42 exercises · 42 automatically checked · Untimed
42 questions · Shuffled order · Untimed practice
Covers topics across Problem-Solving and Data Analysis.
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These three sets revisit every section without topic labels. Use scratch paper, keep track of your reasoning, and leave a note beside any answer that depends on a guess. Calculators are allowed. Unless a question requests rounding, retain exact values when possible.
Each set has 14 questions. These are independent domain-practice sets, not official adaptive modules. Record your time to monitor your own progress; do not translate a raw result into an SAT score.
Before you begin
Questions with four choices have one best answer. For a question without choices, give the requested number. A table’s totals or a graph’s labels are part of the question. All data and studies are hypothetical. Use Check answer or Check all attempted questions when you are ready to review the explanations.
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A recipe uses 240 grams of flour for 8 servings. When all ingredients are scaled proportionally, how many grams of flour are needed for 15 servings?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 450
The recipe uses 240/8
Review worked example 1.03.
An item originally priced at $260 is discounted by 35%. What is its sale price?
Answer: B: $169
After a 35% discount, 65% of the original price remains. The sale price is 0.65(260)
Review worked example 2.03.
The table summarizes a data set. What is its mean?
Value | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
Frequency | 2 | 1 | 4 | 2 | 1 |
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 2.9
There are 2 + 1 + 4 + 2 + 1
Review worked example 3.03.
The graph shows observed data and a fitted line. The labeled points (0, 6) and (6, 18) are on the line. What output does the line predict when x = 4?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 14
The line has slope (18 − 6)/(6 − 0)
Review worked example 4.03.
A workshop records the following registrations and attendance. A person is chosen at random from all registrants. Given that the person attended, what is the probability that the person registered for the morning session?
Attended | Did not attend | |
|---|---|---|
Morning | 18 | 12 |
Evening | 30 | 40 |
Answer: C: 18/48
The condition restricts the eligible group to attendees: 18 + 30
Review worked example 5.06.
A simple random sample of 150 customers from a population of 4,200 all respond to a survey. Twenty-seven use a particular service. Estimate the number of all customers who use it.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 756
The sample share is 27/150
Review worked example 6.02.
Sixty plants are randomly assigned to two watering schedules, with other conditions kept comparable. A well-conducted analysis finds convincing evidence of greater mean growth under schedule A. Which statement is justified?
Answer: B
The researcher randomly assigned the treatment, making the comparison capable of supporting causal inference. With the stated quality and convincing evidence, an average growth advantage can be attributed to the schedule under the studied conditions. The study does not guarantee individual effects or universal generalization.
Review worked example 7.02.
An area is 32,000 square centimeters. What is this area in square meters? Use 1 m = 100 cm.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 3.2 A square meter contains 1002
Review worked example 1.10.
A participation rate rises from 44% to 55%. What is the relative percent increase in the rate?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 25
The increase is 11 percentage points, and 11/44
Review worked example 2.05.
Twenty observations have mean 64. Thirty additional observations have mean 74. What is the mean of all 50 observations?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 70
The group totals are 20(64)
Review worked example 3.07.
The quantities in the table follow an exponential model. Which equation fits?
t | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
Q | 8 | 12 | 18 | 27 |
Answer: D: Q
At time 0 the value is 8, setting the initial factor. Each one-unit interval multiplies the quantity by 12/8 = 18/12 = 27/18 = 1.5. Thus Q
Review worked example 4.10.
Of 80 readers, 45 read magazine A, 35 read magazine B, and 20 read both. What is the probability that a reader chosen at random from all 80 reads at least one of the two magazines?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 3/4
The union contains 45 + 35 − 20
Review worked example 5.07.
A survey reports an estimated population percentage of 62%, with a margin of error of 5 percentage points. What is the lower endpoint of the reported interval, expressed as a percentage?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 57
Subtract the margin from the estimate: 62 − 5
Review worked example 6.04.
Researchers select a simple random sample of adults from a city and record their self-selected commuting modes and commute times. All selected adults respond. Which claim is supported by the design alone?
Answer: C
The random sample represents the city’s adult population, so it supports describing a population association. Mode was not randomly assigned, so distance from work and other factors could differ across modes. The design does not by itself isolate a causal mode effect.
