Algebra 2

Use this for “(2, 4) is on y = 2ˣ. Where is it on y = −3 × 2ˣ⁺¹ + 5?”

Use this for “(4, 2) is on y = √x. Where is it on y = √(2x)? On y = √(−x)?”

Use this for “Which change is f(x − 3), and which is f(x) − 3?”

Use this for “(4 − 2i) − (−1 + 5i)”.

Use this for “Solve x² − 4x + 13 = 0.”

Use this for “Simplify i²⁷.”

Use this for “Divide (3 + 4i) ÷ (1 + 2i).”

Use this for “Divide 2x³ − 3x² + x − 5 by x − 2” or “Find P(2) by the remainder theorem.”

Use this for “Divide x³ + 2x² − 5x + 7 by x² − x + 2.”

Use this for “Describe the end behavior of y = −3x⁵ + 2x² − 1.”

Use this for “Write the polynomial of least degree with zeros 1 and 2 + 3i.”

Use this for “Solve x⁴ − 13x² + 36 = 0” when every root is real.

Use this for “Factor 27x³ + 8” or “Factor x³ − 125.”

Use this for “Expand (x + 2)⁴.”

Use this for “Find C(6, 2) from row 5 of Pascal’s triangle.”

Use this for “f(x) = 2x − 1 and g(x) = x + 4. Find (f + g)(3), (f − g)(3), (f · g)(3) and (f ÷ g)(3).”

Use this for “Find f⁻¹(x) for f(x) = 3x − 6, and check f⁻¹(f(x)) = x.”

Use this for “f(x) = 2(x − 1)² + 3 for x ≥ 1. Find f⁻¹(11) and f⁻¹(x).”

Use this for “Solve √(x + 7) = x + 1” and reject the extraneous solution.

Use this for “Graph y = 2√(x + 3) + 1: where it starts, which way it goes, and y at x = 6.”

Use this for “Graph y = 2∛(x + 1) − 3: its center, and y at x = 7” or “Find x where y = 5.”

Use this for “Evaluate 82/3”, “Graph y = 2x−1/2” or “Solve x3/2 = 27.”

Use this for “Estimate log₃ 20” with the log key on a calculator.

Use this for “Find log 3,000 using log 3 ≈ 0.4771.”

Use this for “Expand log₅(25/y)” or “Is log(x + y) = log x + log y true?”

Use this for “Solve 4⁶ = 8ˣ” by writing both sides as powers of 2.

Use this for “$2,000 grows at 5% a year compounded continuously. How long until it reaches $3,000?”

Use this for “Solve log₃(2x − 1) = 4.”

Use this for “Solve log₃ x + log₃(x − 8) = 2.”

Use this for “Write 3/(x − 1) + 2/(x + 4) as one fraction.”

Use this for “Simplify (x − 4)/(x + 1) × (x + 1)/(x − 6)” or a quotient of two such fractions.

Use this for “Solve x/(x − 2) = 2/(x − 2) + 3/x” and reject the extraneous solution.

Use this for “6 workers take 10 days. How long do 4 workers take?”

Use this for “Find the sum of the first 10 terms of 5, 9, 13, ….”

Use this for “Evaluate the sum from k = 1 to 8 of (3k − 1).”

Use this for “Find the sum of 12 + 3 + 3/4 + ….”

Use this for “Convert 225° to radians” or “Convert 7π/6 to degrees.”

Use this for “Find the coterminal angle of −495° from 0° to 360°, its quadrant and its reference angle.”

Use this for “(−3, 4) is on the terminal side of θ. Find sin θ, cos θ and tan θ.”

Use this for “Write a cosine with amplitude 4, period π/2 and midline y = −1.”

Use this for “Find the period and asymptotes of y = 2 tan(x/2).”

Use this for “A Ferris wheel is 42 m at the top, 2 m at the bottom and turns once in 8 min. How high is a rider after 2 min?”

Use this for “tan θ = −12/5 in quadrant IV. Find sec θ and cos θ.”

Use this for “Simplify (1 − cos θ)(1 + cos θ)” or “sin²(3x) + cos²(3x)”.

Use this for “A spinner pays −2, 0, 5 or 20 points with chances 0.5, 0.3, 0.15, 0.05. What is the expected value?”

Use this for “A fair coin is tossed 5 times. What is the chance of at least 4 heads?”

Use this for “A school picks 20 students at random from each grade. Which sampling method is this?”

Use this for “Researchers compare the heart rates of runners and non-runners. What kind of study is this?”

Use this for “A website asks readers to vote in a poll. What kind of bias is this?”

Use this for “Scores have μ = 50 and σ = 5. What share is between 45 and 60, and how many of 400?”

Use this for “Weights have μ = 500 g and σ = 2 g. How many of 500 packages are more than 3 g off?”

Use this for “IQ scores have μ = 100 and σ = 15. About what percent are between 70 and 130?”

Use this for “Scores have μ = 500 and σ = 100. What score is at the 90th percentile?”

Use this for “In a random sample of 400, 60% said yes. What is the margin of error?”