Mathematics: Arithmetic Through Advanced Algebra
What is covered
The math test spans arithmetic (fractions, decimals, percents, ratios, unit rates), elementary algebra (linear equations and inequalities, slope, systems, exponents, polynomials, factoring), and advanced topics (quadratic and rational expressions, functions and function notation, radicals, geometry, and basic probability and statistics).
Traps
- Order of operations with negatives. In $-3^2$ the exponent applies before the negative, giving $-9$; $(-3)^2$ is $9$.
- Percent language. Percent of means multiply; percent increase or decrease means change divided by the original amount. A 20 percent drop followed by a 20 percent rise does not return to the start.
- Distribution. $-2(x-5)$ is $-2x+10$, not $-2x-10$.
- Slope from standard form. For $Ax+By=C$, the slope is $-A/B$ - do not read the coefficient of $x$ as the slope.
- Inequalities. Multiplying or dividing by a negative flips the direction of the sign.
- Language reversal. Five less than a number is $x-5$, not $5-x$.
- Rounding too early. Carry exact values until the final step.
Rule of thumb
Write an equation before you compute. For word problems, define the variable in words, translate each clause, then solve - and check whether the answer is reasonable in context.
Worked example
Solve $3(x-4)=2x+5$. Distribute: $3x-12=2x+5$. Subtract $2x$ from both sides: $x-12=5$. Add 12: $x=17$. Verify: $3(13)=39$ and $2(17)+5=39$.