpendicular bisector theorem for a chord?
The perpendicular from the circleβs center to a chord bisects the chord into equal halves.
What does the angles in the same segment theorem say?
Angles from the same arc in the same segment are equal.
What is the cyclic quadrilateral theorem?
Opposite angles in a cyclic quadrilateral add up to 180Β°
How can you prove that a triangle is right-angled using a circle?
If the hypotenuse is the diameter of the circle, the triangle is always right-angled.
What happens when two tangents are drawn from a point outside a circle?
They are equal in length.
A data set has 20 values. What position is the lower quartile (Q1) in?
At the 5th value.
(Q1 is at 25% of the data)
A student scored in the 80th percentile of a test. What does this mean?
They scored higher than 80% of the other students.
What is a secant in a circle?
A straight line that intersects a circle at two points (it extends beyond the circle, unlike a chord)
What is the general shape of an exponential graph?
A curve that increases or decreases rapidly and has a horizontal asymptote.
