ACCUPLACER QAS cheat sheet

Percent change = (new − old) / old × 100%; a decrease gives a negative result.

Ratios compare parts to parts; set up a proportion a/b = c/d and cross-multiply to solve.

Unit rate = quantity ÷ time or cost ÷ count; use it to scale to any quantity.

Direct variation: y = kx. Inverse variation: y = k/x. Find k from one known pair.

Density/rate problems: total = rate × time; combined rates add as 1/t = 1/a + 1/b.

Estimate first by rounding to one significant figure to catch order-of-magnitude errors.

A percent increase of p followed by a decrease of p does not return to the original value.

Scientific notation: a × 10^n with 1 ≤ a < 10; multiply coefficients and add exponents.

Slope m = (y2 − y1)/(x2 − x1); parallel lines share m, perpendicular lines have m1·m2 = −1.

Slope-intercept y = mx + b; point-slope y − y1 = m(x − x1).

Linear system: substitute or eliminate; no solution when slopes equal but intercepts differ.

Quadratic formula: x = [−b ± √(b² − 4ac)]/(2a); discriminant b² − 4ac gives 0, 1, or 2 real roots.

Factor by finding two numbers that multiply to ac and add to b for ax² + bx + c.

Rules of exponents: x^a·x^b = x^(a+b); (x^a)^b = x^(ab); x^(−a) = 1/x^a; x^0 = 1.

Isolate a variable by reversing operations in reverse order; whatever is done to one side is done to the other.

Inequalities: multiplying or dividing both sides by a negative number flips the inequality sign.

Mean = sum ÷ count; median = middle value of ordered data; mode = most frequent value.

Range = max − min; interquartile range IQR = Q3 − Q1.

Standard deviation measures typical distance from the mean; larger spread means larger value.

Adding a constant to every value shifts the mean and median but leaves standard deviation unchanged.

Outliers can pull the mean far from the median; the median resists extreme values.

In a normal distribution about 68% of data lie within 1 SD of the mean and about 95% within 2 SD.

Correlation r ranges from −1 to 1; r near 0 means weak linear relationship, not necessarily no relationship.

A line of best fit predicts y from x; the residual is actual y minus predicted y.

P(event) = favorable outcomes ÷ total equally likely outcomes; 0 ≤ P ≤ 1.

Complement rule: P(not A) = 1 − P(A).

Addition rule: P(A or B) = P(A) + P(B) − P(A and B); subtract overlap to avoid double counting.

Mutually exclusive events have P(A and B) = 0.

Independent events: P(A and B) = P(A)·P(B).

Conditional probability: P(A|B) = P(A and B)/P(B).

With replacement, probabilities stay constant; without replacement, the denominator shrinks each draw.

Expected value = sum of (each outcome × its probability).

Read table axes and units before computing; totals in a row or column may be given or must be summed.

Percent of a total = part ÷ whole × 100; part = percent × whole when the whole is known.

In a two-way table, P(A|B) uses the B row or column total as the denominator.

Bar and line graphs: compare heights or slopes; a steeper line means a faster rate of change.

Pie charts: each slice's share × 360° gives its central angle; shares should sum to 100%.

Scatterplots: describe trend, strength, and direction; a cluster of points suggests association.

Percent change between two data points = (later − earlier) / earlier × 100%.

When comparing groups of different sizes, use rates or percentages rather than raw counts.