Note: This math packet will help any high school student with the necessary math skills needed in any high school math

course, as well as, portions of the LEAP 2025 State Assessment (Algebra I and Geometry) and ACT Math Section.

For additional online resources go to jpschools.org/learnathome

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Monday-Thursday • 8:00 am–8:00 pmFriday • 8:00 am–4:00 pm

Available for families who have questions about either the online learning resources or printed learning packets.

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Book 1

High School MathAlgebra I

Algebra II

Geometry

HIGH SCHOOL DAILY SCHEDULE (PACKET) Time Acvity Details 8:30 Wake up and prepare for the day ● Get dressed

● Eat breakfast 9:00 Morning Physical Acvity ● Take a walk/jog/run

● Try some simple exercises (jumping jacks, pushups, situps, running in place, high knees, kick backs

● Stretch ● Play a sport

9:30 - 10:45

Academic Time: Math

At-home learning packet: Math

10:45 - 12:00

Academic Time: ELA

At-home learning packet: ELA

12:00 Lunch and break ● Eat lunch

● Take a break ○ Video game or TV me ○ Rest

1:00 - 2:15

Academic Time: Social Studies

At-home learning packet: Social Studies

2:15 Break Take a brain break away from a screen. Try to walk around outside for a few minutes, and grab a snack if you need an a�ernoon boost.

2:30 - 3:45

Academic Time: Science

At-home learning packet: Science

Tiempo Actividad Detalles 8:00 Despierta y Prepárate para el día • Vístete

• Desayuna

9:00 Actividades Física Matutina

• Dar un paseo/trotar o correr • Hacer simple ejercicios (saltos de tijeras,

lagartijas, abdominales, correr en el mismo lugar, rodillas altas, Patadas hacia atrás

• Estirarse • Jugar Deportes

9:30-10:45 Tiempo Académico: Matemática

Paquete de aprendizaje en casa: Matemática

10:45-12:00

Tiempo Académico: ELA

Paquete de aprendizaje en casa: ELA

12:00p Almuerzo y Descanso • Comer almuerzo • Tomar un descanso

o Este es tiempo para jugar videos y ver televisión

o Descansar 1:00- 2:15 Tiempo Académico:

Estudios Sociales Paquete de aprendizaje en casa: Estudios Sociales

2:15 Descanso Tomar un descaso cerebral alejándose de la pantalla, caminar afuera por unos minutos, Tomar una merienda si es necesario.

2:30-3:45 Tiempo Académico: Ciencia

Paquete de aprendizaje en casa: Ciencia

Para recursos adicionales en línea, vaya a jpschools.org/learnathome Para familias que necesitan apoyo académico, por favor llamar al 504-349-8999 De lunes a jueves • 8:00 am – 8: 00 pm Viernes • 8:00 am – 4: 00 pm Disponible para familias que tienen preguntas ya sea sobre los recursos de aprendizaje en línea o los paquetes de aprendizaje impresos.

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Content Page

Algebra (I, II, and III)

Polynomials Evaluating Functions Simplifying Radicals Rational Exponents Systems of Linear Equations

Geometry --- Trigonometry

Basic Trigonometry Using basic Trigonometry to find side lengths of a Right

Triangle Law of Sines and Law of Cosines (Trigonometry-PreCalculus

Only)

Probability and Statistics

Conditional Probability Compound Events

Additional Topics

Solving Quadratic Equations by Factoring Linear Equation Word Problems Volume Word Problems

*Helpful Video(s): Khan Academy, ACT, MathLearnZillion, and Fort Bend Tutoring

These videos can be watch from a computer, cell phone and iPad.

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Algebra (I, II and III) Polynomials

Adding and Subtracting Polynomials

Example 1: (3x2+14x – 10) + (4x2 -10x + 4) = ___________

Step One: Combine Like terms (3x2 +4x2) + (14x -10x) + (-10+4)

Step Two: Solve: 7x2 +4x -6

For Subtracting Polynomials Change the Subtraction to plus sign and change all of the terms to the opposite sign, then repeat steps one and two.

Multiplying Polynomials

Here are the steps required for Multiplying Polynomials:

Step 1: Distribute each term of the first polynomial to every term of the second polynomial. Remember that when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents.

Step 2: Combine like terms (if you can).

Dividing Polynomials

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Polynomials

Practice

Add or subtract.

1. (3x3 + 4x2 + 1) + (2x2 + 10) 2. (-4x2 + 3x – 1) – (4x + 2)

3. (-8x3 + 4x – 1) – (4x2 – x) 4. (7x3 + 6x2 + x – 1) + (9x3 + 4x2 – x + 10)

5. (9x5 – 7x3 + x) + (6x4 + 9x3)

Multiplying

6. 3x2 (2x2 + 2x + 1) 7. (x + 1) (x + 10)

8. (x + 2) (x – 2) 9. (x2 + 1) (x2 – 5)

Dividing Polynomials

10. (x2 + 10x + 16) (x + 2) 11. (x3 – 4x2 + 7x – 6) (x – 2)

Problem 12

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Evaluating Functions

Practice

In this example we will evaluate a function for a given value

of x.

