Flashcard Set

SAT Math: Problem-Solving and Data Analysis

14 cards

Exam-grade practice on ratios, rates, percentages, unit conversion, and interpreting data for the digital SAT.

1
Term
A rug has an area of 12 square yards. To convert this area to square feet, by what number must you multiply 12? (Note: 1 yard = 3 feet)
Definition
Because area is two-dimensional, the conversion factor must be squared: (3 ft / 1 yd)^2 = 9 sq ft / sq yd.
2
Term
An item's price is increased by 20%, and then the new price is decreased by 20%. What is the net percent change from the original price?
Definition
A 4% decrease. If the original price is P, the final price is P * 1.20 * 0.80 = 0.96P, which is a 4% reduction.
3
Term
In a box of red and blue pens, the ratio of red to blue pens is 3 to 5. If there are 80 pens in total, how many blue pens are in the box?
Definition
The fraction of blue pens is 5 / (3 + 5) = 5/8 of the total. Total blue pens = 80 * (5/8) = 50.
4
Term
A linear model predicts a student's test score, y, based on the number of hours spent studying, x. The equation is y = 5.5x + 48. What is the contextual meaning of the slope, 5.5?
Definition
For every additional hour spent studying, the predicted test score increases by 5.5 points.
5
Term
In a scatterplot, a data point has coordinates (5, 12). The line of best fit predicts a value of y = 14 when x = 5. What is the residual for this data point?
Definition
-2. Residual is calculated as: Actual y - Predicted y = 12 - 14 = -2.
6
Term
A survey asks students for their favorite pet:

Grade 9: 15 Dog, 25 Cat

Grade 10: 30 Dog, 10 Cat If a Grade 9 student is selected at random, what is the probability that their favorite pet is a cat?
Definition
5/8 (or 0.625). Restrict the pool to only Grade 9 students (40 total) and find the portion who prefer cats (25 out of 40 = 5/8).
7
Term
A dataset of home prices in a town has a strong right skew due to several extremely expensive mansions. Which measure of center will be greater: the mean or the median?
Definition
The mean. High-value outliers pull the mean upward, while the median remains highly resistant to extreme values.
8
Term
Dataset A and Dataset B both have a mean of 50. Dataset A's values are concentrated closely around 50, while Dataset B's values are widely spread out. Which dataset has the larger standard deviation?
Definition
Dataset B. Standard deviation measures the typical distance (spread) of data points from the mean; greater spread means a larger standard deviation.
9
Term
How does increasing the sample size of a random survey affect its margin of error if the confidence level remains constant?
Definition
It decreases the margin of error. A larger sample size provides a more precise estimate of the population parameter.
10
Term
A population of bacteria decreases by 15% of its current value every hour. Is this relationship linear or exponential?
Definition
Exponential. A constant percentage change over equal time intervals represents exponential change (whereas a constant absolute change represents linear change).
11
Term
A researcher wants to generalize the results of a high school homework study to all high school students in a state. What sampling method is required for this generalization to be valid?
Definition
A random sample of high school students from that entire state. Results can only be generalized to the population from which the sample was randomly selected.
12
Term
A machine prints 150 pages in 3 minutes. At this rate, how many seconds does it take the machine to print 10 pages?
Definition
12 seconds. Convert 3 minutes to 180 seconds. The rate is 150 pages per 180 seconds, or 5/6 pages per second. To print 10 pages: 10 / (5/6) = 12 seconds.
13
Term
If x is 150% of y, what percent of x is y?
Definition
66.7% (or 66 2/3%). Since x = 1.5y, solving for y gives y = x / 1.5 = (2/3)x, which is approximately 66.7% of x.
14
Term
A dataset consists of the numbers {10, 12, 15, 18, 20}. If the number 25 is added to this dataset, how is the range affected?
Definition
The range increases from 10 to 15. The original range was 20 - 10 = 10; the new range is 25 - 10 = 15.