Which of these is equivalent to



Algebra Review First Semester

1. Solve the following equation for x.

[pic]

2. Solve for x.

(x – 5)(x + 4) = (x – 2)(x + 10)

3. Solve for x using any method you prefer. Check your solutions by testing them in the original equation.

a. |12 – 7x| = 26

b. |2(x – 3)| = 14

c. –3|5 – 2x| = –1

4. Solve the following equations for the indicated variable.

a. 5(3x + 7) = 20 – 2(x + 1) for x

b. m(3 – 4m) = 7 + 4(8 – m2) for m

c. 5x(x + 3) = (x)(5x – 3) + 36 for x

5. Write an algebraic equation for each figure below to express the relationship, “Area as a product equals area as a sum.”

a. b.

6. Simplify:

a. [pic] b. [pic]

7. Solve each system of equations below. Show all your work and check your solutions, if possible.

a. [pic] b. [pic]

8. At right is a scatterplot with a least squares regression line

added. Consider the points A, B, C, and D. Which has the

largest residual? Which has the smallest? List the

four points by largest to smallest residual.

9. Examine the graphs below and explain what real-world quantities the slope and y-intercepts represent. Then find the slope and y-intercept for each

10. Consider the following data comparing height and shoe length for a group of students.

[pic]

a. Graph the data on separate graph paper. Be sure to label your axes. Write the equation of a line of best fit.

b. Describe the relationship between a person’s height and shoe size.

11. Determine whether the relation represented is a function. State the domain and range.

1.

c.

b.

d.

12. [pic] 13. [pic]6)[pic]

14. [pic] 15. [pic]

16. Ranger Sarah is responsible for monitoring the population of the elusive Gray’s nightingale in Holly State Park. She would like to find a relationship between the Maile oak trees (their preferred nesting site) and the number of nightingales in the park. She randomly selects 7 different areas in the park and painstakingly counts the Maile oaks and Gray’s nightingales in each area.

[pic]

a) Make a scatterplot on graph paper and describe the association. 

b) Calculate the LSRL and then sketch the line of best fit on your scatterplot. Round to the nearest tenth. 

c) Interpret the slope and y-intercept of your model in context.

d) About how many nightingales would Ranger Sarah expect to find in a particular area with 6 oaks?

e) Sarah went back to Holly Park and observed 4 nightingales on the plot with 6 oaks. What is the residual for this particular area?

f) Draw the upper and lower bound lines by hand on your scatterplot. What are the equations for these lines? 

g) What is the upper and lower bound of your prediction in part (a)? 

17. Use the graph at right to complete parts (a) through (c) below.

a) What is the multiplier for this sequence?

b) Write an explicit equation for this sequence.

c) Write a recursive equation for this sequence.

18. In 2012 the average cost for a new, midsized car was about $31,000.

New car prices tend to go up about 2% every year.

a) What is the multiplier for this situation?

b) If this trend continues, what will be the cost in 4 years?

c) Write an equation that represents the cost in n years.

19. Elliot's dad bought a new car for $31,000 in 2012. Elliot read that a new car loses about 15% of its value each year. Make a table for the predicted value of the car for the first 5 years, then write a function that represents the value in t years.

20. Find an equation to represent each table as a sequence.

a) [pic] b) [pic]

21. As treasurer of his school’s FFA club, Kenny wants to buy gifts for all 18 members.  He can buy t-shirts for $9 and sweatshirts for $15.  The club has only $180 to spend.  If Kenny wants to spend all of the club’s money, how many of each type of gift can he buy?

a) Write a system of equations representing this problem.

b) Solve your system of equations and figure out how many of each type of gift Kenny should buy.

22. Write an explicit and recursive formula for the sequences or data shown below.

a) 2, 5, 8, 1, 14, 17

b) 4, 9, 14, 19, 24, 29

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[pic]

6

2x

3x

2x

–3

x

+1

[pic]

[pic]

[pic]

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