PCTI Algebra II Summer Packet

Resources to use for assistance: http://www.khanacademy.org http://www.purplemath.com/modules http://www.hippocampus.org http://www.virtualnerd.com/algebra-1/all http://www.mathsisfun.com/algebra/index.html

PCTI Mathematics Department Sal F. Gambino, Supervisor

Summer Packet Grading

• On the first day of school, the teacher will check for

completion/effort of the packet. • This will be weighted at 50%.

• Teacher will then review the packet with the students.

• Upon completion of the review, the students will be given an

assessment based on the summer packet.

• The assessment will be weighted at 50%.

• The two weighted scores combined will count as one project grade.

• Therefore, the grade for the summer packet will be placed under the “project” category.

Multi-Step Equations Solve each equation. Show all work and check your solutions

https://www.khanacademy.org/math/in-eighth-grade-math/linear-equations-one-variable/solvingequations-variable-both-sides/v/multi-step-equations-1

1. 6 = 1 − 2𝑛 + 5

2. 4𝑚 − 4 = 4𝑚

3. −18 − 6𝑘 = 6(1 + 3𝑘)

4. −3(4𝑥 + 3) + 4(6𝑥 + 1) = 43

5. 24𝑎 − 22 = −4(1 − 6𝑎)

6. −5(1 − 5𝑥) + 5(−8𝑥 − 2) = −4𝑥 − 8𝑥

Evaluating Functions Evaluate each function.

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8thfunctions-and-function-notation/v/understanding-function-notation-example-1

1. 𝑓(𝑥) = −2𝑥 + 1; Find 𝑓(−7)

2. 𝑓(𝑥) = 4𝑥 + 2; Find 𝑓(3𝑥)

3. 𝑓(𝑥) = 4𝑥 − 2; Find 𝑓(𝑥 + 3)

4. 𝑓(𝑥) = 𝑥 − 2; Find 𝑓(𝑥2)

5. 𝑓(𝑥) = 𝑥2 − 5; Find 𝑓(𝑥 + 3)

6. 𝑓(𝑥) = 2 ∙ 3𝑥+3; Find 𝑓(4 + 𝑥)

Properties of Exponents Simplify. Your answer should contain only positive exponents.

https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponentrules-part-1

1. 2𝑚2 ∙ 2𝑚3

2. 𝑚4 ∙ 2𝑚−3

3. 4𝑎2𝑏2 ∙ 3𝑎−4𝑏−3

4. (4𝑎3)2

5. (𝑥2)0

6. (2𝑥2)−4

7. 6𝑛4

2𝑛3

8. 𝑟2

2𝑟3

9. 3𝑚−4

𝑚3

10. 2𝑥4𝑦−4𝑧−3

4𝑥2𝑦−3𝑧4

Factoring Trinomials Factor each expression completely.

https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/factoringquadratic-expressions-core-algebra/v/factoring-polynomials-1

https://www.khanacademy.org/math/algebra2/polynomial-functions/factoring-polynomials-quadraticforms-alg2/v/factoring-trinomials-by-grouping-4

1. 𝑛2 + 4𝑛 − 12

2. 𝑏2 + 16𝑏 + 64

3. 𝑚2 + 2𝑚− 24

4. 𝑘2 − 13𝑘 + 40

5. 𝑛2 − 𝑛 − 56

6. 𝑛2 + 4𝑛 − 12

7. 𝑝2 + 3𝑝 − 18

8. 2𝑛2 + 6𝑛 − 108

9. 5𝑛2 + 10𝑛 + 20

10. 3𝑝2 − 2𝑝 − 5

11. 3𝑛2 − 8𝑛 + 4

12. 5𝑛2 + 19𝑛 + 12

13. 9𝑘2 + 66𝑘 + 21

14. −6𝑎2 − 25𝑎 − 25

Factoring By Grouping Factor each completely.

https://www.khanacademy.org/math/algebra2/polynomial-functions/factoring-polynomialsquadratic-forms-alg2/v/factor-by-grouping-and-factoring-completely

1. 8𝑟3 − 64𝑟2 + 𝑟 − 8

2. 12𝑥3 + 2𝑥2 − 30𝑥 − 5

3. 63𝑛3 + 54𝑛2 − 105𝑛 − 90

4. 25𝑣3 + 5𝑣2 + 30𝑣 + 6

5. 96𝑛3 − 84𝑛2 + 112𝑛 − 98

Factoring Special Cases Factor each completely.

https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/factoring-specialproducts-core-algebra/v/factoring-special-products

