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Pre-Algebra Review (Grade 8)

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Pre-Algebra Review

1. 
Premix concrete uses a mixture of [math]5 2/3[/math] pounds of gravel for every [math]3 1/3[/math] pounds of cement. If the plant operator needs to make a batch of premix using 4,300 pounds of gravel, how much cement will be needed?
  1. 2,529 pounds
  2. 6,318 pounds
  3. 4,516 pounds
  4. 2,689 pounds
2. 
Which are equivalent ratios?
  1. 4:8 and 1:2
  2. 8:6 and 6:8
  3. 3:7 and 5:14
  4. 5:3 and 12:15
3. 
Tina drives 40 miles per hour. At this rate, how long will it take her to travel 120 miles?
  1. 2 hrs
  2. 4 hrs
  3. 3 hrs
  4. 5 hrs
4. 
A factory is producing smart phones. In one hour, they can produce 14,000 smart phones ([math]y[/math]). Write the equation that represents how many smart phones they can produce per hour ([math]t[/math]).
  1. [math]y=14000t[/math]
  2. [math]t=14000y[/math]
  3. [math]y=1/14000t[/math]
  4. [math]t=1/14000y[/math]
5. 
In a class of 50 students, 36% own a bicycle.

How many students in the class own a bicycle?
  1. 18
  2. 15
  3. 20
  4. 45
6. 
A clothing shop has a markup of 45% on the wholesale price of shirts. If the wholesale price of men's shirts is $35.00, what will be the retail price?
  1. $80.00
  2. $52.50
  3. $57.50
  4. $50.75
  5. $45.00
7. 
If you were to place a point at [math]+2[/math] on the number line, add [math]-5[/math] to that number, and move the point to the location of the new number, how many units and in what direction would you have to move the new point in order to bring it back to where it originally was?
Number Line -5 to 5
  1. 3 units to the right
  2. 5 units to the right
  3. 0 units in either direction
  4. 2 units to the left
8. 
A plane takes off from an airport that is 1,500 feet above sea level. If the plane ascends 6,000 feet from the ground, how many feet will the plane have to descend if it wants to land at another airport that is also 1,500 feet above sea level?
  1. 9,000 feet
  2. 7,500 feet
  3. 4,500 feet
  4. 6,000 feet
9. 
Which of the following has a sum of 0?
  1. [math]3 + | -3|[/math]
  2. [math]-3 + | 3|[/math]
  3. [math] |3| + |3|[/math]
  4. [math] | -3| + | -3|[/math]
10. 
What number should be placed in the square to make the equation true?

[math]5.32 - square = 5.32 + (-7.89)[/math]
  1. 2.57
  2. -2.57
  3. -7.89
  4. 7.89
11. 
If you add [math]-3/4[/math] and [math]-2/8[/math], where would your answer be on the number line?
Number Line -5 to 5 4
  1. A
  2. B
  3. C
  4. D
12. 
All non-terminating decimals are irrational numbers.
  1. True
  2. False
13. 
[math]pi[/math] is a rational number.
  1. True
  2. False
14. 
Which of these numbers is irrational?
  1. [math]sqrt49[/math]
  2. [math]16/3[/math]
  3. [math]24/3[/math]
  4. [math]sqrt5[/math]
15. 
[math]sqrt2[/math] is what type of number?
  1. integer
  2. irrational
  3. rational
  4. whole
16. 
Choose the best answer.

[math]sqrt(20)[/math] is between which two numbers?
  1. 2 and 3
  2. 3 and 4
  3. 4 and 5
  4. 5 and 6
17. 
Expand.

[math]4(5x+3)[/math]
  1. [math]20x+7[/math]
  2. [math]20x+1[/math]
  3. [math]20x-1[/math]
  4. [math]20x+12[/math]
18. 
Factor.

[math]48x+8 [/math]
  1. [math] 8(6x+1) [/math]
  2. [math] 8(x+6) [/math]
  3. [math] 40x [/math]
  4. [math] 6(x+8) [/math]
19. 
Combine like terms.
[math]3x-2y+4z-x+5y+z[/math]
  1. [math]12x+7y+4z[/math]
  2. [math]2x-3y+5z[/math]
  3. [math]2x+3y+5z[/math]
  4. [math]5xy+4xz+5yz[/math]
20. 
Tristan wants to replace his computer screen. Which of these equations would represent Tristan's scenario if the screen costs $87 plus 16% in taxes, and x represents the total amount he must pay?
  1. [math]x=87xx0.16[/math]
  2. [math]x=87xx1.16[/math]
  3. [math]x=0.16/87[/math]
  4. [math]x=87/1.16[/math]
21. 
Solve.
[math]a-2+3=-2[/math]
  1. [math]a=-3[/math]
  2. [math]a= -1[/math]
  3. [math]a=7[/math]
  4. [math]a=0[/math]
22. 
During the third quarter of a basketball game between the Tigers and the Bears, four different players scored all of the points for the Tigers. Player A scored [math]1//2[/math] of the Tigers points. Player B scored [math]1//3[/math] of the Tigers points. Player C made one three-point basket. Player D scored the last point by sinking a free throw. How many points did the Tigers score in the third quarter?
  1. 24 points
  2. 21 points
  3. 18 points
  4. 12 points
23. 
Solve for x.
[math]7x+5=61[/math]
  1. x=7
  2. x=8
  3. x=9
  4. x=10
24. 
The price of tickets in a group when purchased in bulk can be found with the equation [math]C=px+24[/math] where [math]C[/math] is the cost, [math]p[/math] is the number of people, and [math]x[/math] is the price per ticket. What is the price of each ticket if it costs $189 to buy tickets for 15 people?
  1. $8
  2. $24
  3. $9
  4. $11
25. 
Which graph shows the solution to the inequality?

