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Mixed skills
10 original practice questions · Untimed · Fractions and exact decimals accepted
1. An arithmetic sequence starts at 4 and has common difference 4. What is term 6?
clep-arithmetic-term-12. Factor 8x² + 12x as 4x(ax + b). What is b?
clep-common-factor-13. Let f(x)=√(x−3) and g(x)=x−6. Among x=2, 3, 6, 7, how many are excluded from the domain of f(x)/g(x)?
Answer: __________________
clep-x2-quotient-exclusions-24. Solve (2x − 2)/3 = 5. What is x?
clep-fraction-linear-15. What is the remainder when P(x) = x² + 2x + 3 is divided by x − 4?
clep-remainder-theorem-26. What is the principal square root of (-9)²?
clep-principal-square-root-47. In A = P(1 + rt), let A = 400, P = 200 and t = 5. What is r?
clep-literal-formula-18. Solve log₂(x)−log₂(x−4)=1 over the reals.
Optional written extension · self-assessment only
Show substituted work, state the required domain or geometric condition, and refute a competing method. This extension is not automatically scored.
Show your reasoning for each part. This task is not automatically scored.
9. In the identity (2x + 2)(3x − 4) = 6x² + bx − 8, what is b?
clep-nonmonic-factor-110. The system is x + y = 17 and 2x − y = 10. What is x?
clep-system-coordinate-3Answers & reasoning
1. 24 · Choice A
Count one fewer step than the term number. Add that many common differences to the first term. The requested value is 24. Substitute or reverse the operation to check this result.
clep-arithmetic-term-12. 3 · Choice D
Divide the linear term by the factored-out term. The x cancels and the remaining coefficient is b. The requested value is 3. Substitute or reverse the operation to check this result.
clep-common-factor-13. 2
The square root requires x≥3; the denominator also requires x≠6. The inputs 2 and 6 violate those conditions. Two listed inputs are excluded; x=3 is allowed because a zero numerator is valid.
clep-x2-quotient-exclusions-24. 17/2 · Choice C
Multiply both sides by 3. Add the subtracted constant before dividing by the coefficient of x. The requested value is 17/2. Substitute or reverse the operation to check this result.
clep-fraction-linear-15. 27 · Choice D
The remainder theorem gives P(a) for a divisor x − a. Evaluate P at the positive value indicated by the divisor. The requested value is 27. Substitute or reverse the operation to check this result.
clep-remainder-theorem-26. 9 · Choice D
Square the negative input first. The principal square root is the nonnegative magnitude. The requested value is 9. Substitute or reverse the operation to check this result.
clep-principal-square-root-47. 1/5 · Choice C
Divide by P before isolating the product rt. Subtract one and divide by t, keeping r as a rate rather than a percent. The requested value is 1/5. Substitute or reverse the operation to check this result.
clep-literal-formula-18. 8 · Choice C
The original arguments require x>4. The quotient rule gives x/(x−4)=2, so x=2x−8. Thus x=8; both original arguments are positive.
Optional written extension · self-assessment only
Show substituted work, state the required domain or geometric condition, and refute a competing method. This extension is not automatically scored.
- Select and explain the required mathematical condition. (1 points)
- Show substituted calculation and the requested result. (1 points)
- Demonstrate why one competing method fails. (1 points)
The original arguments require x>4.
The quotient rule gives x/(x−4)=2, so x=2x−8.
Thus x=8; both original arguments are positive.
The competing operation 4 gives 4. Accept an input where the second logarithm has zero argument. It does not meet the condition used above.
9. -2 · Choice C
The two cross products supply the x coefficient. Add their signed coefficients rather than multiplying them. The requested value is -2. Substitute or reverse the operation to check this result.
clep-nonmonic-factor-110. 9 · Choice A
Add the equations to eliminate y. Divide the resulting 3x equation by 3. The requested value is 9. Substitute or reverse the operation to check this result.
clep-system-coordinate-3Original parameterized practice, independently checked by computation. Educator review pending. Not an official exam paper.