Example1: f(x) = 3x2 – 8, find f (-4)

Substitute f(x) = 3x2 - 8

Simplify f(-4) = 3(-4)2 – 8

f(-4) = 3(16) – 8

f(-4) = 48 – 8

f(-4) = 40

Practice

1. If f(x) = - 3x + 8, find f(5) 2. If g(x) = ¾ x + 2, find g (-12)

3. If g(x)= – 10x + 6, find g(0) 4. If g(x) = 4x2 + 6, find g (3)

5. If g(x)= 3x+4, find g (-4) 6. If g(x) = -√2𝑥𝑥 + 4 , find g (30)

Problem 7

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Simplifying Radicals

Practice problems

1. √𝟕𝟕𝟕𝟕 2. √𝟐𝟐𝟐𝟐

3. √𝟕𝟕𝟐𝟐 4. 𝟑𝟑√𝟖𝟖

5. 𝟕𝟕√𝟑𝟑𝟐𝟐

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Rational Exponents

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Systems of Linear Equations

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Geometry and Trigonometry

Basic Trigonometry: Sine, Cosine, and Tangent

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Practice

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Law of Sines and Law of Cosines (Trigonometry Only)

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1. Find the missing dimensions of the triangle

below. Round your answers to the nearest

whole number.

2. Find the missing dimensions of the triangle

below. Round your answers to the nearest

whole number.

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Probability and Statistics

The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This probability is written P(B|A), notation for the probability of B given A. In the case where events A and B are independent (where event A has no effect on the probability of event B), the conditional probability of event B given event A is simply the probability of event B, that is P(B).

If events A and B are not independent, then the probability of the intersection of A and B (the probability that both events occur) is defined by P(A and B) = P(A)P(B|A).

From this definition, the conditional probability P(B|A) is easily obtained by dividing by P(A):

Example

In a card game, suppose a player needs to draw two cards of the same suit in order to win. Of the 52 cards, there are 13 cards in each suit. Suppose first the player draws a heart. Now the player wishes to draw a second heart. Since one heart has already been chosen, there are now 12 hearts remaining in a deck of 51 cards. So the conditional probability P (Draw second heart|First card a heart) Answer = 12/51.

Suppose an individual applying to a college determines that he has an 80% chance of being accepted, and he knows that dormitory housing will only be provided for 60% of all of the accepted students. The chance of the student being accepted and receiving dormitory housing is defined by P(Accepted and Dormitory Housing) = P(Dormitory Housing|Accepted)P(Accepted) = (0.60)*(0.80) = Answer: 0.48.

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Conditional Probability

Practice

1. A bag contains five green gumdrops and six red gumdrops. If Kim pulls a

green gumdrop out of the bag and eats it, what is the probability that the next gumdrop she pulls out will be red? a)

b)

c)

d)

2 Gabriella has 20 quarters, 15 dimes, 7 nickels, and 8 pennies in a jar. After taking 6 quarters out of the jar, what will be the probability of Gabriella randomly selecting a quarter from the coins left in the jar? a)

b)

c)

d)

3. A fast-food restaurant analyzes data to better serve its customers. After its

analysis, it discovers that the events D, that a customer uses the drive-thru, and F, that a customer orders French fries, are independent. The following data are given in a report:

Given this information, is a) 0.344 b) 0.3648 c) 0.57 d) 0.8

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4. Consider the probability statements regarding events A and B below.

; ; and What is ? a) 0.1 b) 0.25 c) 0.375 d) 0.667

5. Suppose events A and B are independent and is 0.2. Which statement could be true?

a) b) c) d)

Compound Events A compound event is one in which there is more than one possible outcome.

Determining the probability of a compound event involves finding the sum of the probabilities of the individual events and, if necessary, removing any overlapping probabilities.

Probability is the likelihood that an event will occur. It is written as a fraction with the

number of favorable outcomes as the numerator and the total number of outcomes as the denominator. Favorable just means that a particular outcome is what you are curious about, not that it is necessarily positive.

