Name:____________________________________________
Teaneck Public Schools
Summer Assignment
TEAMS 10 - Algebra II Trig Honors
Below are the directions and policies for the summer packet
This is a summer packet for students entering into Algebra II/H Algebra II with Trig course. This packet
is due on the first day of school.
The summer assignment is due the first day of class. On the first day of class, teachers will collect summer
assignments. Any student who does not have the assignment will be given one by the teacher. Late projects
will lose 10 points each day.
This summer assignment will be graded on completion. Completion is defined as having all work shown in
the space provided to receive full credit, and a parent/guardian signature. A preliminary assessment
(administered during the first week of school) will be based on the topics covered in this packet.
Any student who registers as a new attendee of Teaneck High School after August 15
th
will have an extra week
to complete the summer assignment.
Summer assignment packets will be available on the district web site and available in the THS guidance office.
The list below contains topics covered in Algebra I that students are expected to know upon entering
Algebra II. Each section contains 3 steps: Step 1 allows students to review the mathematical concept with
Khan Academy and/or Desmos, Step 2 shows how the concepts are used in problems with detailed
solutions, and Step 3 provide opportunities for students to try the problems on their own.
Check (✓) as you complete each section:
Part 1: Solving Systems of Linear Equations
______1.1. Solving Systems of Linear Equation by Graphing
______1.2. Solving Systems of Linear Equations by Substitution
______1.3. Solving Systems of Linear Equations by Elimination
______1.4. NJSLA Questions
Part 2: Solving Quadratic Equation
______2.1. Solving Quadratic Equations by Graphing
______2.2. Solving Quadratic Equations by Using Square Roots
______2.3. Solving Quadratic Equations by Completing the Square
______2.4. Solving Quadratic Equations by Using the Quadratic Formula
Part 3: Putting it all together…
______3.1. Solving Nonlinear Systems of Equations
______3.2. NJSLA Questions
Part 1: Solving Systems of Linear Equations
1.1. Solving Systems of Linear Equation by Graphing
Step 1: Watch this video: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-
systems-graphically/v/solving-linear-systems-by-graphing
Then, go to student.desmos.com and type in Q N J U W Z and complete the task.
Step 2: Review the solved examples
Example 1) Solve the system of linear equations by graphing:
𝑦 = −𝑥 + 5 𝑦 = 2𝑥 − 1
Example 2) Solve the system of linear equations by graphing:
2𝑥 + 𝑦 = 5 3𝑥 − 2𝑦 = 4
Step 3: Solve the system of equations by graphing.
1.
3 5 2
2
xy
y
2.
4 10
2 3 5
xy
xy
3.
3
2
1
2
3
5
yx
yx
4.
3 3 3
5 2 1
xy
xy
5. For each rectangle below, write a linear equation that represents the area y of the rectangle. Solve this system of two
linear equations by graphing. Interpret your solution.
1.2. Solving Systems of Linear Equations by Substitution
Step 1: Watch the video: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-
systems-with-substitution/v/the-substitution-method
Step 2: Review the solved examples
Example 1) Solve the following equations by substitution
Example 2) Solve the system of equations by substitution
2𝑥 − 𝑦 = 2 2𝑥 + 𝑦 = 6
Step 3: Solve the systems of equations by substitution.
1.
2 2 4
12 3
xy
yx
2.
5 5 10
3 7 4
xy
xy
3.
4
2 3 3
xy
xy
4. Write an equation that represents the sum of the angle measures of the parallelogram and use your
equations and the equation shown to find the values of x and y.
Step 3. Solve the systems of equations by elimination.
1.
45
39
xy
xy
2.
2 7 5
10
xy
xy
3.
10 3 30
15 8 45
xy
xy
4.
