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Block _________________________
Algebra 2 Midterm Review
PART 1 – MULTIPLE CHOICE
Write the letter for the correct answer at the left of each question.
1.
(1.2) Name the sets of numbers to which each number belongs.
2.
√7
(6.1) If f(x) = 𝑥 and g(x) = 3x – 1 find [ g ◦ f](4) and [ f ◦ g](4).
3.
4.
5.
2
(2.7) Write the equation of the given function in vertex form and state the domain and
range.
(2.8) Graph the inequality y > –3 |x + 1| – 2 and state the domain range.
(2.6) Which is not a part of the definition of the piecewise function
shown at the right?
6. (6.3) The diameter of a tree d (in inches) is related to its basal area BA
(in square feet) by the formula d = √
576(𝐵𝐴)
𝜋
. If the basal area of a tree is
12.4 square feet, what is the diameter of the tree? Use a calculator to approximate your
answer to three decimal places. Use 3.14 for π.
7.
(5.4) Solve 𝑥 2 = 4𝑥 by graphing. If exact roots cannot be found, state the consecutive integers
between which the roots are located.
8.
(4.8) Which quadratic inequality is graph at the right?
9.
(5.3) For each graph,
a. describe the end behavior,
b. determine whether it represents an odd-degree or an even-degree function, and
c. state the number of real zeroes.
d. label the maximum and minimum
10. (5.6) Use synthetic substitution to find f (2) for each function.
f(x) = 𝑥 4 – 3𝑥 3 + 2𝑥 2 – 2x + 6
11. (5.6) Given a polynomial and one of its factors, find the remaining factors of the polynomial.
𝑥 3 – 19x + 30; x – 2
12. (5.7) Given a polynomial and one of its factors, find the remaining factors of the
polynomial.
g(x) = 3𝑥3 – 4𝑥2 – 17x + 6
13.
(4.4) Simplify:
(5 + 2𝑖)(1 + 3𝑖)
14.
(4.4) Simplify:
15.
(6.3) State the domain and range of the function graphed.
16.
(5.1) Simplify:
17.
(5.1) Simplify:
18.
(5.1) Simplify:
1+2𝑖
2−3𝑖
(3𝑎0 𝑏 2 )(2𝑎3 𝑏 2 )2
4𝑎4 𝑏 2 𝑐
12𝑎2 𝑏 5 𝑐 3
(7𝑚 − 8)2
𝑦 3 − 64
19.
(5.5) Factor completely:
20.
(5.6) One factor of 𝑥 3 + 2𝑥 2 – 23x – 60 is x + 4. Find the remaining factors.
PART 2 – SHORT ANSWER
Answer each of the following short answer questions completely. Be sure to show ALL your work!
21.
(6.1) . If f(x) = 3 – x and g(x) = 𝑥 2 – 4, find [ g ◦ f ](x).
22.
(6.3) Graph and state the domain and range:
23.
(5.1) Simplify:
24.
(6.2) Determine if g(x) and h(x) are inverses, explain your reasoning.
y ≥ √2𝑥 + 2
(11𝑘 6 + 10𝑘 4 − 4𝑘 2 )(3𝑘 2 − 2𝑘)
𝑔(𝑥) = 2𝑥 − 8 𝑎𝑛𝑑 ℎ(𝑥) =
1
2𝑥
+4
25.
(5.2) Use long division to find (8𝑥 3 − 10𝑥 2 + 9𝑥 − 10) ÷ (2𝑥 − 1).
26. (5.8) . List all of the possible rational zeros of f(x) = 2𝑥 3 + 𝑥 2 – 4x + 8.
27.
(5.5) Write each expression in quadratic form, if possible.
3𝑦8 – 4𝑦2 + 3
28.
(5.5) Solve each equation.
𝑎3 – 9𝑎2 + 14a = 0
PART 3 – ESSAY
Solve each part of the following essay problems by showing ALL your work. Be sure to write a sentence
explaining your answer for each part!
29.
𝒇
(6.1) Find (f + g)(x), (f – g)(x), (f ⋅g)(x), and (𝒈) (x) for each f(x) and g(x).
f(x) = 3𝑥 2
g(x) =
5
𝑥
30.
(5.2) ERROR ANALYSIS Dylan, Patrick, and Thomas are practicing synthetic division together in
their Algebra 2 class. Each of the 3 group members found a different solution to the same
problem.
(𝒙𝟑 − 𝒙𝟐 − 𝟔) ÷ (𝒙 + 𝟐)
a. Find and explain the error in Dylan’s solution if there exists any. If he is correct, write his
solution as a polynomial expression.
−2
1
−1
6
↓
−2
6
1
−3
0
b. Find and explain the error in Patrick’s solution if there exists any. If he is correct, write his
solution as a polynomial expression.
2
1
−1
0
−6
↓
2
−2
−4
1
−1
−2
−10
c. Find and explain the error in Thomas’ solution if there exists any. If he is correct, write his
solution as a polynomial expression.
−2
1
−1
0
−6
↓
−2
6
−12
1
−3
6
−18
d. If you were a member of their group, which person would you agree with?