Review worked example 7.04.
Printer A produces 12 pages per minute and printer B produces 18 pages per minute. Both work at constant rates on separate pages of the same 450-page job. If they start together, how many minutes do they need?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 15
The simultaneous rates add: 12 + 18
Review worked example 1.12.
A product’s price decreases by 15%, and the quantity sold increases by 40%. What is the percent increase in total revenue?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 19
The revenue multiplier is 0.85(1.40)
Review worked example 2.15.
The histogram summarizes 12 measurements. Each interval includes its left endpoint and excludes its right endpoint. Which statement is necessarily true?
Answer: C
The first bin contains 2 observations and the second contains 5, so positions 3 through 7 fall in [5, 10). The median averages positions 6 and 7, both in that interval. The histogram does not locate exact observations within bins and therefore does not establish an exact median, mean, or maximum.
Review worked example 3.05.
A model is = 50 − 2x. An observation at x = 5 has y = 44. Using residual = observed − predicted, what is the residual?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 4
At x
Review worked example 4.07.
A group contains x members who renewed a subscription and 15 who did not. A member is selected uniformly at random. The probability that the member renewed is 0.70. What is x?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 35
Set x/(x + 15)
Review worked example 5.08.
A study reports a 95% confidence interval of 32.6 to 37.4 minutes for a population mean. Which statement is appropriate?
Answer: C
The interval targets an average for the population. It is centered at 35 with margin 2.4, but neither the midpoint nor membership in the interval is guaranteed. The confidence level describes the method’s long-run coverage under its assumptions, not a percentage of individual observations.
Review worked example 6.05.
A town wants to estimate residents’ opinions about bus service. Which plan most directly supports representative inference, assuming everyone selected responds?
Answer: B
Random selection from the complete target-population list gives all residents a chance to be represented. The other plans systematically favor particular groups. Their larger counts do not repair the restricted or self-selected sampling mechanisms.
Review worked example 7.11.
A material sample has mass 150 grams and volume 60 cubic centimeters. What is its density in kilograms per cubic meter? Use 1 kg = 1,000 g and 1 m = 100 cm.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 2,500 First calculate density: 150/60
Review worked example 1.11.
Positive quantities satisfy X = 80% of Y and Y = 125% of Z. Quantity X is what percent of Z?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 100
Translate both statements into factors: X
Review worked example 2.08.
A data set has mean 2 and standard deviation 1.2. Each value x is replaced by 5x + 3. What is the new standard deviation?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 6
Multiplication by 5 scales all deviations from the mean by 5; addition of 3 shifts the distribution without changing spread. Therefore the new standard deviation is 5(1.2)
Review worked example 3.11.
A quadratic model fits all entries in the table exactly. What value does it predict at x = 4?
x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
y | 9 | 6 | 5 | 6 |
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 9
The equal outputs at inputs 1 and 3 put the quadratic’s symmetry axis at 2. The table gives vertex (2, 5), so write y
Review worked example 4.12.
A bag contains 3 green and 5 yellow counters. Two counters are selected sequentially at random without replacement. What is the probability that both are yellow?
Answer: B: 5/14
The first-yellow probability is 5/8. After a yellow is removed, the second-yellow probability is 4/7. Multiply: (5/8)(4/7) = 20/56 = 5/14. Choice A would use replacement and unchanged counts.
Review worked example 5.12.
For a particular survey design, a supplied model states E = k/ with k fixed. When the sample size is 900, the margin of error is 4. What sample size makes the margin of error 3?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 1,600
The original data give k = 4 = 120. The target equation is 3
Review worked example 6.11.
A researcher gives fertilizer A to all plants in a sunny room and fertilizer B to all plants in a shaded room. The A plants grow more. Which issue most directly limits a causal fertilizer conclusion?
Answer: C
The groups differ in both fertilizer and sunlight. Either difference, or both, may explain the growth difference. Assigning both fertilizers randomly within each light condition would help separate treatment from location.
Review worked example 7.14.