Probability can be used to determine many things, from the likelihood that you will

win the jackpot in the lottery to the likelihood that a baby will be born with a certain birth defect and anything in between. Probability is used extensively in the sciences, investing, weather reporting and many other areas

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Multiple Choice Choose the correct answer 1 Selena and Tracey play on a softball team. Selena has 8 hits out of 20 times at

bat, and Tracey has 6 hits out of 16 times at bat. Based on their past performance, what is the probability that both girls will get a hit next time at bat? a) 1 b)

c)

d)

2 The probability that the Cubs win their first game is . The probability that the

Cubs win their second game is . What is the probability that the Cubs win

both games? a)

b)

c)

d)

3 The probability that Jinelle’s bus is on time is , and the probability that Mr.

Corey is driving the bus is . What is the probability that on any given day

Janelle’s bus is on time and Mr. Corey is the driver? a)

b)

c)

d)

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4 The probability it will rain tomorrow is . The probability that our team will win

tomorrow’s basketball game is . Which expression represents the probability

that it will rain and that our team will not win the game? a)

b)

c)

d)

5. .Keisha is playing a game using a wheel divided into eight equal sectors, as shown

in the diagram below. Each time the spinner lands on orange, she will win a prize.

If Keisha spins this wheel twice, what is the probability she will win a prize on both spins? a)

b)

c)

d)

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Challenge Problem

Brianna is using the two spinners shown below to play her new board game. She spins the arrow on each spinner once. Brianna uses the first spinner to determine how many spaces to move. She uses the second spinner to determine whether her move from the first spinner will be forward or backward.

Find the probability that Brianna will move fewer than four spaces and backward.

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Solving Quadratic Equations by Factoring

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II. Practice solving quadratics by factoring

1. X2+5x+6 = 0 2. X2-x-12= 0

3. a2-9a+18= 0 4. T2-2t -19 = 5

5. 2x2+6x+4 = 0 6. h2 – 7 = 9

7. 3x3+ 21x2+36x = 0

Challenge Problem

Problem 8

Find the dimensions of the rectangle below.

Problem 9

Find the dimensions of the rectangle below.

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Linear Equation Word Problems

I. Model Problems

A linear model is a linear equation that represents a real-world

scenario. You can write the equation for a linear model in the same way

you would write the slope-intercept equation of a line. The y-intercept

of a linear model is the quantity that does not depend on x. The slope is

the quantity that changes at a constant rate as x changes. The change

must be at a constant rate in order for the equation to be a linear model.

Example 1: A machine salesperson earns a base salary of $40,000 plus

a commission of $300 for every machine he sells. Write an equation

that shows the total amount of income the salesperson earns, if he sells

x machines in a year.

The y-intercept is $40,000; the salesperson earns a $40,000 salary in a

year and that amount does not depend on x.

The slope is $300 because the salesperson’s income increases by $300

for each machine he sells.

Answer: The linear model representing the salesperson’s total income

is y = $300x + $40,000.

Linear models can be used to solve problems.

Example 2: The linear model that shows the total income for the

salesperson in example 1 is y = 300x + 40,000. (a) What would be the

salesperson’s income if he sold 150 machines? (b) How many

machines would the salesperson need to sell to earn a $100,000

income?

(a) If the salesperson were to sell 150 machines, let x = 150 in the linear

model; 300(150) + 40,000 = 85,000.

Answer: His income would be $85,000.

(b) To find the number of machines he needs to sell to earn a $100,000

income, let y = 100,000 and solve for x:

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y = 300x + 40,000 Write the linear model. 100,000 = 300x + 40,000 Substitute y = 100,000. 60,000 = 300x Subtract. x = 200 Divide. Answer: To earn a $100,000 income the salesperson would need to sell 200 machines. You can also use the standard form to write a linear model. Use this form if you are analyzing two quantities that increase at different rates. Example 3: At a school play, children’s tickets cost $3 each and adult tickets cost $7 each. The total amount of money earned from ticket sales equals $210. Write a linear model that relates the number of children’s tickets sold to the number of adult tickets sold. Let x = the number of children’s tickets sold and y = the number of adult tickets sold The amount of money earned from children’s tickets is 3x. The amount of money earned from adult tickets is 7y. The total amount of money earned from ticket sales is 3x + 7y, which is equal to $210. Answer: 3x + 7y = 210. Example 4: In the ticket sales example above, how many children’s tickets were sold if 24 adult tickets were sold? If 24 adult tickets were sold, y = 24. Substitute y = 24 into the linear model above: 3x + 7y = 210 Write the linear model. 3x + 7(24) = 210 Substitute y = 24. 3x + 168 = 210 Simplify. 3x = 42 Subtract. x = 14 Divide. Answer: 14 children’s tickets were sold.

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II. Practice

Solve.

1. Lin is tracking the progress of her plant’s growth. Today the plant is

5 cm high. The plant grows 1.5 cm per day.

a. Write a linear model that represents the height of the plant after d

days.

b. What will the height of the plant be after 20 days?

2. Mr. Thompson is on a diet. He currently weighs 260 pounds. He

loses 4 pounds per month.

a. Write a linear model that represents Mr. Thompson’s weight after

m months.

b. After how many months will Mr. Thompson reach his goal

weight of 220 pounds?

