ACCUPLACER QAS flashcards
ACCUPLACER QAS · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Percent change formula
- (New value minus old value) divided by old value, times 100. A positive result is an increase; a negative result is a decrease.
- Unit rate
- A ratio that compares a quantity to exactly one unit of another quantity, such as miles per hour or dollars per item.
- Direct variation
- A relationship of the form y = kx, where k is a constant. As x increases, y increases proportionally through the origin.
- Inverse variation
- A relationship of the form y = k/x. As x increases, y decreases, and the product xy stays constant.
- Combined work rate
- When two workers or machines work together, their rates add: 1/t = 1/a + 1/b, where t is the combined time.
- Scientific notation
- A number written as a times 10 to a power, where a is at least 1 and less than 10.
- Slope formula
- The slope of a line through two points equals the change in y divided by the change in x, often called rise over run.
- Slope-intercept form
- The equation y = mx + b, where m is the slope and b is the y-intercept, the value of y when x is zero.
- Perpendicular line slopes
- Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so their product equals negative one.
- Quadratic formula
- x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a, for ax² + bx + c = 0.
- Discriminant
- The expression b² − 4ac from a quadratic equation. Positive gives two real roots, zero gives one, negative gives none.
- Negative exponent rule
- A base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, so x to the negative a equals 1 over x to the a.
- Inequality sign flip
- Multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality symbol.
- System with no solution
- A linear system has no solution when the two lines have the same slope but different y-intercepts, meaning they are parallel.
- Mean
- The arithmetic average, found by adding all data values and dividing by the number of values. It is affected by extreme values.
- Median
- The middle value when data are ordered from least to greatest. With an even count, average the two middle values.
- Interquartile range
- The difference between the third quartile and the first quartile, measuring the spread of the middle half of the data.
- Standard deviation
- A measure of how far data values typically fall from the mean. Larger values indicate more spread-out data.
- Shifting all data values
- Adding the same constant to every data value changes the mean and median by that constant but leaves standard deviation unchanged.
- Effect of outliers
- Extreme values pull the mean strongly toward them, while the median changes little, so the median resists outliers.
- Normal distribution rule
- In a normal distribution, roughly 68 percent of values lie within one standard deviation of the mean and 95 percent within two.
- Residual
- The difference between an actual data value and the value predicted by a line of best fit, calculated as actual minus predicted.
- Basic probability
- The probability of an event equals the number of favorable outcomes divided by the total number of equally likely outcomes.
- Complement rule
- The probability that an event does not occur equals one minus the probability that it does occur.
- Addition rule
- For two events, the probability of either equals the sum of their probabilities minus the probability of both occurring together.
- Independent events
- Two events are independent when the occurrence of one does not change the probability of the other; multiply their probabilities.
- Conditional probability
- The probability of event A given that event B occurred equals the probability of both divided by the probability of B.
- Expected value
- The long-run average outcome, computed by multiplying each possible outcome by its probability and adding the products.
- Two-way table conditional
- To find a probability given a category, divide the cell count by the row or column total for that category, not the grand total.
- Pie chart slice angle
- A slice's central angle equals its percent share written as a decimal multiplied by 360 degrees.
- Comparing groups of unequal size
- When group sizes differ, compare percentages or rates rather than raw counts, because raw counts can mislead about relative frequency.
- Reading a line graph slope
- A steeper segment indicates a faster rate of change, while a flat segment indicates no change during that interval.