AFOQT Math Practice

Geometry

Right triangles with whole sides

3, 4, 56, 8, 109, 12, 155, 12, 138, 15, 177, 24, 2520, 21, 29

Any multiple of one works too. If two sides are 15 and 20, the third is probably 25 (5 × the 3-4-5 triangle). Otherwise, $a^{2} + b^{2} = c^{2}$ , where $c$ is the longest side.

Special right triangles

45-45-90: sides $x$ , $x$ , $x \sqrt{2}$ . 30-60-90: sides $x$ , $x \sqrt{3}$ , $2 x$ , where the shortest side faces the 30° angle.

Formulas

Rectangle	$area = length \times width$ , $perimeter = 2 (length + width)$
Triangle	$area = \frac{1}{2} \times base \times height$ ; the angles add to 180°
Circle	$area = π r^{2}$ , $circumference = 2 π r = π d$
Trapezoid	$area = \frac{1}{2} \times ({base}_{1} + {base}_{2}) \times height$
Box	$volume = length \times width \times height$
Cylinder	$volume = π r^{2} h$
Any polygon	the inside angles add to $(n - 2) \times 180 °$ , where $n$ is the number of sides
Distance between points	$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$ , the Pythagorean theorem in disguise

A circle that fits exactly inside a square has a diameter equal to the side of the square. Doubling every side of a shape multiplies its area by 4 and a solid's volume by 8.

AFOQT questions on this: Circles · Circle inside a square · Distance · Volume · Sine, cosine, tangent

Drill it

Quick questions on just this skill, to build speed before the practice tests. Type the answers; a clock keeps your time.

Study guide

Geometry

Right triangles with whole sides

Special right triangles

Formulas