Writing and Solving Linear Equations & Inequalities
Linear Functions
Systems of Equations
Miscellaneous Math
For Funsies (1 of these for every 3 other questions)
100
Solve for x:
3x-5=16
x=7
100
What is the slope of a line that passes through (2, 5) and (6, 13)?
m = 2
100
Is the point (1, 4) a solution to the system below?
y = 2x + 2
y = −x + 5
Show work for credit!
Yes, (1, 4) is a solution to the system.
100
The data set below shows test scores for 7 students:
72, 85, 90, 85, 78, 92, 85
Find the mean, median, and mode.
Mean ≈ 83.86
Median = 85
Mode = 85
100
This animal has three hearts, nine brains, and blue blood, and is considered one of the most intelligent invertebrates on Earth.
Octopus
200
What is the solution to the inequality:
3(x + 2) − 4 ≥ 2x + 8?
x ≥ 6
200
The point (−2, k) lies on the graph of y = −3x + 1. What is the value of k?
k = 7
200
Solve the system algebraically:
y = 3x − 1
2x + y = 9
Use substitution!
Solution: (2, 5)
200
a) y = 59.22x + 167.70
b) r = 1.00
c) r = 1.00 indicates a very strong positive linear relationship between the number of gym members and monthly revenue.
200
Which planet is known to have the Great Red Spot?
Jupiter
300
Solve algebraically for x:
0.04(x + 5) = 0.20x − 3.4
x=22.5
300
A taxi service charges a flat fee of $3.50 plus $2.25 per mile. Write a function c(m) for the total cost.
Double points: What does the y-intercept tell you in this context?
c(m) = 2.25m + 3.50
The y-intercept of $3.50 represents the flat fee charged before any miles are driven.
300
At a bake sale, cookies cost $1.25 and brownies cost $2.00. Sophie bought 12 items and spent $19.50. Write a system of equations to find how many of each she bought.
c + b = 12
1.25c + 2.00b = 19.50
300
A student says a correlation coefficient of r = −0.91 means the data has a weak relationship because the number is negative. Explain why the student is incorrect, and what r = −0.91 actually indicates.
The sign of r indicates direction, not strength. r = −0.91 indicates a strong negative linear relationship.
300
This is the hardest substance in the human body, making up the outer layer of your teeth.
Enamel
400
A school store sells pens for $0.75 and notebooks for $2.50. Marcus bought twice as many pens as notebooks and spent exactly $20.00.
Write and solve an equation to find how many of each he bought.
0.75(2n) + 2.50n = 20
n = 5 notebooks, 10 pens
400
The table below shows a car's value over time.
What is the average rate of change from year 1 to year 7, and what does it represent in context?
-1800
The car loses an average of $1,800 in value each year between year 1 and year 7.
400
A school store sold notebooks and pens. Notebooks cost $4 each and pens cost $2 each. Students bought 30 items in total and spent $84.
Write a system of equations and use elimination to find how many notebooks and how many pens were sold.
n + p = 30
4n + 2p = 84
n = 12, p = 18
400
The linear regression equation for a data set relating study hours (x) to quiz scores (y) is y = 4.3x + 51.2, with r = 0.87.
State what the slope means in context.
Predict the score for a student who studied 6 hours.
Slope: For each additional hour studied, the predicted quiz score increases by about 4.3 points.
Prediction at x = 6: 77 points
400
What is the largest ocean on Earth?
Pacific Ocean
500
A jar contains nickels, dimes, and quarters. There are three times as many dimes as quarters, and 8 fewer nickels than dimes. The total value is $6.60.
Write and solve an equation to find the number of each coin.
Let x = quarters, dimes = 3x, nickels = 3x − 8
0.25(x) + 0.10(3x) + 0.05(3x − 8) = 6.60
10 quarters, 30 dimes, 22 nickels
500
Write an equation of the line that passes through (−1, 5) and has a slope of −3.
Put your answer in point slope form or slope-intercept form!
y − 5 = −3(x + 1)
or
y = -3x + 2
500
Maya joined a movie club. In March she saw 3 matinees and 2 regular-priced shows and spent $36.00. In April she saw 1 matinee and 4 regular-priced shows and spent $38.00. Prices stayed the same both months.
Write a system of equations to represent the cost m of a matinee and r of a regular show.
3m + 2r = 36
m + 4r = 38
m = 6.80, r = 7.80
500
If
f(x) = (20x² + 4) / (x + 3)
determine the value of
f(1/4)
f(1/4) = 21/13 or 1.62
500
What is the only English word that ends with -mt?
Dreamt