Welcome to your Math 1 EOC A
1.
Which expression is equivalent to \((x + 3)(5x - 5)\)?
3.
Which system of equations can be used to determine the number of dimes, \(d\), and nickels, \(n\), Lisa has in her purse if the following is true:
Lisa has a total of 45 coins in her purse. The coins are either dimes or nickels. The total value of the coins is \($3.05\).
4.
A truck's fuel tank holds \(23\) gallons of gasoline when full. The function \(f(x) = -0.075x + 23\) models how many gallons of gasoline is left in the fuel tank after driving \(x\) miles.
6.
A truck's fuel tank holds \(23\) gallons of gasoline when full. The function \(f(x) = -0.075x + 23\) models how many gallons of gasoline is left in the fuel tank after driving \(x\) miles.
8.
A dance team started with 14 members. Each month, the dance team added two members. Which function can be used to determine the number of members \(x\) months after the club began?
9.
Which equation represents the line that is perpendicular to the graph of \(3x + 6y = 10\) and passes through the point \((-3, 5)\)?
10.
Does the following system of equations have 1 solution, no solutions, or infinitely many solutions?
\(2x - 3y = 15\)
11.
A dance team started with 3 members. Each month, each member brought one new member. Which function can be used to determine the number of members \(x\) months after the club began?
12.
Does the following system of equations have 1 solution, no solutions, or infinitely many solutions?
\(3x - 2y = -14\)
14.
Does the following system of equations have 1 solution, no solutions, or infinitely many solutions?
\(4x - y = 1\)
17.
A clothing store company uses the formula \(T = 29s + 41p\) to determine the total cost to purchase \(s\) shirts and \(p\) pants. Which formula can be used to determine the number of pants purchased given the total cost, \(T\), and the number of shirts purchased?
19.
Which choice is the graph of \(y = (3 - x)(x + 4)\)?
Each graph has a scale of 1 for the x and y coordinates.
21.
Sand is being pumped into a 7 foot tall rectangular prism-shaped object at a constant rate.
The depth of the sand is increasing linearly. At 2:30 p.m., the sand depth was 2.3 feet deep. It is now 6:00 p.m., and the sand depth is 4.05 feet deep. What will the depth of the sand be at 8:00 p.m.?
22.
A statistician collected the following data points to explore the relationship between \(x\) and \(y\).
\((x, y)\)
Based on the residual plot, the statistician decided to exclude one data point. The statistician then performed linear regression on the set of remaining data points. The result was that the new linear model fit the remaining data more closely than the original model fit the original data. Which data point did the statistician exclude?
23.
A set of 11 data points are shown below
{8, 24, 10, 12, 20, 15, 14, 13, 13, 8, 9} Which statement is true if the last data point (the 9) is removed from the data set?
25.
The function \(g(x) = 3n^2 - 2\) represents the value of the \(n\)th term in a sequence.
What is the square of the sum of the 1st and the 2nd terms in the sequence?
26.
Two functions are shown below.
27.
In which graph does the shaded region represent the solution set for the inequality shown below?
28.
Two functions are shown below.
29.
Peter owns a company.
\(x\) represents the number of units his company sales in one week. \(y\) represents the profit for one week's sales after paying the weekly software fee of $125. The above statement is modeled by the equation: \(y = 500x - 125\) Peter knows that even after profiting \(y\) dollars for selling \(x\) units, he still has 2 additional expenses: His company pays 3 employees who each work 40 hours per week and make $15.00 per hour. His company pays $200 each week for advertising.
30.
Laura has a savings account. Some of the money she saves each month goes into a college fund.
\(x\) represents Laura's monthly savings and \(y\) represents the portion of her savings that goes toward her college fund. Each month, Laura's monthly savings is at least 500 dollars, and at most 800 dollars. Laura will put at most 20 dollars more than \(1 \over 2\) of her monthly savings into her college fund. Laura will put at least 10 dollars more than \(1 \over 3\) of her monthly savings into her college fund. Which system of inequalities represents these constraints?
31.
There are two different gyms located in a town, Gym A and Gym B. Jane is trying to choose which gym is the best deal.
In addition to standard machines and exercise equipment, Gym A and Gym B offer group workout classes that are one hour long. Gym A charges a membership fee of \$8.50 per month plus an extra $5.50 per class. Gym B charges only \$1.00 for its monthly membership fee plus $8.00 per class. Jane will spend most of her time during the month on the standard machines and exercise equipment. Jane will spend no more than 3 hours in extra classes for any month Which statement is true?
32.
There are two different gyms located in a town, Gym A and Gym B. Jane is trying to choose a gym.
