Free Printable ALG1_Prep

1.

Blair recorded the number of customers who visit her business during a certain time period each week for 4 weeks. She calculates the average rates of change in the number of customers for various weeks.

Arrange the average rates of change in the number of customers from least (left) to greatest (right).

a)

Week 1 to Week 2

b)

Week 1 to Week 4

c)

Week 2 to Week 4

d)

Week 3 to Week 4

1)

2)

3)

4)

2.

A taxi company charges $2.70 per mile and a waiting charge of $0.50 per minute for each trip. Which graph shows the equation that relates a trip involving a distance of 𝑥 miles, and a waiting time of 𝑦 minutes, if the total bill for the trip is $50.00?

a)

b)

c)

d)

3.

Jennifer has a small business mixing and selling essential oils. One product is a mixture of two oils, lavender and peppermint. She asked her assistant, Carmen, to check on two suppliers to determine the costs for her next batch. Carmen contacted the suppliers and got quotes from each for the order. Unfortunately, she misplaced the number of ounces of each oil she needed to purchase. The information she has is:

Supplier A: lavender: $5.80/ounce; peppermint: $4.20/ounce; total cost: $128.40

Supplier B: lavender: $4.50/ounce; peppermint: $5.00/ounce; total cost: $124

Carmen needs to order (a) ounces of lavender and (b) ounces of peppermint.

Choose from the below words

12

14

8

10

4.

Consider the equation shown.

$\frac{1}{4}\left(x+1\right)=3\left(1-x\right)+\frac{1}{2}x$

What value of 𝑥 makes this equation true?

(a)

5.

Which inequality matches the graph?

a)

$y<x+2$

b)

$y>x+2$

c)

$y\le x+2$

d)

$y\ge x+2$

6.

Scientists studied the decay of a radioactive element. The mass of the element reduces by a factor of $\frac{1}{2}$ , after each half-life, as shown in the table. Which equation represents the relationship shown in the table?

a)

$m=20t^{\frac{1}{2}}$

b)

$m=20t^2$

c)

$m=20\left(\frac{1}{2}\right)^t$

d)

$m=\frac{1}{2}\left(20\right)^t$

7.

For this item, select the phrase from the drop-down menu that best completes the sentence.

Arya and Cody each manage a landscaping business. The equation $y=15x+30$ represents the total cost, 𝑦, of 𝑥 hours of landscaping through Arya’s business. The table shows the total cost, 𝑦, of different hours, 𝑥, of landscaping through Cody’s business.

Arya charges (a) than Cody.

Choose from the below words

$10 more per hour

$10 less per hour

$5 less per hour

$5 more per hour

8.

A quadratic function is shown on the graph below. Which statement best describes its domain and range?

a)

The domain is all real numbers and the range is all real numbers.

b)

The domain is all real numbers and the range is all real numbers greater than or equal to 2.

c)

The domain is all real numbers greater than or equal to 3 and the range is all real numbers.

d)

The domain is all real numbers greater than or equal to 3 and the range is all real numbers greater than or equal to 2.

9.

Match each equation with the best description of its solution(s).

a)

$-3x+12-9x+8=-3\left(4x-7\right)$

1.

No solutions.

b)

$-2\left(3x-10\right)+8x=7x+20+7x$

2.

One solution.

c)

$2+4x-10+6x=2\left(5x-4\right)$

3.

Infinite solutions.

10.

Which of the following options describes the domain and range for $f\left(x\right)=2\left(x-5\right)^2+4$ ?

a)

$D:\ x\ge0$

$R:\ y\ge0$

b)

$D:\ -\infty<x<\infty$

$R:\ y\ge4$

c)

$D:\ x\ge4$

$R:\ -\infty<y<\infty$

d)

$D:\ -\infty<x<\infty$

$R:\ -\infty<y<\infty$

11.

A farmer is monitoring the water content of the soil during a dry summer. The water content of the soil is decreasing at a rate of 2.5% per week. If a certain soil sample contains 200 grams of water on July 1st, which equation describes the relationship between y, amount of water in grams, and t, time in weeks after July 1st?

a)

$y=200\left(0.75\right)^t$

b)

$y=200\left(0.975\right)^t$

c)

$y=200-0.025t$

d)

$y=200-0.25t$

12.

Place the correct value to complete the sentence. The value of 𝑥 that satisfies the equation $\frac{2}{3}x+4=\frac{3}{2}\left(x-4\right)$ is (a) .

Choose from the below words

\frac{1}{7}

$12$

\frac{9}{4}

6

13.

Which of the following inequalities is shown in the graph below?

a)

$y-4\le0$

b)

$y+4\ \le0$

c)

$y-4\ge0$

d)

$y+4\ge0$

14.

Select the coordinate pair that best completes the sentence.

A system of equations is shown. The solution to this system of equations is the point (a) .

Choose from the below words

$\left(3,3\right)$

\left(0,-3\right)

\left(3,0\right)

\left(-3,-3\right)

15.

In the graph shown, which of the following values represents the x-value where line $l$ and the line $y=2x-1$ intersect?

a)

-1

b)

0

c)

1

d)

2

ALG1_Prep_May17-21

Total questions: 15

Worksheet time: 4hrs 45mins

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