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OpenExam.SAT MATH · FOUNDATION PRACTICE

Mixed skills

Name: __________________________Date: __________________

10 original practice questions · Untimed · Fractions and exact decimals accepted

1. Of 30 students, 9 walk to school. A student is selected at random. What is the probability that this student does not walk?

A. 7/100B. 7/10C. 1/2D. 3/10
probability-010

2. If x + y = 9 and x − y = 1, what is x?

A. 5B. 9C. 10D. 1
systems-001

3. In a study of a plant fertilizer, volunteers are randomly assigned to a treatment or a control. The groups otherwise receive the same procedures and adherence is complete. What does random assignment chiefly support?

A. Automatic generalization to every person or setting.B. A causal comparison of the treatment in the studied setting.C. A guarantee that the treatment works equally well for every subject.D. Proof that no chance variation remains between the groups.
sat2-sampling-claims-4-2

4. What is the greatest integer x satisfying 6x + 7 ≤ 56?

A. 49/6B. 9C. 8D. 7
inequalities-013

5. A line passes through (1, 8) and (4, 29). What is its slope?

A. 1/7B. -7C. 7D. 29/4
slope-017

6. If 7x + 8 = 6x + 17, what is the value of 2x + 1?

A. 20B. 18C. 9D. 19
linear-019

7. For x > 0, (x^5)^6 = x^n. What is n?

A. 5B. 15625C. 6D. 30
exponents-010

8. For x > 0, x^3 · x^4 = x^n. What is n?

Answer: __________________

exponents-001

9. One person is selected uniformly from all 31 people in the table. What is the probability this person swims or cycles or both?

Survey counts. : Swims, Cycles: 9, Does not cycle: 5; : Does not swim, Cycles: 7, Does not cycle: 10Open full-size diagram ↗
A. 12/31B. 21/31C. 10/31D. 9/31
sat2-two-way-tables-2-3

10. If 7x + 8 = 71, what is the value of x?

A. 9B. 79/7C. 63D. 71/7
linear-017
OpenExam.ANSWER KEY · KEEP SEPARATE

Answers & reasoning

1. 7/10 · Choice B

The probability of walking is 9/30 = 3/10. Use the complement: 1 − 3/10. The probability of not walking is 7/10.

probability-010

2. 5 · Choice A

Add the equations: 2x = 10. Divide by 2: x = 5. Then y = 4; substitution verifies both equations.

systems-001

3. A causal comparison of the treatment in the studied setting. · Choice B

Random assignment decides treatment allocation; it is not a method for selecting volunteers from the world. It reduces systematic confounding in the comparison under the stated conditions. It supports evaluating a causal treatment effect in this setting, while broad generalization still needs evidence.

sat2-sampling-claims-4-2

4. 8 · Choice C

Subtract 7: 6x ≤ 49. Divide by positive 6: x ≤ 49/6. The greatest permitted integer is 8.

inequalities-013

5. 7 · Choice C

The change in y is 29 − 8 = 21. The change in x is 4 − 1 = 3. Slope = 21/3 = 7.

slope-017

6. 19 · Choice D

Subtract 6x and 8 from both sides: x = 9. The question asks for 2x + 1, so compute 2(9) + 1. The requested expression is 19.

linear-019

7. 30 · Choice D

The inner power x^5 is raised to the power 6. A power of a power multiplies the exponents. n = 5 × 6 = 30.

exponents-010

8. 7

The bases are the same and the powers are multiplied. Add the exponents rather than multiplying them. n = 3 + 4 = 7.

exponents-001

9. 21/31 · Choice B

The disjoint union regions contain 9, 5, and 7 people. The total sample size is 31. Add each region once and divide: 21/31=21/31.

sat2-two-way-tables-2-3

10. 9 · Choice A

Subtract 8 from both sides: 7x = 63. Divide both sides by 7: x = 9. Check: 7(9) + 8 = 71.

linear-017

Original parameterized practice, independently checked by computation. Educator review pending. Not an official exam paper.