Unit 5 · Core unit
Circle relationships and the wider family of curves that come from slicing a cone. Completing the square is the recurring technique.
What a strong answer looks like
A strong answer converts a general second-degree equation to standard form before naming any feature.
Know
A central angle equals its arc; an inscribed angle is half its arc; a radius perpendicular to a chord bisects it.
Apply
Name the angle type before choosing between the whole arc and half of it.
Watch out
Using the central-angle rule for an inscribed angle, which halves the answer incorrectly.
Study move
Find an inscribed angle and the central angle on the same arc.
Know
Completing the square converts a general form into centre-radius form, which displays both directly.
Apply
Group the x and y terms, complete both squares, and move the constant.
Watch out
Forgetting to add the completing constants to both sides.
Study move
Convert a general circle equation into centre-radius form and state both.
Know
Which variables are squared and the sign between them distinguish circle, ellipse, parabola, and hyperbola.
Apply
Classify by inspection first, then complete the square for details.
Watch out
Confusing the ellipse relationship, which subtracts, with the hyperbola one, which adds.
Study move
Classify four second-degree equations by inspection.
Modeling drill
Convert a general circle equation to standard form, then find the length of its horizontal chord along a given line.
