2. The Formula Sheet (incl. the harder formulas)

You get a formula sheet on test day -- the hard questions on this exam lean on the geometry and algebra formulas, so know which to grab.

Area

• Triangle: \(A = \tfrac{1}{2}bh\) | Trapezoid: \(A = \tfrac{1}{2}(b_1 + b_2)h\) | Circle: \(A = \pi r^2\)

Volume

• Cylinder: \(V = \pi r^2 h\)
• Cone: \(V = \tfrac{1}{3}\pi r^2 h\)
• Sphere: \(V = \tfrac{4}{3}\pi r^3\)

Surface area

• Cylinder: \(SA = 2\pi r^2 + 2\pi r h\)

Algebra & coordinate geometry

• Pythagorean theorem: \(a^2 + b^2 = c^2\)
• Distance: \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
• Midpoint: \(\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)\)
• Slope: \(m = \dfrac{y_2-y_1}{x_2-x_1}\) | Perpendicular slopes multiply to \(-1\)
• Quadratic formula: \(x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)

Two facts the sheet won't state but you'll need:

• For similar figures, areas scale by the square of the scale factor (and volumes by the cube).
• A repeated percent change of \(r\) over \(n\) periods multiplies by \((1+r)^n\).