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OpenExam.ACT MATH · FOUNDATION PRACTICE

Mixed skills

Name: __________________________Date: __________________

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

1. A code consists of one of 3 letters followed by one of 4 digits. Repetition restrictions do not apply. How many codes are possible?

A. 7B. 9C. 24D. 12

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2. f(x) = 2x + 3 for x < 0 and f(x) = x² − 3 for x ≥ 0. What is f(−4)?

A. -19B. 13C. -11D. -5

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3. θ is in quadrant II and sin θ=12/20. What is cos θ?

A. -3/5B. -4/5C. 2/5D. -16/25

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4. A line has slope 3/3. What is the slope of a perpendicular line?

A. 0B. -1C. 1D. -1/2

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5. What is the greatest integer x satisfying 5x + 2 < 22?

A. 5B. 20C. 3D. 4

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6. Row [6, 2] is multiplied by column [7, 3]. What is the resulting scalar?

A. 32B. 18C. 48D. 42

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7. A line parallel to y = 3x + 9 passes through (2, 8). What is its y-intercept?

A. 14B. 2C. 8/3D. 5

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8. Two residuals for a model are −5 and 7. What is their sum of squared residuals?

A. 74B. 24C. 4D. 2

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9. An arithmetic sequence begins 3, 6, 9. What is its 4th term?

A. 12B. 9C. 81D. 15

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10. What is the x-coordinate of the midpoint of (5, −2) and (10, 8)?

A. 15B. 5C. 5/2D. 15/2

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OpenExam.ANSWER KEY · KEEP SEPARATE

Answers & reasoning

1. 12 · Choice D

For each possible letter, every digit is allowed. Use the product rule for the two stages. The requested value is 12.

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2. -5 · Choice D

The input is negative, so use the first branch. Substitute the negative input into the linear rule. The requested value is -5.

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3. -4/5 · Choice B

Use sin²θ+cos²θ=1 to find the cosine magnitude. Choose the negative cosine because the angle is in quadrant II. sinθ=12/20=3/5; cos²θ=1−9/25=16/25; quadrantII gives cosθ=−4/5. Therefore the requested value is -4/5.

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4. -1 · Choice B

For two nonvertical perpendicular lines, the slopes multiply to −1. Take the reciprocal and change its sign. The requested value is -1.

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5. 3 · Choice C

Subtract 2 and divide by the positive coefficient. The strict inequality gives x below an integer boundary, so use one less. The requested value is 3.

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6. 48 · Choice C

Multiply entries in corresponding positions. Add the two products to obtain the row-column dot product. The requested value is 48.

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7. 2 · Choice B

Parallel lines have equal slopes. Use the known point in y=mx+b and solve for the intercept. The requested value is 2.

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8. 74 · Choice A

Square each residual separately, making both contributions nonnegative. Add the squared misses using the same observations. Substitute the given numbers: (-5)^2+7^2 = 74. Therefore the requested value is 74.

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9. 12 · Choice A

The common difference is 3. Starting at the first term, take one fewer steps than the term number. The requested value is 12.

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10. 15/2 · Choice D

A midpoint lies halfway between the endpoint coordinates. Average the x-values; the y-values do not affect this requested coordinate. The requested value is 15/2.

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