AFOQT Math Practice

Algebra

Patterns to recognize

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$	${(x + 3)}^{2} = x^{2} + 6 x + 9$
${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$	${(x - 5)}^{2} = x^{2} - 10 x + 25$
$(a + b) (a - b) = a^{2} - b^{2}$	$x^{2} - 49 = (x + 7) (x - 7)$

Factoring $x^{2} + b x + c$

Find two numbers that multiply to $c$ and add to $b$ . For $x^{2} + 7 x + 12$ : 3 × 4 = 12 and 3 + 4 = 7, so it is $(x + 3) (x + 4)$ . If $c$ is negative, the two numbers have opposite signs.

Multiplying two binomials (FOIL)

First, Outer, Inner, Last: $(x + 2) (x - 5) = x^{2} - 5 x + 2 x - 10 = x^{2} - 3 x - 10$ .

Solving

Whatever you do to one side, do to the other. When you multiply or divide an inequality by a negative number, flip the sign: $- 2 x > 6$ becomes $x < - 3$ . For two equations, add or subtract them so one letter cancels.

Lines

Slope is rise over run: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ . In $y = m x + b$ , $m$ is the slope and $b$ is where the line crosses the y-axis. Written as $A x + B y = C$ , the slope is $- \frac{A}{B}$ .

AFOQT questions on this: Factoring trinomials · Multiplying binomials · Systems of equations · Inequalities · Slope

Drill it

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