Quiz Lessons 1-3:
Name:_______________
1. Simplify
2. Simplify
3.
Simplify
Period: ________________
𝑎+𝑏
𝑎2 −𝑏2
𝑥 2 +3𝑥−10 𝑥 2 +5𝑥+6
∙
𝑥 2 +8𝑥+15 𝑥 2 +4𝑥+4
4𝑥 2 𝑦
15𝑎3 𝑏3
÷
2𝑥𝑦 2
5𝑎𝑏3
4. What is the simplest form of the complex fraction?
5. What is the least common multiple (LCM) of
𝑎2 − 6𝑎 + 9 𝑎𝑛𝑑 𝑎2 + 𝑎 − 12.
1 3
−
𝑥 𝑦
2
𝑦
WARM-UP
WARM-UP DAY 1:
Factor.
1. 𝑥 2 − 9
2. 𝑥 2 + 7𝑥 + 12
3. 𝑧 3 − 𝑧 3 𝑦
WARM-UP DAY 2:
Simplify
3
4
1. 20 + 25
1
2
2. 10 − 15
Solve each equation.
2
4
3. 3 + 𝑥 = − 9
3
5
4. 𝑥 − 8 = − 24
WARM-UP DAY 3:
Find the LCM of 𝑥 2 − 2𝑥 − 3, 𝑥 2 − 𝑥 − 6
WARM-UP DAY 4:
Under what conditions is
WARM-UP DAY 5:
𝑥2
𝑦2
− 20 = 1
16
𝑎2 +𝑎𝑏+𝑏2
𝑎2 −𝑏2
undefined?
HOMEWORK How will students practice what they learned?
Homework Day 1:
1. Review all examples, solve them, and write them along with important terms in your journal. Bring
your questions to the class. Be prepared for the quiz.
2. I want to bring candies for all of you next month. The grocery store told me that I have to purchase
them by the pound. One of their items is a mixture of M&Ms and Starbursts candies. The mixture
is made with 2 pounds of M&Ms and 3 pounds of Starburst candies. If I tell the store manager that
I want to purchase them for my students, they will add an additional x pounds of Starburst candies
to the mixture, then how many mixtures of Starburst Candies, I will have. Create a rational
expression only.
Solve each equation by factoring
3. 𝑥 2 − 3𝑥 = 4
4. 18𝑥 2 − 3𝑥 = 1
4. Simplify the ___________. (Complete the sentence.)
𝑥+𝑦
2𝑥 − 𝑦
𝑥+𝑦
2𝑥 + 𝑦
Homework Day 2:
1. Review all examples, solve them, and write them along with important terms in your journal. Bring
your questions to the class. Be prepared for the quiz.
2. Find the LCM of 18𝑟 2 𝑠 5 , 24𝑟 3 𝑠𝑡 2 , 𝑎𝑛𝑑 15𝑠 3 𝑡
3. Simplify
𝑥 2 +3𝑥−10 𝑥 2 +5𝑥+6
∙
𝑥 2 +8𝑥+15 𝑥 2 +4𝑥+4
7
11
4. Simplify 𝑦−2 − 2−𝑦
5. The band has 30 more members than the school chorale. If each group had 10 more members, the
ratio of their membership would be 3:2. How many members are in each group?
Homework Day 3:
1. Review all examples, solve them, and write them along with important terms in your journal. Bring
your questions to the class. Be prepared for the quiz.
Simplify.
4
2.
16
− 8𝑥 ÷ 𝑥𝑦2
3.
5
𝑛+6
4
− 𝑛−1
4. The sum of a number and 8times its reciprocal is 6. Find the number(s).
Homework Day 4:
1. Review all examples, solve them, and write them along with important terms in your journal. Bring
your questions to the class. Be prepared for the quiz.
2.
Solve each inequality. Check your solutions.
3.
7
𝑎+1
>7
4.
1
2𝑝
3
1
+ 4𝑝 < 2
Homework Day 5:
1. Review all examples, solve them, and write them along with important terms in your journal. Bring
your questions to the class. Be prepared for the quiz.
2. Graph 𝑓(𝑥) =
𝑥 2 +2𝑥+1
𝑥+1
𝑥−4
3. Graph the rational function. 𝑓(𝑥) = 𝑥+3
4. Solve the equation algebraically and confirm your solution using a graphing calculator.
1
2
=
𝑥2 − 1 𝑥2 + 𝑥 − 2