7 6 9
5 2 19
xy
xy
5. You are ordering T-shirts for Teaneck HS. The table shows the order for 45 students.
a. How many students ordered medium and large shirts?
b. The number of students who ordered a medium T-shirt was two less than the number of students who
ordered a large T-shirt. Write a system of linear equations that represents the number of students who
ordered medium and large T-shirts.
c. Solve the system of linear equations by elimination.
d. You are ordering 10 additional medium and large T-shirts for new members who might join the school.
Based on your answers in part c, how many of each size would you order? Explain.
Small
Medium
Large
11
x
y
1.4. NJSLA Questions
Make sure to show all work!
Answer:
Answer:
Part 2: Solving Quadratic Equation
2.1. Solving Quadratic Equations by Graphing
Step 1. Watch the video: https://www.khanacademy.org/math/algebra2/advanced-functions/systems-of-quadratic-
equations/v/non-linear-systems-of-equations-1
Then, go to student.desmos.com and type in X N 6 X 5 A and complete the task.
Step 2. Review the solved examples.
Step 3. Solve the quadratic equations by graphing. Feel free to utilize Desmos calculator!
1.
2
3 6 0xx
2.
2
8 15xx
3.
2
98xx
4.
2
23xx
5. The height h (in feet) of a ball in a baseball game can be modeled by
2
16 28 8,h t t
where t is the
time (in seconds).
a. Do both t-intercepts of the graph of the function have meaning in this situation? Explain.
b. No one caught the ball. After how many seconds did the ball hit the ground?
Step 3. Solve the equations using square roots.
1.
2
8 10x
2.
2
25 25x
3.
2
29x
4.
2
2 10 0x
Determine the number of real solutions of the equation. Then, solve the equation using square roots.
5.
2
36x
6.
2
16x
7.
2
0x
8. A can of juice has a height of 10 inches and a volume of
160 cubic inches.
The volume of a can with radius r is
given by the formula
2
.V r h
a. Write an equation describing this situation, where r is the radius of the can.
b. Find the radius of the can.
2.3. Solving Quadratic Equations by Completing the Square
Step 1. Watch the video: https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-by-completing-
the-square/v/solving-quadratic-equations-by-completing-the-square
Step 2. Review the solved examples: https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-
by-completing-the-square/e/completing_the_square_in_quadratic_expressions
Step 3. Solve the equations by completing the square.
1.
2
6 18 0xx
2.
2
2 15 0xx
3.
2
4 16 19 17xx
4.
2
2 16 20 0xx
5.
2
37xx
6.
2
15 12xx
7. The product of two consecutive odd integers that are positive is 323.
a. Write an equation to find the integers.
b. Find the two integers.
Step 3. Solve the equations by using the quadratic formula.
1.
2
5 14 0xx
2.
2
3 2 1 0xx
3.
2
5 9 3xx
4.
2
3 2 6xx
5.
2
7 21xx
6.
2
5 4 10xx
7. Consider the equation
2
3 5 6 0.xx
a. Use the discriminant to determine the number of solutions. (Discriminant review:
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-
formula/a/discriminant-review)
b. Change the sign of c in the equation. Write the new equation:________________________________________
c. Use the discriminant to determine the number of solutions of the new equation. Did your answer change? Explain.
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
Step 3.
#1-2. Solve each system by graphing.
1.
2
2 3 1
1
y x x
yx
2.
2
1
2
23
1
y x x
yx
#3-6. Solve each system by substitution.
3.
2
4
34
yx
y x x
4.
2
3
37
yx
yx
5.
2
6
9
yx
yx
6.
2
3
3
yx
y
#7-10. Solve each system by elimination.
7.
2
4 8 8
84
y x x
yx
8.
2
26
2
y x x
yx
9.
2
22
26
y x x
yx
10.
2
47
11
y x x
yx
11. The graphs of
2
1.6 2 0.6f x x x
and
2
2.5 2 4.2g x x x
do not intersect. Change the value(s) of c
in one or both functions of f and g until the two graphs do intersect. Write your new system of equations and determine
the intersection point(s), rounding to the nearest hundredth, if necessary.
3.2. NJSLA Questions
Make sure to show all work!
