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OpenExam.AP PRECALCULUS · FOUNDATION PRACTICE

Mixed skills

Name: __________________________Date: __________________

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

1. The table uses equally spaced inputs. What is its second difference?

A. -6B. 6C. 9D. 12

model-selection-01-1

2. What is the remainder when P(x)=x³ + 3x + 4 is divided by x−2?

A. -10B. 4C. 10D. 18

polynomial-factors-01-1

3. For log₂(y)=4−2t, what is y at t=1?

A. 14B. 64C. 4D. 2

semi-log-04-2

4. A culture begins with 30 cells and triples each hour in a model. How many cells does the model predict after 3 hours?

A. 90B. 2430C. 810D. 39

exponential-growth-01-1

5. The product (4x² − 1)(2x³ + 5) has what leading coefficient?

A. 6B. 5C. 8D. 20

polynomial-structure-04-2

6. A linear model has f(6)=25 and f(8)=31. What is f(0)?

A. -7B. 3C. 7D. 25

function-change-04-4

7. An exponential model has f(0)=3, f(1)=6. What is f(4)?

A. 24B. 48C. 11D. 12

exponential-growth-04-1

8. Evaluate arccos(cos(270°)) in degrees using the principal inverse cosine.

Answer: __________________

inverse-trig-02-3

9. If x² + 7x + 12=(x+3)(x+c), what is c?

A. 12/7B. 12C. 4D. 7

polynomial-factors-04-1

10. A model is A(t)=400(1+5/100)^t. What is the percentage growth rate per time unit?

A. 400B. 5C. 105D. 95

exponential-growth-02-3

OpenExam.ANSWER KEY · KEEP SEPARATE

Answers & reasoning

1. 6 · Choice B

The first differences are 3 and 9. Subtract the earlier first difference from the later one. The second difference is 9−3=6.

model-selection-01-1

2. 18 · Choice D

Use the remainder theorem at x=2. Compute 2³+3(2)+4. The remainder is 18.

polynomial-factors-01-1

3. 4 · Choice C

Evaluate the log coordinate 4−2, then invert the base-two logarithm. Using these quantities: 2^(4-2) = 4. Check the original domain, requested quantity and units; do not substitute a related parameter.

semi-log-04-2

4. 810 · Choice C

There are three one-hour growth intervals. Multiply by 3 in each interval. 30×3×3×3=810.

exponential-growth-01-1

5. 8 · Choice C

The largest exponent comes from x² times x³. Multiply the coefficients of those terms. The resulting leading term is 8x⁵.

polynomial-structure-04-2

6. 7 · Choice C

The output increases by 6 while input increases by 2, giving rate 3. Write f(x)=3x+b and substitute (6,25). Solving 25=3(6)+b gives b=7.

function-change-04-4

7. 48 · Choice B

Find the factor f(1)/f(0)=2. Four unit intervals multiply the initial value by 2⁴. f(4)=3×16=48.

exponential-growth-04-1

8. 90

Reflect the angle into [0°,180°] while preserving its cosine. Using these quantities: 360-270 = 90. Check the original domain, requested quantity and units; do not substitute a related parameter.

inverse-trig-02-3

9. 4 · Choice C

The constant product requires 3c=12. Dividing by 3 gives c=4. Check the middle coefficient: 3+4=7.

polynomial-factors-04-1

10. 5 · Choice B

Compare the base with 1+r. The rate as a fraction is the amount above 1. 5/100 corresponds to 5 percent.

exponential-growth-02-3

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