Red and blue counters initially have ratio 4 ∶ 7. After 15 red counters are added, the ratio of red to blue becomes 3 ∶ 4. No blue counters are added or removed. How many red counters were there initially?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 48
Write the original counts as 4k and 7k. Then (4k + 15)/(7k)
Review worked example 1.14.
A quantity is reduced by p% and then reduced again by p% of the new value, where 0 < p < 100. The final quantity is 64% of the original. What is p?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 20 The retained fraction at each stage is 1 − p/100. Thus (1 − p/100)2
Review worked example 2.07.
A data set contains three observations equal to 2 and k observations equal to 5. It contains no other values and has mean 4. What is k?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 6
The total is 3(2)+5k
Review worked example 3.14.
The model = 2.5(t − 2000) + 36 predicts a quantity in calendar year t. According to the model, how much does the predicted quantity increase from 2005 to 2011?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 15
The time difference is 2011−2005
Review worked example 4.05.
Line A produces 75% of components and has a 4% defect rate. Line B produces 25% and has an 8% defect rate. Given that a randomly selected component is defective, what is the probability that it came from A?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 3/5
The share of all components that are defective from A is 0.75(0.04)
Review worked example 5.15.
A district has 800 students at School A and 1,200 at School B. Separate random samples estimate support for a proposal as 25% at A and 50% at B. What is the best estimate of the percentage of all district students who support it?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 40
Estimate the support counts by school: 0.25(800)
Review worked example 6.14.
Participants are randomly assigned to two programs. A sound analysis finds that the observed small difference in mean outcomes could reasonably occur by chance under no treatment advantage. Which statement is most appropriate?
Answer: D
Random assignment supports the validity of a treatment comparison; it does not ensure a convincing result. A difference compatible with ordinary assignment variability does not provide strong evidence of superiority. Failure to establish a benefit is not proof of exact equality.
Review worked example 7.15.
A pipe delivers water at a constant rate of 0.4 liter per second for 45 minutes. What volume does it deliver, in cubic meters? Use 1 m3 = 1,000 L.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 1.08
Convert 45 minutes to 45(60)
Review worked example 1.06.
Twenty percent of positive quantity A equals 35% of positive quantity B. Quantity A is what percent of B?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 175
The equation is 0.20A
Review worked example 2.08.
Data set A is 0, 5, 5, 10, and B is 0, 0, 10, 10. Which statement is true?
Answer: C
Both means are 5, and both ranges are 10. A’s squared deviations from 5 sum to 50; B’s sum to 100. With the same number of observations, B has greater standard deviation under either consistent convention. Equal endpoints do not determine the full spread.
Review worked example 3.12.
Which type of model most reasonably matches the curved pattern in the scatterplot over the observed input range?
Answer: D
The outputs decrease toward a low point near x
Review worked example 4.12.
A club has 90 members. Thirty members both own a bicycle and use public transit; 20 own a bicycle but do not use transit; 10 use transit but do not own a bicycle; and 30 do neither. Given that a randomly selected member owns a bicycle, what is the probability that the member uses transit?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 3/5
There are 30 + 20
Review worked example 5.05.
Two groups’ mean estimates are 123 ± 5 and 127 ± 5 at the same confidence level. Which statement follows directly from these summaries?
Answer: B
The intervals are [118, 128] and [122, 132], which overlap from 122 to 128. Their sample-based point estimates differ by 4, but the unknown population means need not. Each interval has width 10. Overlap by itself is not a proof of equality or a universal test of the difference.
Review worked example 6.15.
A district randomly samples 180 eighth graders, all of whom participate, and randomly assigns them to new or existing study materials. The study is well conducted and finds convincing evidence of greater mean improvement with the new materials. Which conclusion is best supported?
Answer: C
The random sample supports the population scope: this district’s eighth graders. Random treatment assignment supports a causal comparison, and the stated convincing result supports an average advantage. None of these features establishes identical individual effects or unrestricted generalization to other ages and districts.
Review worked example 7.06.
Review Problem Solving and Data Analysis
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Check answers after completing the questions. Each explanation shows how the answer was obtained and links to a related worked example.
Numeric answers are shown in readable mathematical form. When practicing test entry, omit units, commas, and symbols as described in the calculator and answer-entry reference.