1. 4𝑏2 − 4𝑏 + 1

2. 3 + 6𝑏 + 3𝑏2

3. 10𝑛2 + 100𝑛 + 250

4. 200𝑚4 + 80𝑚3 + 8𝑚2

5. 𝑛2 − 25

6. 9𝑥2 − 1

7. 98𝑛2 − 200

8. 81𝑣4 − 900𝑣2

Solving Quadratic Equations by Factoring Solve each equation by factoring.

https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/solving-quadraticsfactoring/v/example-1-solving-a-quadratic-equation-by-factoring

1. 𝑘2 − 4𝑘 − 5 = 0

2. 4𝑘2 + 9𝑘 + 5 = 0

3. 𝑥2 − 11𝑥 + 19 = −5

4. 6𝑛2 − 18𝑛 − 18 = 6

5. 7𝑟2 − 14𝑟 = −7

Solving Quadratic Equations Using the Quadratic Formula Solve each equation with the quadratic formula.

https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadraticformula/v/quadratic-formula-1

1. 4𝑏2 + 8𝑏 + 7 = 42

2. 𝑚2 − 7𝑚− 13 = −10

Solving Quadratic Equations with Square Roots Solve each equation by taking square roots.

https://www.khanacademy.org/math/algebra/quadratics/quadratics-square-root/v/solving-quadraticequations-by-square-roots

1. 𝑎2 = 4

2. 𝑘2 = 16

3. −2𝑛2 = −162

4. 𝑚2 + 7 = 88

5. 2𝑚2 + 10 = 210

6. 𝑥2 + 8 = 28

7. 𝑘2 = 76

8. 16𝑛2 = 49

9. 𝑛2 + 8 = 80

10. 10𝑛2 + 2 = 292

Graphing Quadratic Functions Sketch the graph of each function.

https://www.khanacademy.org/math/algebra/quadratics/graphing-quadraticfunctions/v/graphing-a-quadratic-function

1. 𝑓(𝑥) = 14𝑥 + 2

2. 𝑓(𝑥) = −13𝑥 + 3

3. 𝑓(𝑥) = −6𝑥 + 3

4. 𝑓(𝑥) = 𝑥2 − 2𝑥 + 3

5. 𝑓(𝑥) = −𝑥2 + 2𝑥 + 1

Using the Pythagorean Theorem Find the missing side of each triangle. Round your answers to the nearest tenth if

necessary. https://www.khanacademy.org/math/basic-geo/basic-geometry-pythagorean-theorem/geo-pythagorean-theorem/v/the-pythagorean-theorem

Special Right Triangles Find the missing side lengths. Leave your answers as radicals in simplest

form. https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/v/45-45-90-triangles

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/v/30-60-90-triangle-side-ratios-proof

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/v/30-60-90-triangle-side-ratios-proof

Inverse Trigonometric Ratios Find each measure to the nearest degree.

https://www.khanacademy.org/math/precalculus/trig-equations-and-identities-precalc/inverse-trig-functions-precalc/v/inverse-trig-functions-arccos

https://www.khanacademy.org/math/precalculus/trig-equations-and-identities-precalc/inverse-trig-functions-precalc/v/inverse-trig-functions-arcsin

https://www.khanacademy.org/math/precalculus/trig-equations-and-identities-precalc/inverse-trig-functions-precalc/v/inverse-trig-functions-arctan

1. sin𝐵 = 0.4848 2. cos𝐴 = 0.7431 3. tan𝑊 = 19.0811

Find the measure of the indicated angle to the nearest degree.

4.

5.

6.

Solve Right Triangles List all side lengths and angle measurements for each triangle.

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-a-side/v/example-trig-to-solve-the-sides-and-angles-of-a-right-triangle

Word Problems

1. PCTI is selling tickets to a spring musical, In the Heights. On the first day of ticket sales the school sold 27 regular priced tickets and 15 senior tickets for a total of $360. The school took in $420 on the second day by selling 30 regular tickets and 20 senior citizen tickets. What is the price each of one senior citizen ticket and one child ticket?

2. In 2015 PCTI won the Football State Championship at Metlife Stadium. As a prize

for winning, Metlife has agreed to allow PCTI to play a flag football game at the stadium. The team will be given a rectangular piece of the field with an area of 320 yards. The length is two more than three times the width. Find the dimensions of the field.

3. PCTI’s is installing a banner on the top of the scoreboard in the gym honoring the 2017 Cheerleader’s Division State Championship. The banner will be 50 ft high. In order for the ladder to support the person hanging the banner, the ladder must be at a 40° angle of elevation.

a. Draw a sketch of the scenario. b. How long is the ladder? c. How far is the base of the ladder from the wall.