System of Equations
Inequalities
Property names
Quadratic
Foil
Data Sets
100
2x+3y=9
x=2y+1
(3,1) or x=3 y=1
100
4x+7 > 2x+15
x>4
100
6y^3/2y^1=3y^2
Quotient of Powers and 3y^2
100
What is the standard form layout of any quadratic equation?
ax^2+bx+c
100
(x+5) (x+2)
x^2+7x+10
100
A city hospital tracked how many patients visited its ER over 9 days. Using the data below, write out the five number summary and make a box and whisker plot.
4, 16, 24, 21, 7, 22, 8, 9, 14
Minimum: 4 Maximum: 24 Q1 : 8.5 Median : 14 Q3 : 23
200
5x+2y=16
3x+2y=8
(4,-2) or x=4 y=-2
200
6x-3 < 3x-18
x<-5
200
(x^2)^2=x^4
Power of a Power and x^4
200
When completing the square for 2x^2 + 12x = 4, what is the first step you must take to address the leading coefficient?
divide by 2
200
(x+3) (x-8)
x^2-5x-24
200
.One soccer team logged the number of games they won over the course of 13 seasons. Using the data below, write out the five number summary and make a box and whisker plot.
10, 21, 14, 19, 4, 23, 9, 13, 20, 11, 16, 1, 24
Minimum: 1 Maximum: 24 Q1 : 6.5 Median : 14 Q3 :19.5
300
10x-7y=42
5x+3y=11
(2.1,-3) x=2.1 y=3
300
2x+9 ≥ 7x-16
x ≤ 5
300
(3x10^4)x(2x10^5)
Power of a Product and 6x10^9
300
What are the factored form and the roots of the equation x^2 - 5x - 6 = 0?
The factored form is (x - 6)(x + 1) = 0, and the roots are x = 6 and x = -1
300
(-5x+7) (2x+3)
10x^2-x+21
300
A football team took data on the amount of shots they made throughout the 10 games they played. Using the data below, write out the five number summary and make a box and whisker plot.
5, 4, 3, 2, 1, 8, 15, 16, 17, 18
Minimum: 1 Maximum: 18 Q1: 3 Median:6.5 Q3:16
400
x + y = 10
x - y = 4
(7,3) or x=7 y=3
400
5x+1 ≤ 3x-17
x ≤ -9
400
5^2 * 6^2
Product of Powers and 30^2=900
400
What are the coordinates of the vertex for the parabola defined by y = x^2 - 6x + 11, and is it a maximum or a minimum?
The vertex is at (3, 2), and it is a minimum because the coefficient of x^2 is positive.
400
(-8x+25) (3x+5)
24x^2+35x+125
400
The bakery took data on how many cakes they make in 14 days. Using the data below, write out the five number summary and make a box and whisker plot.
12, 13, 14, 12, 18, 20, 8, 7, 6, 19, 1, 5, 16, 11
Minimum: 1 Maximum: 20 Q1: 9.5
Median: 12 Q3: 23
500
y = 2x
x + y = 9
(3,6) or x=3 y=6
500
2x+8 ≥ 4x+32
x ≤ -4
500
4x^3/2x
Quotient of Powers and 2x^2
500
Use the quadratic formula to find the exact solutions for 2x^2 + 5x - 3 = .
The solutions are x = 0.5 and x = -3.
500
(-9x+5) (67x-41)
603x^2+704x-205
500
Nick collected data on how many gifts he gets for his birthday up to his 9th birthday. Using the data below, write out the five number summary and make a box and whisker plot.
6, 5, 9, 10, 16, 12, 8, 6, 7
Minimum: 5 Maximum: 16 Q1: 6
Median:8 Q3: 16
600
A farmer counts a total of 46 legs among the chickens and cows in his yard. He notices that he has 3 more cows than chickens. How many chickens and how many cows are in the yard?
4 chickens and 6 cows
600
You have $100 to spend on a birthday party. The venue costs $40 to rent, and each guest’s meal costs $15. How many guests can you afford to invite?
Inequality: 100≥40+15x
Answer: 4≥x
600
A tech lab is studying a new strain of bacteria. The bacteria double every hour. If there are 2^3 bacteria at noon, and this population multiplies by 2^4 by 4:00 PM, write an expression for the total number of bacteria. How many bacteria are there?
Product of Powers and 2^7 =128 bacteria
600
A toy rocket is launched vertically upward from the top of a 10-meter platform. Its height h(in meters) after t seconds is modeled below: h(t)=-5t^2+15t+10
21.25 meters after 1.5 seconds.
600
A movie theater is installing a new rectangular screen. The height of the screen is (x + 3) feet and the width is (x + 4) feet. Write an expression in standard form to represent the total area of the screen.
(x^2 + 7x + 12) square feet
600
What's the Mode? 
7 and 9
700
A local theater sold a total of 150 tickets for a play. Student tickets cost $5 each, and adult tickets cost $8 each. If the theater made a total of $930 in ticket sales, how many of each type of ticket were sold?
