1
Analysis 2 Summer Assignment
Complete the following summer assignment based on content from Analysis I by the first day
of class next year. Show all work with solutions on a separate piece of paper for full credit.
There will be an assessment based on these topics at the beginning of the school year.
Factor the following expressions:
1. 𝑥 4 − 16
2. 𝑥 2 + 2𝑥𝑦 + 𝑦 2
3. 𝑥 2 + 5𝑥𝑦 + 4𝑦 2
4. 3𝑎2 − 10𝑎 − 25
5. 𝑥 2 𝑎 + 𝑥 2 𝑏 − 16𝑎 − 16𝑏
6. 𝑥 2 + 4𝑦 2
7. 6𝑧 3 − 3𝑧 2 − 30𝑧
8. 8𝑎3 + 27
Solve the following:
1.
1
𝑥−2
=
3
𝑥+2
−
6𝑥
2.
𝑥 2 −4
15
𝑥
6
−4= +3
𝑥
Simplify the following expressions:
1.
4.
3𝑎+3𝑏
2.
𝑎2 +2𝑎𝑏+𝑏2
𝑏2 −3𝑏−10
8𝑏2
÷
2𝑏−10
16𝑏2
5.
(𝑥−𝑦)2
3.
𝑦−𝑥
𝑥+𝑦
𝑥
𝑥2 −𝑦2
𝑥2 𝑦
6.
𝑎2 −4𝑏2
𝑎2 −𝑏2
∙
3𝑎2 𝑏2
𝑎+𝑏
1
𝑡+1
3
1+
𝑡−1
1+
Graph the following linear equations:
1. 3𝑥 − 2𝑦 = 6
4
2. 𝑦 = 𝑥 − 3
5
Write a linear equation for each scenario in point-slope form and slope-intercept form:
1. Having an 𝑥-intercept of 5 and a 𝑦-intercept of −2.
2. Passing through the points (−1,2) and (3,4)
3. A line passing through the point (2,1) and
A. Parallel to 2𝑥 − 7𝑦 = 12
B. Perpendicular to 𝑦 = 3𝑥 − 1
2
Sketch the given parabola. Be sure to identify the vertex and all intercepts.
1. 𝑦 = 𝑥 2 + 8𝑥 + 12
2. 𝑦 = 𝑥 2 − 25
3. 𝑦 = 2𝑥 2 − 4𝑥 + 5
Solve the following:
1. 𝑛2 − 7 = 12
2. 𝑎2 + 4𝑎 = 5
3. 3𝑥 2 − 𝑥 − 2 = 0
4. 4𝑦 2 − 5 = 3𝑦
Solve each by completing the square:
1. 𝑥 2 + 7𝑥 + 2 = 0
2. 3𝑦 2 − 𝑦 = 2
Find all roots of the given polynomial then sketch. Use a graphing calculator to find
maximum and minimum values.
1. 𝑦 = −(𝑥 − 3)2 (𝑥 + 4)
2. 𝑦 = 𝑥 4 − 37𝑥 2 + 36
3. 𝑦 = 4𝑥 3 + 4𝑥 − 17𝑥 2
4. 𝑦 = (4 − 𝑥)(𝑥 + 7)2 (𝑥 − 1)3
Solve each and graph the solution on a number line.
(𝑥−3)2 (𝑥−5)
1. 𝑥 2 − 7𝑥 + 10 ≥ 0
2.
3. 3|𝑥| + 7 > 5
4. |2𝑥 − 13| ≤ 2
𝑥+1
<0
Sketch each graph:
3
1. 𝑦 = |𝑥 − 7| − 2
2. 𝑦 = √−𝑥 + 3 + 1
3. 𝑦 = − √𝑥 − 4
4. 𝑓(𝑥) = 2(𝑥 + 5)2 + 6
5. 𝑦 ≥ −𝑥 2 + 9
6. −2𝑦 > 𝑥 + 4
Determine if the given function is even, odd, neither, or not a function.
1. 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 1
2. 𝑔(𝑥) = 𝑥 3 − 7
3. ℎ(𝑥) = ±√𝑥 2 − 3
4. 𝑘(𝑥) = 𝑥 2 − 4𝑥 4
3
Find g-1(x) and the domain and range of g(x) and g-1(x)
1. g(x) = 9 – x2, x ≤ 0
2. g(x) = (x – 1)2 + 1, x ≤ 1
Sketch the following:
1. ℎ(𝑥) = 2−𝑥+1 − 4
2. 𝑚(𝑥) = log 2 (𝑥 + 2) + 6
Solve the following equations:
1. 𝑥 2 + 16 = 0
2. 𝑥 = √12 − 𝑥
3. √𝑥 − 5 + √𝑥 = 5
4. √4𝑥 + 5 − √𝑥 + 4 = √𝑥 − 1
Simplify the following expressions
3𝑎𝑏 2
2. 𝑎𝑏 −3 + 𝑎−4 𝑏 2
1. (− 2 )
2𝑎 𝑐
3.
(𝑝𝑞)3
4.
(𝑝2 𝑞 −1 )2
9𝑡 −2
𝑟
+ 3𝑟𝑡 −3 −
3
𝑡3
Solve the following equations:
1. 23𝑥 =
4.
3000
2+𝑒 2𝑥
4𝑥−1
8𝑥+5
=2
2. ln(𝑥) − ln(2) = 0
3. log(𝑥) − 2 = 0
5. 𝑒 2𝑥 − 4𝑒 𝑥 − 5 = 0
6. log(𝑥 2 ) = 6
7. log 3 𝑥 + log 3 (𝑥 2 − 8) = log 3 (8𝑥)
8. ln(√𝑥 − 8) = 5
Simplify the following:
𝑥𝑦
5
2. log √
1. log ( 2 )
𝑧
𝑎4
𝑏2
Identify if the given functions are one-to-one:
1. 𝑓(𝑥) = 𝑥 3 − 7𝑥
2. 𝑔(𝑥) = √𝑥 − 3 + 1
3. ℎ(𝑥) = 4𝑥 4 − 2𝑥 2 + 1
Sketch the following semicircles:
1. 𝑓(𝑥) = √4 − 𝑥 2 + 1
2. 𝑥 = √9 − (𝑦 + 1)2 − 4
4
Find the distance and midpoint of the segment containing the given endpoints.
1. (3, −7), (5,6)
2. (3, 𝑘), (𝑘, −3)
Simplify the following:
1. 𝑖 213
2. (3 − 4𝑖) − (−6 + 7𝑖)
5. √75 − √125 + √200
3.
6.
4+𝑖
4. (3 + 2𝑖)(2 − 5𝑖)
6−𝑖
3
7. (4 + √3)(1 − 2√3)
4−√5
Calculate the following:
1. If Ron put $1000 of his money into a bank account that earns a 2.3% annual interest rate,
how much will he earn after 10 years if the interest is compounded
A. yearly?
B. monthly?
C. continuously?
Solve:
1. The second and fifth terms of an arithmetic sequence are 5 and 38 respectively. Find the
explicit formula for the sequence.
2. Accurately classify the sequence and then create a corresponding explicit and recursive
formula for finding the nth terms of each sequence.
A.
32, 30, 28, 26,…..
B.
9, -3, 1, - 1 ,…..
3. Find a quadratic model and term number for the last given term for:
10, 12, 16, 22, 30, 40, …. 516
4. Determine the sum.
A.
B.