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Cumulative Review Problems - Math 71
Chapter 1
  14    9 
1. Simplify: 


 8   20 
3 1
2. Subtract:
5 2
7
1
4 + 2
8
2
4. Translate to algebra: Five less than the product of six and a number.
5. Simplify: 10 – 2(3 – 5) – 22
6(8  4)
6. Simplify:
32  1
3
7
7. Simplify: 98 +  (57)  + 2
7
3
8. Evaluate the expression for p = -1: p2 – 5p + 4
9. Simplify completely, with no absolute value signs in your final answer: - |3 – 8|
10. Is – 2 a solution of the equation: – x2 + 3x = -2? Show work to justify your answer.
11. Simplify: -3(x + 5) – (x – 6) – 2x + 11
12. Simplify: -2x2 – x + 1 + x2 – 3x + 13
3. Add:
Chapter 2
1. Solve: -14 + 4x = 37
8
1
2. Solve: x  5  x - 3
7
7
-9
3
x
3. Solve:
5
10
4. If 2 times the sum of a number and 7 is equal to the product of 5 and that number,
find the number.
x 4
 2
5. Solve:
2 3
6. Solve: 3(2x + 4) – 7 = 6(x – 3)
7. Solve: 3.5p – 2.7 = p + 2.3
8. Ana has 12 more classical CDs than rock CDs. If there are a total of 86 CDs of
these 2 types in her collection, how many of each type does she have?
9. In Triangle ABC, Angle A is 20 degrees more than twice as much as Angle B.
Angle C is equal to Angle B. Find all 3 angles in the triangle.
10. Find two consecutive integers where twice the smaller number is 10 more than the
larger number.
11. Find the angle whose supplement is 6 times its complement.
12. If a living room has an area of 180 sq. ft and its width is 12 ft, what is its length?
13. Find the circumference of a circle whose radius is 10 inches. Use 3.14 as an
approximation for "pi".
14. Find the measure of the marked angles:
2
15. Solve the formula F = V + 2as for a.
16. Solve the equation:
2k - 5 =
k + 10
8
3
17. Property taxes of $1600 are paid on a house which is valued at $200,000. How
much property tax must be paid on a house valued at $250,000?
18. Which is a better buy: 5-lb bag of pasta for $10, or a 10-oz bag for $1? Note: 1 lb
= 16 oz.
19. How much pure (fat-free) ground beef must be added to 5 lb. of ground beef that is
30% fat to make a mix that is only 10% fat?
20. Hot dogs cost $3 and sodas cost $1. If 5 more sodas than hot dogs are bought,
and a total of $33 is spent, how many of each type are bought?
21. Two trains are 260 miles apart. They travel toward each other and meet 2 hours
later. If one train is 30 mph faster than the other, find the speed of each train.
22. Money is divided between 2 accounts paying 3% and 5%, and the total interest
earned is $570. The amount invested at 3% is $3000 more than the amount
invested at 5%. How much is invested in each account?
1
x2
23. Solve and graph the inequality:
3
24. Solve and graph the inequality: - 1 < 2x + 5 < 9
Chapter 3
1. For each of the 4 quadrants, tell whether x and y are positive or negative.
Quadrant
x
y
1
2
3
4
2. For the equation 2x - 3y = 12, complete the ordered pairs: (0,
), (
, 0),(-1,
)
3. Graph the equation 2x – 3y = 12 (same equation as above) and give its intercepts:
4. Graph the equation y = 2x - 4 and give its intercepts.
5. Find the slope of the line passing through the points (2, -3) and (1, -7).
6. Find the slope of the line 3x – 7y = 11
7. For the lines y = - 3x -1 and 3x + 2y = 4:
a) Give the slopes of both lines
b) Are the lines parallel, perpendicular or neither?
8. Find the equation of the line through the point (-5, 2) with slope = 0.
9. Find the equation of the line through the points (0, -1) and (-3,5).
10. For the function f(x) = x2 - 3x + 5, find: a) f(0) b) f(-1)
11. Graph the linear inequality y < -x + 4.
12. Graph the linear inequality 2x + 5y > 10.
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13. Write “yes” for each of the following if it is a function; write “no” if it is not a function.
a) The set of ordered pairs {(1,5), (3,5), (4, 7) (5, -1)}
b) The equation y = x2 + 2
c) The graph:
14. A car salesman receives $400/month in salary, plus $100 for every car sold,
described by the formula: S(x) = 100x + 400, where S is salary, x is the # of cars
sold. a) Find S(2) and S(20) b) What do S(2) and S(20) represent in real-life?
Chapter 4
1. Graph each of the 2 lines below, then give the ordered pair solution found by
graphing
2x + 3y = 12
x = -3
2. Is the ordered pair (5, -5) a solution to the system below? You must justify your
answer to receive full credit.
5x + 2y = 15
2x – y = -6
3. For each type of lines how many solutions are there?
a) Parallel lines have ____________________ solution(s).
b) Intersecting lines have ____________________solution(s).
c) Lines on top of each other have ____________________ solution(s).
4. Solve the system by the method of your choice:
7x + 4y = 13
x=1–y
5. Solve the system:
2x – y = 4
3x + y = 21
6. Solve the system:
2x + 3y = - 5
3x + 4y = - 8
7. Solve the system:
3x - 12y = 10
-x + 4y = 10
8. Solve the system:
3x - 4y = 0
2x + 5y = 0
9. Solve the system:
-8y + 2 + 3y = 5y – 2x + 16
5x – 2y = x + 28
10. A plane flies at 320 mph with the wind. Against the wind, it flies at 260 mph. Find
the plane speed and the wind speed.
11. A job placement service received a total of 483 applications. Thirty-nine more
women than men applied. How many of each gender applied?
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12. Children’s tickets to a museum cost $4, while adult tickets cost $7. If 18 tickets are
bought which cost a total of $90, how many are there of each type?
13. Graph the solution of the system of inequalities:
2x – y < -2
x+y>1
14. Graph the solution of the system of inequalities:
x+y< 3
x + y > -2
Chapter 5
1. Simplify: x 3  x 5  x
2. Simplify: (-2x3y5)(x4y)(-7xy3)
3 -2 x -3 y 2 z
3. Simplify completely:
x 5 yz -1
4. Simplify completely: 25 0  2 3
x 3m  x 7m
5. Simplify completely: 4m 2m
x x
6. Convert to scientific notation: a) 207,500 b) .0000314
7. Convert to place value form: a) 8.027 X 107 b) 1.62 X 10–3
8. Americans spend approximately $50,000,000,000 on cosmetics each year. The
population of the U.S. is approximately 250,000,000.
a) Convert these 2 numbers to scientific notation:
b) Divide the first number by the second to calculate how much the average
American spends on cosmetics. Express your final answer in place value form.
9. Simplify: (2x5 + 3x3 + 2x2 – x – 4) + (3x4 + 12x3 – 6x+ 7)
10. Subtract (2p3 + 3p – 4) from (p3 – 2p2 + 7p)
11. Multiply: -3y(-y4 + 4y3 - 2y – 7)
12. Multiply: (x3 – 4x2 + 3x)(x2 + 5x – 2)
13. Multiply: (2x – 3)(x + 8)
14. Multiply: (z + ½)(z – ½)
15. Find the area of the square with the marked sides:
16. Divide:
x  7 x 2  3x - 28
17. Divide:
2x  3 2x 2 - 5x  11
18. Divide:
x - 2 x 4 - 2x 3  3x 2 - 11x  10