Introduction To Formal Geometry
Summer Packet
North Valleys High School
Name:_____________________________________________________
Incoming Grade Level:__________
*Packet due the first day of class
For questions, e-mail Mrs. Landis at dlandis@washoeschools.net
Check out mrslandis.weebly.com for resources
Materials required for the course:
-compass (find a good one, the plastic ones will frustrate!)
-protractor
Recommended but not required:
-scientific calculator
**See examples of each on the website listed above**
Topic 1: Solving Linear Equations
Solve each equation and explain each step. The first one is done for you.
1. (𝑥 + 6) + 2(2𝑥 − 4) = 180
2. (5𝑥 + 6) − 4(𝑥 − 8) = 72
3. −3(4𝑥 + 3) + 4(6𝑥 + 1) = 43
4. 5(2𝑥 + 3) − 9(6𝑥 + 1) = 5𝑥 + 19
5. (𝑥 + 1) + (𝑥 + 2) + (𝑥 + 3) = 180
6. (3𝑥 + 2)(𝑥 − 4) = 3𝑥 2 + 10𝑥
7. −(1 + 7𝑥) − 6(−7 − 𝑥) = 36
8. −4(𝑥 − 13)(2𝑥 + 1) = −8𝑥(𝑥 − 13)
9. 15 − 21𝑥 = 8𝑥 + 7𝑥(4 − 3𝑥)
10. −18 − 6𝑘 = 6(1 + 3𝑘)
11. 3𝑛 − 5 = −8(6 + 5𝑛)
12. 𝑝 − 4 + 16 = 8𝑝 − 6𝑝 + 15
Topic 2: Order of Operations
Simplify each expression and explain each step. A few are done for you to serve as examples.
1. √(5 − 1)2 + (6 − (−1))2
2. √(4 − 6)2 + (−2 − 1)2
3. √(−4 − 1)2 + (9 − (−2))2
4. √(2.5 − 1.7)2 + (−0.9 − (−0.5))2
5. √(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2 if 𝑥1 = 3, 𝑥2 = −4, 𝑦1 = −1, 𝑦2 = 5
6. √(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2 if 𝑥1 = 4, 𝑥2 = −2, 𝑦1 = 1, 𝑦2 = −2
1
3
7. √(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2 if 𝑥1 = 2 , 𝑥2 = 2 , 𝑦1 = 6, 𝑦2 = −6
8. √(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2 if 𝑥1 = 10, 𝑥2 = 25, 𝑦1 = −15, 𝑦2 = −5
2
1
9. √(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2 if 𝑥1 = 3 , 𝑥2 = 1, 𝑦1 = 4 , 𝑦2 = 2
10. √(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2 if 𝑥1 = 3, 𝑥2 = −2, 𝑦1 = −5, 𝑦2 = 7
11. (2𝑥 − 5)2
12. (3𝑥 − 4)2
13. (2𝑥 + 8)2
14. (5𝑥 + 12)2
15. (2𝑥 − 3)2 (𝑥 + 7)
16. (𝑥 − 9)2 (14𝑥 + 1)
Topic 3: Graphing Linear Equations
Graph each linear equation and identify the slope, y-intercept and x-intercept. The first one is
done for you.
Topic 4: Solving Systems of Equations
Solve each system of equations using substitution or elimination. The first one is done for you.
15) {
𝑥 + 2𝑦 = 3
2𝑥 + 3𝑦 = 3
16 {
2𝑥 − 3(𝑦 + 1) = 8
3(𝑥 + 2) + 5𝑦 = −6
Topic 5: Simplifying Radical Expressions
Simplify each expression and explain each step. A few are done for you to serve as examples.
1. √72
2. √200
3. √27
4. 5√18
5. √3² + 4²
6. √4 + 9
7. √5² + 12²
10.
1
√2
13. 4√3 + 7√3
8. √49 ⋅ 3
11.
9. 6√24
1
12.
√5
14. √12 + √27
6
√3
Topic 6: Find Area of Polygons and Circles