Scholarship Algebra II Exam Review Questions
These are required exam review questions. Follow the directions for each question, and show all of your
work on separate sheets of paper. Do the questions IN ORDER! Most of these problems require work
to be shown (indicated by *). I will not grade papers that do not follow these requirements. The answers
will be posted on my website. This review will account for 10% of your exam grade, and is due the day
of your exam before you take your exam. Your exam will consist of a mixture of multiple choice
questions and open-ended questions.
Solve 5 – 3x > 2x + 10*
Solve |3x + 4| = 12*
Solve |2x – 5| ≥ 10*
Solve |1 – 4x| < 9*
-3 < 2x + 3 < 9*
A = {(3, -1), (2, 3), (-1, 2), (4, 3)} State the domain and range of set A. Is A a function? How do you
know?
7. f(x) = 3x3 – x2 + 2x – 5. Find f(-2).*
8. g(x) = -2x2 + 5. Find g(1).*
9. Is (3, 2) on the graph 4x – 2y = 8?*
10. Find the slope of the line containing the points (-2, 4) and (3, 8).*
11. What is the slope of a horizontal line?
12. What is the slope of a vertical line?
1
13. In point-slope form, what is the equation of a line containing (3, -5) with a slope of ?
2
14. What is the slope of the line 2x – 5y = 12?*
15. Convert 3x + 4y = 16 to slope-intercept form.*
2
16. Consider the equation y = x + 4. What is the slope of a parallel line? Perpendicular
line?

3
4 x  5 y  12
17. Solve the system by any method: 
*
3x  4 y  22

3x  y  4
18. Write the matrix product that would solve the following: 
*
2 x  4 y  7
2 1 0
1.
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3.
4.
5.
6.
19. Evaluate 3
1
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1
2
2 *
1
State each x-intercept and whether the graph will cross or bounce: y  x 4  x  2   x  3 x  1
Multiply: (2x + 3)2
Multiply: (x + 3)(3x – 4)
Multiply: (x + y)3*
Factor: x3 – 64
Factor by grouping: 2x3 + 3x2 – 6x – 9*
Solve: 2x2 = 8x*
3
2
27.
28.
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31.
32.
Solve: 2w2 + 7w = 15*
Solve: x2 + 49 = 0*
Solve: 3x2 + 12x = 33*
Solve: 2x2 – 11x + 3 = 0.*
What would you need to add to x2 + 8x to complete the square?
Perform  2 x3  3x 2  5x  2    x  2  . You may do this two different ways.*
33.
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37.
Solve for a: 2ax + 3 = 4a*
Graph: y < -x + 3.
What is the vertex of the parabola y = -3(x + 1)2 + 2?
What is the vertex of the parabola y = 2x2 – 6x + 3?*
A polynomial with rational coefficients has roots 2, 1 – i, and 2  6 . What other roots MUST it
have?
Know the following polynomials by degree: constant, linear, quadratic, and cubic. Also know the
meaning of the terms monomial, binomial, and trinomial.
Multiply: (4 – 2i)2*
List the possible rational roots of 2x3 – x2 – 12 = 0 and then find all complex roots.*
a) What is the discriminant?
b) Sketch a parabola with a positive discriminant.
c) Sketch a parabola with a negative discriminant.
d) Sketch a parabola with a zero discriminant.
Draw a zebra for this problem.
Use your graphing calculator to find the quadratic equation that passes through the points (2, 5),
(3, -1) and (4, 1).
State the Fundamental Theorem of Algebra in your own words.
Consider the function y  x3  x 2  4  x 2  9  . Indicate the x-intercepts.
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46. Cucumbers cost 25 cents each and heads of lettuce cost 75 cents each. Bob bought 12 vegetables (a
mixture of cucumbers and lettuce) for a total cost of $7.50. Find the number of each that he
bought.*
47. Find three consecutive odd integers whose sum is 13 more than twice the largest of the three.*
48. The length of a rectangle is four more than three times its width. The perimeter is 80 feet. What are
the dimensions of the rectangle?*
49. The length of a rectangle is 3 more than its width. The area is 70 m2. What are the dimensions of the
rectangle?*
50. A car leaves a town traveling at 50 miles per hour. Two hours later, a second car, traveling 70 miles
per hour, leaves along the same route as the first car. How long will it take for the second car to
overtake the first car?*
51. A sea lion swims 18 km downstream from one feeding ground to another in 27 min. The return trip
against the current takes 36 min. How fast does the sea lion swim in still water? (Remember to
convert time to hours.)*
* Indicate problems that require work to be shown