Download SVCC MAT-080 test 3, version A

Algebra Refresher
Take about twenty minutes to work problems 1 through 14. If you do not know
how to do a problem, move on to the next. Scratch paper is available if you need
it. When you finish, keep your paper.
1. Simplify (4b)(3b2 )3
2. Corresponding sides of similar triangles are proportional. Draw a picture and write an
equation that expresses this fact.
3. Solve the equation 3x − 7 = 2.
4. Solve the equation 2 + 5x = 3.
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5. Solve the equation.
10 − 3x
x
+4=
8
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6. A grocer mixes two kinds of coffee costing $4.00 per pound and $6.75 per pound to
make 100 pounds of a mixture costing $5.50 per pound. How many pounds of each
kind of coffee does the grocer put into the mixture?
7. Calculate the distance between the points (−3, 4) and (4, 2).
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8. What is the slope-intercept equation of the line passing through (0, −4) and (2, 4)?
9. A strip of width x is cut from each side of a square that is originally thirty-two inches
on a side. Write the area A of the remaining square as a function of x.
10. Write in slope-intercept form the equation of the line 4y − x = −4.
11. Determine the average of the two real numbers x, and x/3.
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12. In any right triangle, the sum of the squares on the sides next to the right angle is
equal to the square opposite the right angle. Draw a picture and write an equation
that expresses this fact.
13. Solve the equation and check your solution.
6.5(1 + 2x) = 13
14. Fifteen thousand dollars is invested in two bonds that pay 9% and 11% simple interest.
The total interest received in a year is $1470. How much is invested in each bond?
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Part Two
Take about thirty minutes to work the remaining problems. If you do not
know how to do a problem, move on to the next. Scratch paper is available
if you need it. When you finish, keep your paper.
15. Solve the equation by using the quadratic formula.
2x2 + 2x − 4 = 10
16. Solve the equation.
√
3t − 9 = 3
17. Write expressions for the perimeter and area of the region.
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2x − 3
?
3x − 1
5
-
18. Translate the verbal phrase into an algebraic expression.
(a) The total of two times a number n and twenty-five
(b) The product of a number y and 10 is decreased by 3.5
19. Solve this system of linear equations.
(
3y − x = 12
5y + 2x = 31
20. The area of a rectangle is fifty-four square inches. Its length is one and one-half times
its width. Find the dimensions of the rectangle.
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21. Solve the equation x2 − x − 6 = 0.
22. Evaluate each expression.
(a) 93/2
(b)
√ √
3 12
√
23. The velocity v (in feet per second) of an object is given by v = 2gh, where g equals
thirty-two feet per second per second and h is the distance (in feet) the object has
fallen. Find the height from which the object has been dropped if it strikes the ground
with a velocity of ninety-six feet per second.
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24. What shape does this function describe?
y = x2 + 3x − 4
25. Find a number such that the sum of the number and its reciprocal is
26. Solve the equation by using the quadratic formula.
2x2 + 2x − 4 = 10
27. What shape does the equation describe?
x2 + 2y 2 = 10
8
37
.
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28. The width of a rectangle is eight feet less than its length. The area of the rectangle is
two hundred forty square feet. Find the dimensions of the rectangle.
29. A ball is dropped from a height of seventy-five feet above ground. Its height h (in feet)
and at any time t is given by h = −16t2 + 75 where t is measured in seconds. Find the
time required for the object to fall to the ground.
30. Solve the equation.
1
1
2
+
= 2
x+1 x−1
x −1
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