[math]x + 4 <= 4[/math]
  1. Inequality 2
  2. Inequality 1
  3. Inequality 6
  4. Inequality 5
26. 
[math]1/32[/math] can also be written which way?
  1. [math]2^-3[/math]
  2. [math]2^-4[/math]
  3. [math]2^-5[/math]
  4. [math]2^-6[/math]
27. 
Which of these is equivalent to [math]4^-3?[/math]
  1. [math]1/4 xx 1/4 xx 1/4[/math]
  2. [math]-4 xx -4 xx -4[/math]
  3. [math]3^4[/math]
  4. [math]4 xx 3[/math]
28. 
Simplify the following expression.
[math]3x^5*2x^12[/math]
  1. [math]5x^17[/math]
  2. [math]5x^60[/math]
  3. [math]6x^17[/math]
  4. [math]6x^60[/math]
29. 
Find the square root.

[math]sqrt144[/math]
  1. 72
  2. 12
  3. 6
  4. 3
30. 
Simplify. [math]root3 27[/math]
  1. 9
  2. 3
  3. 2
  4. 4
31. 
Which of the following is a correct notation for 58,000?
  1. [math]5.8xx10^4[/math]
  2. [math]5.8xx10^3[/math]
  3. [math]5.8xx10^2[/math]
  4. [math]5.8xx10^5[/math]
32. 
Which of the following is a correct notation for 0.0000032?
  1. [math]3.2xx10^-6[/math]
  2. [math]3.2xx10^-5[/math]
  3. [math]3.2xx10^-7[/math]
  4. [math]3.2xx10^-4[/math]
33. 
Choose the correct answer.
[math](4.9xx10^9)/(1.6xx10^3)[/math]
  1. [math] 3.02xx10^6 [/math]
  2. [math] 3.2xx10^6 [/math]
  3. [math] 3.6xx10^6 [/math]
  4. [math] 3.06xx10^6 [/math]
34. 
A teacher grades 5 tests in 30 minutes. If a graph was made to show the number of tests per hour that the teacher can grade, what would be the slope of the graph?
  1. [math]6[/math]
  2. [math]1/6[/math]
  3. [math]60[/math]
  4. [math]10[/math]
35. 
An airplane is gaining 1,000 meters of altitude for every 2 kilometers that it travels. This graph
Graph - Linear Function y=1/2x
  1. has a smaller rate of change than the airplane.
  2. has a greater rate of change than the airplane.
  3. has the same rate of change as the airplane.
  4. has no relation than the airplane.
36. 
What is the y-intercept of the equation [math]y=3x-2?[/math]
  1. [math]-3[/math]
  2. [math]3[/math]
  3. [math]2[/math]
  4. [math]-2[/math]
37. 
What is the slope of the graph?
Graph - Linear Function y=-2x
  1. [math] -2[/math]
  2. [math]-1[/math]
  3. [math]1/2[/math]
  4. [math]2[/math]
38. 
What is the slope of the equation [math]y=4x-5[/math]?
  1. 5
  2. -5
  3. 4
  4. -4
39. 
The lines [math]y=2x+5[/math] and [math]3y-2x=2y+5[/math] have
  1. no solutions.
  2. 1 solution.
  3. infinitely many solutions.
  4. 2 solutions.
40. 
The lines [math]4y-5=3x[/math] and [math]y=5x-1[/math] have
  1. no solutions.
  2. 2 solutions.
  3. infinite solutions.
  4. 1 solution.
41. 
Simplify. [math]2y-3x+2=5x+12[/math]
  1. [math]y=4x+5[/math]
  2. [math]y=-4x+14[/math]
  3. [math]y=x+5[/math]
  4. [math]y=x+10[/math]
42. 
The equation [math]-3y+8=2y-6x[/math] is equivalent to which of the following equations?
  1. [math]y=(6x)/5+8[/math]
  2. [math]y=6x+5[/math]
  3. [math]y=(6x)/5+8/5[/math]
  4. [math]y=6x+8[/math]
43. 
What is the solution to [math]y=5x+5[/math] and [math]y=x+5 ?[/math]
  1. [math](0,0)[/math]
  2. [math](0,5)[/math]
  3. [math](5,0)[/math]
  4. No solution
44. 
What is the solution to [math]y=-3x+2[/math] and [math]y=-3x-1 ?[/math]
  1. [math](-3,6)[/math]
  2. [math](3,-6)[/math]
  3. [math](2/3,-3)[/math]
  4. No solution
45. 
Melody and Brigitta open savings accounts at the bank at the same time. Melody deposits $100 and then deposits $20 per week. Brigitta deposits $50 and then $30 per week. Will Melody and Brigitta ever have the same amount of money in their savings accounts? If so when?
  1. After 15 weeks
  2. After 2 weeks
  3. After 5 weeks
  4. Never
46. 
This is a function.
Graph - Quadratic Function y=2x^2
  1. True
  2. False
  3. Sometimes
  4. Not enough information
47. 
Which equation has a smaller rate of change than this graph? Graph - Linear Function y=-1/2x
  1. [math]y=-1/3x[/math]
  2. [math]y=-3x[/math]
  3. [math]y=-5/2x-3[/math]
  4. [math]y=-8x[/math]
48. 
The equation [math]y=-2x^2+2[/math] is
  1. linear.
  2. nonlinear.
  3. not a function.
  4. both b and c.
49. 
Is this graph linear?
Graph - Linear Function y=x
  1. Yes
  2. No
  3. Not enough information
  4. Sometimes
50. 
Given the table and equation below, what is the value of [math]square[/math] that makes the equation true?

[math]y = squarex[/math]
xy
28
312
416
520
  1. 2
  2. 4
  3. 6
  4. 8

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