3. Paul opens a savings account with $350. He saves $150 per month.

Assume that he does not withdraw money or make any additional

deposits.

a. Write a linear model that represents the total amount of money

Paul deposits into his account after m months.

b. After how many months will Paul have more than $2,000?

4. The population of Bay Village is 35,000 today. Every year the

population of Bay Village increases by 750 people.

a. Write a linear model that represents the population of Bay

Village x years from today.

b. In approximately many years will the population of Bay Village

exceed 50,000 people?

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5. Conner has $25,000 in his bank account. Every month he spends

$1,500. He does not add money to the account.

a. Write a linear model that shows how much money will be in the

account after x months.

b. How much money will Conner have in his account after 8

months?

6. A cell phone plan costs $30 per month for unlimited calling plus

$0.15 per text message.

a. Write a linear model that represents the monthly cost of this cell

phone plan if the user sends t text messages.

b. If you send 200 text messages, how much would you pay

according to this cell phone plan?

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Volume

1. A planned building was going to be 100 feet long,

75 feet deep, and 30 feet high. The owner decides

to increase the volume of the building by 10%

without changing the dimensions of the depth and

the height. What will be the new length of this

building? Chose the correct answer choice

a) 106 ft.

b) 108 ft.

c) 110 ft.

d) 112 ft.

2. The volume of a rectangular pool is 1,080 cubic

meters. Its length, width, and depth are in the ratio

10:4:1. Find the number of meters in each of the

three dimensions of the pool. Answer: __________

3. What is the volume of a can of soup that has a

height of 16 cm and a diameter of 8 cm? Answer: _______

4. In the diagram below, a right circular cone with a radius of 3 inches has a slant height of 5 inches, and a right cylinder with a radius of 4 inches has a height of 6 inches.

Determine and state the number of full cones of water needed to completely fill the cylinder with water

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The Math Portion of the ACT Test (10 Sample Problems)

The battery for the math portion of the ACT test itself consists of 60 questions which are to be answered within a 60-minute time limit. The topics that are covered during this portion of the test include pre-algebra, elementary and intermediate algebra, geometry (including both standard and coordinate geometry) as well as elementary trigonometry. The average student will score around 21 while 22 is generally considered to be a score that indicates a test taker is "ready for college" for most people.

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Problem 4

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Problem 5

Problem 6

Problem 7

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Problem 8

Problem 9

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Problem 10

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High School Math Packet Answer Document

Pg. 4 - 5 1. 3x3 + 6x2 + 11 2. -4x2 - x – 3 3. -8x3 – 4x2 + 5x – 1 4. 16x3 + 10x2 + 9 5. 9x5 + 6x4 + 2x3 + x 6. 6x4 + 6x3 + 3x2 7. x2 + 11x + 10 8. x2 – 4 9. x4 – 4x2 – 5 10. x + 8 11. x2 – 2x + 3 12. The student incorrectly added + x2 and -3x2; the answer should be 3x3 – 2x2 – 9x + 8. 13. The student did not include placeholders between x3 and -8. The dividend should be x3 + 0x2 + 0x – 8

Pg. 6 1. -7 2. -7 3. 6 4. 42 5. 1 6. -8 7. When the student

substituted he failed to use parenthesis which resulted in addition rather than multiplication.

Pg. 7

1. 3√5 2. 2√5 3. 6√2 4.

5.

p. 10 1. 5 2. 100 3. 1,331 4. 3/2 5. 1/1024 6. –1/6 7. 5 8. 1/7 9. 8 10. 0.2

p. 14

p. 16 - 18 1. the hypotenuse: YZ 2. the side opposite of <Z: XY 3. the side adjacent to <Z: XZ 4. the hypotenuse: HU 5. the side opposite of <H: IU 6. the side adjacent to <H: HI Part III

1. (1) 2. (1) 3. (1) Error Analysis

Jen is correct. Since triangle 2 is not aright triangle, you can not apply sine, cosine, tangent to the triangle

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P. 21

1. 49.3

2. 49.3

3. 15.42

4. 25.4 m

5. 64.50 cm

Pg. 23

1.

2.

P. 25 1. d 2. a 3. d 4. b 5. b

Pg.27-29 1. d 2. b 3. b 4. d 5. a Challenge Problem

p. 31

5. x = -2, x = -1 6. h = -4, h = 4 1. x = -4, -3,0 2. 8. 26 inches by 20 inches 3. 13 feet by 18 feet

p. 34-35

1. y = 5 + 1.5d; 35 cm 2. y = 260 – 4m; 10 months 3. y = 350 + 150m; 11 months 4. y = 35,000 + 750x; 20 years 5. y = 25,000 – 1,500x; $13,000 6. y = 30 + 0.15t; $60

P. 36 1. (C) 2.

3. 803.84 cm3 4.

p. 37-41 1. E 6.F

2. J 7. B

3. D 8. H

4. K 9. C

5. D 10. J

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