Algebra II
Chapter 1 Review
1. Justify each step by naming the property used. a. 4 −3 1 = 4 1 (−3) 4 4 b. = 4 1 (−3)
4
c. = 1 (−3) d. = −3 2. Evaluate –a2+ 4a – 17; a = 5
3. Evaluate
6(s − 2) − 4(s + 1) ;s = 3 3s + 1
4. The expression 19.95 + 0.02x models the daily cost in dollars of renting a car. In the expression, x represents the number of miles the car is driven. What is the cost of renting a car for a day when the car is driven 50 miles? 5. Solve 3r + 3.7 = 5r – 2.5 6. Solve 3(5t + 2) = 36 7. Solve for x: tx – ux = 3t
8. Solve for x:
x−3 +3= a 6
9. Two buses leave Dallas at the same time and travel in opposite directions. One bus averages 58 mi/h, and the other bus averages 52 mi/h. When will they be 363 mi apart? 10. Solve and graph: 3m + 7 ≥ 4 11. Solve and graph: 3x – 1 5 or 2x – 4 x 12. Solve and graph: –3t 12 and –2t > –6 13. Solve: |2x + 3| = 5
Algebra II
Chapter 2 Review
1. Find the domain and range and determine whether it’s a function: {(2, 1), (–4, 5), (1, 7), (2, -3), (–1, 2)} Suppose f(x) = 3x – 4 and g (x) = |x| + 3. Find each value. 1
3. f + g(−2) 3 5. Find the slope through (–2, 7) and (4, 1) 2. f(2)
3 2
6. Find the slope perpendicular to y = x +
4.
f (1) g(1)
1 4
Using standard form, write the equation of the line with the given slope through the given point. 1
7. slope = 6; ,2 2
1 4
8. slope = ;(4,3)
Using slope-intercept form, write the equation of the line through each pair of points. 9. (0, 0) and (–2, 3) 10. (1, 5) and (–3, 3) Describe each translation of y =| x | then graph each translation. 11. y = x + 3 − 2
\
12. 𝑦 = −2|𝑥 − 4|
Algebra II
Chapter 4 Review
1. Write the equation of the parabola in standard form.
Sketch a graph of the quadratic function with the given vertex and through the given point. 2. vertex (3, 4); point (5, 8)
Graph each quadratic function. Name the axis of symmetry and the coordinates of the vertex. 3. y = x2 + 5 4. y = x2 – 4x – 3
Simplify each expression. 5. (3 + i) – (7 + 6i) 6. (3 – 4i)(5 + 2i) Solve each quadratic equation. 9. x2 – 16 = 0 10. 2x2 – 3x – 11 = 0
7. (–4 – 9i) + (5 – 7i) 11. x2 + 3x – 10 = 0
8. 3 −25 + 4 12. 3x2 + 48 = 0
13. Anthony has 10 ft of framing and wants to use it to make the largest rectangular picture frame possible. Find the maximum area that can be enclosed by his frame. Evaluate the discriminant of each equation. Determine how many real solutions each equation has. 14. x2 + 5x + 6 = 0 15. 3x2 – 4x + 3 = 0 16. –2x2 – 5x + 4 = 0 17. 16x2 – 8x + 1 = 0
Algebra II
Chapter 5 Review 3
Classify by the degree: −2𝑥 − 5𝑥 + 17 Classify by the number of terms: −2𝑥 3 − 5𝑥 + 17 Describe the end behavior: A) 𝑓 (𝑥 ) = −𝑥 5 + 3𝑥 3 + 4𝑥 B) 𝑓 (𝑥 ) = 2𝑥 4 + 3𝑥 2 − 17 3 2 Divide: (−3𝑥 − 2𝑥 − 2𝑥 − 2) ÷ (𝑥 − 4) Divide: (8𝑥 2 + 6𝑥 − 20) ÷ (4𝑥 − 5) Find 𝑃(−4) for 𝑃(𝑥) = 𝑥 4 − 𝑥 3 − 3𝑥 2 − 3𝑥 + 8 Determine which binomial is NOT a factor of 3𝑥 3 + 12𝑥 2 − 3𝑥 − 12 A) 𝑥 + 4 B) 𝑥 − 1 8) Use the Rational Root Theorem to list all the possible rational roots of the polynomial equation 𝑥 3 − 6𝑥 2 + 2𝑥 − 6 = 0. Do not find the actual roots. 6 9) A polynomial equation has the roots: −2 + √7 𝑎𝑛𝑑 13. Find another root. 10) Find the roots of the following equation: 𝑥 3 + 𝑥 2 + 15𝑥 + 15 = 0 11) Find an equation with the given root: 3 and -2 12) Find an equation with the given roots: −4 𝑎𝑛𝑑 2𝑖 1) 2) 3) 4) 5) 6) 7)