In addition to standard machines and exercise equipment, Gym A and Gym B offer group workout classes that are one hour long. Gym A charges a membership fee of \$8.50 per month plus an extra $5.50 per class. Gym B charges only \$1.00 for its monthly membership fee plus $8.00 per class. Jane knows that she wants to take the hour-long extra class 5 times per month. Jane adds up the total cost for the whole year for each gym and decides to choose the more expensive option because the exercise equipment looked newer. The staff also seemed friendlier. How much more will Jane pay
annually for the more expensive gym than the less expensive gym?
33.
The perimeter of \( \triangle DEF\) is 64 units.
34.
What are the solutions to the equation \(7x^2 - 49x + 58 = 184\)?
35.
Every 10 years, the Census counts how many people are living in every town in the United States.
The 2020 census showed that 3,000 people were living in Smallville and 8,000 people were living in Largeville. The population of Smallville is predicted to double every 10 years. The population of Largeville is predicted to increase by 2,000 people every 10 years. If the predictions are true, what will be the first census year that will show Smallville with a larger population than Largeville? (
please type the 4 digit year in the space below )
36.
The table below describes the time, in hours, spent working on a new road and the distance, in miles of the finished road.
Time Distance 75 0.5 110 1.75 166 3.75 264 7.25 278 7.75
37.
What is the midpoint of the longest side of the triangle with vertices \((2, 2)\), \((5, 2)\), and \((5, 7)\)?
38.
The vertices of a square are located at \((0, -2)\), \((-2, 4)\), \((2, 2)\), and \((-4, 0)\). What is the area of the square?
39.
Which choice could be modeled by a linear function?
40.
A company records its gross profit, \(y\), (thousands) over a long period of time, \(x\), (months) on a graph.
41.
The table below shows the average weight, \(y\), (in pounds) of a widget at different decades of its life, \(x\), (in years since birth).
Years Weight 10 40.2 20 45.3 30 47 40 51.4 50 55.2 60 57 70 60.9 80 70.1
What is the meaning of the slope of the linear best-fit equation for the data?
42.
See the data set below, of which \(x\) is a constant.
43.
Sam has 7 tests this semester and has already taken 6 of them.
Sam's test scores so far are 85, 86, 95, 99, 79, and 92. What score does Sam needs on his 7th test in order for his test average to be exactly 90?
44.
There is a right triangle and a rectangle.
The shorter leg of the right triangle is \(2x\) units long. The longer leg of the right triangle is 4 more than the length of the shorter leg. The width of the rectangle is twice the length of the triangle's shorter leg. The length of the rectangle is 4 more than the length of its width Which function, \(f(d)\), represents the difference between the rectangle's area and the triangle's area?
45.
The table below shows the number of employees, \(x\), of 7 businesses and describes each company's daily profit, \(y\).
Company Number of Daily Company A 5 520 Company B 10 900 Company C 15 1,350 Company D 20 2,105 Company E 25 2,000 Company F 30 2,755 Company G 35 4,000
How does Company F's actual profit compare to the profit predicted using the linear best-fit model for companies that have 30 employees?
46.
Choose the correct equation for the line that passes through the point \((5, -3)\) and is perpendicular to the graph of \(y = -{1 \over 2}x + 8\).
47.
A researcher wants to learn more about oak trees. The researcher gathers 10 pieces of data describing the relationship between the oak tree's years alive, \(x\), and its height, \(y\).
The researcher analyzed the data from these 10 different trees by graphing the points and calculating the correlation coefficient, \(r\). The researcher finds there is a strong linear relationship between the years alive and height. Which of the following could be the correlation coefficient between \(x\) and \(y\)?
49.
A teacher has 10 students in class. The grades on a test are shown in the table below. Student G usually studies for tests, so the teacher checked the paper again and noticed a grading mistake.
Student Grade A 100 B 90 C 95 D 86 E 76 F 92 G 18 H 97 I 83 J 68
Which statement is true if the teacher removes Student G's outlier grade of 18 from the data set?
50.
Which situation cannot be modeled by a linear function?
51.
What is the distance between the \(y\)-intercept of the function \(f(x) = 4x^2 - 4x + 3\) and the \(y\)-intercept of the linear function \(g\) represented by the table below?
x g(x) -8 -70 -5 -46 3 18 5 34
52.
The table below shows the relationship between the length, \(x\), and the weight, \(y\), of a widget.
Length (cm) Weight (kg) 1.3 50.1 2.5 95.7 4.1 148.7 7.68 296.36 8.22 302.8 10.4 401.7 11.3 425.3 15.79 480.5 16.8 526.6
Using a linear best fit model for the data, what is the predicted weight of a widget that is 20 cm long?
53.
Consider the data set below.
54.
The perimeter of a rectangle is 50.
Let \(y\) = the width of the rectangle Let \(z\) = the area of the rectangle Which equation can be used to find the area of the rectangle?
