The Murder of Dusty Mantel

Name ______________________
*********Complete and submit this Algebra 1 Midterm Review Packet when you return

1. Write the Order of Operations: __________________________________________ __________________________________________ __________________________________________ __________________________________________ __________________________________________ __________________________________________

Evaluate:

2. 3p – q when p = 7 and q = 3 3. when w = 10 and u = 5

4. for x = 36 and y = 4. 5. 4(c + 2) for c = 3.

6. when x = -2. 7. (2xy) for x = 5 and y = 3.

8. for q = -2 9. (x + 3) (10 – x) for x = 4.

10. Evaluate each expression.

a. 8(3 + 5) – 10 • 3 b. [6(5) – 12] + [15 – 3(7)] c. (4 – 2)2 + (6 – 1)3 – (10 – 6)2

d. e. f.

11. Evaluate each expression when x = 2, w = 6 and a = 8.

a. (a + 2)(w2 – 3x) b. (–w)2 – (5a – 10x) c. (x)3 + (6w – 2a + xw)

12. Translate the following into verbal or mathematical expressions.

a. (2x + 5)2 ________________________________________________________________

b. The difference of seven times a number y and 10 times a number x, divided by the product of 2 and a number p.

c. ____________________________________________________________

13. Solve each equation.

a. x + 316 = – 214 b. – 7x + 17 = 164 c. d.

e. 5t – (2t + 3) = 21 f. 81(t + 2) = 27(t – 2) g.

h. 3 – 4(x – 1) = 5x – 11 i. 2.1x + 45.2 = 3.2 – 8.4x j. 3x – 2(x + 3) = x

k. l. m.

n. o. p.

14. Solve each word problem using equations.

a. Eighty-two increased by some number is -34. Find the number.

b. One and two thirds of a number equals one and a half. What is the number?

c. Four times a number decreased by twice the number is 100. What is the number?

d. Find four consecutive integers whose sum is 130.

e. Find two consecutive integers such that twice the lesser integer increased by the greater integer is 49.

f. The sum of two number is 25. Twelve less than four times one of the numbers is 16 more than twice the other number. Find both numbers.

g. Mary’s test grades are as follows: 82, 96, 74, and 88. The last test of the marking period is coming up and Mary really wants an 86 test average to keep her grade at a B. What would she have to get on the fifth test in order to achieve this?

h. You are driving to visit a friend in another state who lives 440 miles away. You are driving 55 miles per hour and have already driven 275 miles. Write and solve an equation to find how much longer in hours you must drive to reach your destination.

i. School guidelines require that there must be at least 2 chaperones for every 25 students going on a school trip. How many chaperones must there be for 80 students?

j. During the month of February, Fabulous Feet Shoe Mart sold 50 pairs of red loafers. After an ad campaign to boost sales, they sold 60 pairs in March. Find the percent of increase in sales.

15. Solve each equation for the variable specified.

a.) 5x = y; solve for y. b.) ay – b = c; solve for y. c.) yx – a = cx; solve for x.

d. ); solve for x. e.) ; solve for y.

16. Solve each inequality and graph the solution.

a. 7w – 3 < – 24 b. a + 5 > 4a – 10 c. 4 – 3y ≥ 13

d. e. 3 – 9x ≤ 30 f. 6 – 4y > 4 – 3y

17. Solve each compound inequality and graph the solution set.

a. 4r ≥ 3r + 7 AND 3r + 7 < r + 29 b. – 2b – 4 ≥ 7 OR – 5 + 3b ≤ 10

c. – 5 < 2x – 1< 3 d. x – 5 < –2 AND x – 5 > 2 e. 2a + 5 ≤ 7 OR 2a ≥ a – 3

18. Write a solution set for the following graphs.

a.

b.

c.

d.

19. State the formula for slope. ____________________

20. State the Slope-Intercept Form of an equation.

____________________

21. State the Point-Slope Form of an equation.

_____________________

22. State the Standard Form of an equation. _____________________

23. Horizontal lines have ________________ slope.

24. Vertical lines have __________________ slope. 25. The equation of a horizontal equation looks like ______________. Give an example: 26. The equation of a vertical line looks like ________________. Give an example: 27. Parallel lines have ___________________ slope.
Give an example of two parallel line equations:

28. Perpendicular lines have ______________________ slope.
Give an example of two perpendicular line equations:

29. Find the slope between the following points.

a. (4, -2) and (10, -7) b. (-34, 16) and (-34, - 5) c. (-11, 25) and (12, 25)

30. Graph each point and name the quadrant in which each point is located.

Point Quadrant

a) (6, 8) _______

b) (–3, – 7) _______

c) (–2, 5) _______

d) (9, –4) _______

31. Graph each linear equation using X and Y Intercepts.
a) y = 4x – 8 b) y = – x + 3

32. Graph a line using the given information.

a) point: (4, –6); slope: b) point: (– 7, 2); slope: 0 c) point: (5, 9); slope: undefined

33. Identify the slope and y – intercept for each equation AND graph the line.

a) y = x – 5 b) 4x – 6 = 12 c) x = 8

slope: ______ slope: ______ slope: ______

y – intercept: ______ y – intercept: ______ y – intercept: ______

34. a) Write the equation of the line given the following information. b) Graph the line.
a) The slope m = – 4, and the y-intercept b = 2. b) Goes through the point (1, 2) and has slope

c) Goes through the points (8, –6) and (5, 2). d) Has an x-intercept of –4 and a y-intercept of –5.

35. Parallel and Perpendicular Lines

a) Write the equation of the line parallel to 4x – 7y = 9 and passes through (1, – 3).

b) Write the equation of the line perpendicular to y = x – 6 and passes through (–10, 8).

c) Write the equation of the line perpendicular to 4x – 7y = 9 and passes through (1, – 3).

d) Write the equation of the line parallel to y = x – 6 and passes through (–10, 8).

36. Graph the following inequalities.

a) y ≥ 3x + 4 b) y < – 4x – 2 c) y ≤ 3

d) x > -5 e) 5x – 10y ≥ 20

37. Solve each system by graphing.

a) x + y = 6 b) 2x + 4y = 6 c) 3x + y = –8 x – y = 2 x + 2y = 3 x + 6y = 3

38. Solve each system by substitution.

a) y = 2x – 7 b) x + 2y = 6 c) y = 2x x + y = 11 2y – 8 = – x x + 2y = 8

39. Solve each system by elimination.

a) x – y = 9 b) 2m + n = 1 c) 3a – 2b = – 4 x + y = 11 m – n = 8 3a + b = 2

d) 3x – y = 1 e) x – 5y = 0 f) 2x + 3y = 8 2x + 4y = 3 2x – 3y = 7 x – y = 2

g) 9x + 8y = 7 h) 6x + 7y = 5 i) 9x + 2 = 3y 18x – 15y = 14 2x – 3y = 7 y – 3x = 8

40. Solve each word problem using a system of equations.

a. The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle?

b. A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Find the amount of nickels and dimes that are in the jar.

c. An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?