60 adult tickets, 90 student tickets
700
You need to earn at least $450 this week. You get paid a base salary of $150, plus $20 for every lawn you mow. How many lawns do you need to mow?
Inequality: 450≤150+20x
Answer: 15≤x
700
Adeola is having a birthday party. She needs to buy 5x^8 cupcakes for all of her guests but 5x^3 are spoiled. How many cupcakes are still good?
5x^8-5x^3 - Subtraction of Polynomials
700
Convert the quadratic equation y = x^2 + 8x + 10 into vertex form by completing the square.
y=(x+4)^2 -6
700
A community garden coordinator designs a new rectangular vegetable plot. The width of the plot is represented by the expression (x + 4) meters. The length of the plot is 3 meters longer than twice the variable value, represented by (2x + 3) meters. Write an expression in standard polynomial form that represents the total area of the garden plot.
(2x^2 + 11x + 12)
700
whats the median?
15
800
A piggy bank contains 30 coins, consisting only of nickels and quarters. The total value of the coins is $4.10. How many nickels and quarters are in the bank?
17 nickels, 13 quarters
800
An elevator has a maximum weight capacity of 2,000 pounds. A delivery driver who weighs 180 pounds is loading identical 45 pound boxes into the elevator. What is the maximum number of boxes the driver can safely take up at one time?
Inequality: 2,000 ≥ 180+45x
Answer: 40≥ x
800
The distance from Earth to the Sun is around 10^12 kilometers. The distance from Earth to the Moon is about 10^5 kilometers. How many times further is the Sun than the moon?
10^7 - Quotient of Powers
800
A firework is launched up into the air. Its height h (in feet) over time t (in seconds) is modeled by the equation: 16t^2 +64t+5. How many seconds would it take for the firework to reach its maximum height.
The firework reaches its maximum height of 69ft in 2 seconds.
800
A rectangular community pool is undergoing a renovation. The pool's length is currently represented by the expression (2x + 5) meters, and its width is represented by (x - 3) meters.
(2x^2 - x - 15) square meters.
800
What's the maximum?
10
900
A quiz has 10 total questions. It is made up of multiple choice questions and true/false questions. There are 4 more multiple-choice questions than true/false questions. How many of each type are there?
7 multiple choice questions, 3 true/false questions
900
Maya wants to buy a laptop that costs $650. She already has $120 saved, and she saves $40 each week from her babysitting job. What is the minimum number of weeks she needs to work to afford the laptop?
Inequality: 650≤120+4x
Answer: 14≤x
900
A computer storage drive holds 2^10 bytes of data per sector. The drive has a total of 2^3 sectors per cluster. If a server contains 2^4 clusters.
(2^10)^3)^4)= 2^17 bytes - Product of Powers
900
A toy rocket is shot upwards. Its height h (in meters) at any time t (in seconds) is shown in the equation: h(t)= -5t^2 +20t+15. Find the maximum height of the rocket and the time it takes to reach that height.
Time t = 2 seconds Maximum height h =35 meters
900
A school club is selling custom t-shirts to raise money. They currently sell (x) t-shirts per week at a price of (x + 12) dollars per shirt. The club decides to change their strategy. They expect that for every 2-dollar decrease in the price of the shirt, they will sell 4 more shirts per week. Write a simplified polynomial expression in standard form that represents the club's total weekly revenue under this new strategy.
(x^2 + 14x + 40) dollars.
900
What is the minimum?
1
1000
Two coffees and one muffin cost $7. One coffee and two muffins cost $8. How much does a coffee cost, and how much does a muffin cost?
7 multiple choice questions, 3 true/false questions
1000
Plan A charges a flat $30 monthly fee plus $0.05 per text message. Plan B charges a flat $10 monthly fee plus $0.13 per text message. For how many text messages is plan A cheaper than Plan B?
Inequality: 30+0.05x<10+0.13x
Answer:250<x
1000
A scientist measures the thickness of a specialized computer microchip. The chip has a thickness of 10^-3 meters. A new experimental coating applied to the chip is even thinner, measuring 10^-6 meters thick. How many times thinner is the experimental coating compared to the microchip?
10^-3/10^-6=10^3 - Negative Exponent
1000
A ball is shot from a cannon into the air at 40 feet per second. Its height h (in feet) over time t (in second) is modeled by the equation shown below: h(t)= 16t^2 + 40t+ 1.5.
The ball hits the ground at about 2.54 seconds.
1000
An artist is designing a rectangular painting that is (2x + 5) inches long and (x + 4) inches wide. She places a uniform wooden frame around it. The total outer dimensions of the framed piece are (2x + 9) inches long and (x + 8) inches wide. Write a simplified polynomial expression that represents only the area of the wooden frame itself.
(2x+9)(x+9) - (2x+5)(x+4) = 14x+61
1000
What's the Interquartile range?
7