MAT0028: Final Exam Review
Test 1: Sections: 1.1, Summary Exercises p.89, 2.1-2.6
1. Perform each indicated operation.
a. 7 − 3[(5 − 9)3 ÷ 4 − 2]
b.
−9−|−4+3|
−8−(−5)
c. −
7
2 2
1
÷ (− ) −
24
4
12
2. Write the equation and then solve. The product of 9 and 4, divided by the sum
of 6 and 3.
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3. Solve each equation.
a. 4(𝑥 − 5) − 2(𝑥 + 3) = −6
b. 0.25(𝑥 + 40) = 9 − 0.30𝑥
c.
1
2
1
(𝑥 + 7) = 𝑥 − 3
5
4. Find two consecutive odd integers such that when the smaller is added to twice
the larger, the result is 24 more than the larger integer.
5. Find the circumference of a circle with a radius of 8 inches.
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6. Find the measure of each marked angle:
(3𝑥 + 15)𝑜
(4𝑥 − 5)𝑜
7. The formula for perimeter of a rectangle is 𝑃 = 2𝐿 + 2𝑊
a. Solve for W.
b. Evaluate W if P=116 and L= 40.
8. Solve each equation for the indicated variable.
a. Solve 𝑦 = 𝑚𝑥 + 𝑏 for the variable 𝑥 .
1
b. Solve 𝑉 = 𝑏ℎ for the variable ℎ.
3
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9. Solve the following equations.
a.
b.
𝑥
5
=
6𝑥−5
5
2𝑦+1
11
=
3
𝑦−2
10. John Brown’s monthly salary is $2800. He saves 15% of this amount each
month. How much does he save in one year?
11. 44% of what number is 60?
12. What percent of 45 is 130?
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Test 2: Sections: Other Applications Handout, 2.7, 3.1-3.4, 5.1
13. Perform the following conversions using dimensional analysis.
a. 8.5 lb = ____________ kg
b. 250 mL = ____________ fl oz
c. 7 m = ______________ feet
14. Three less than seven times a certain number is 27 more than twice the number.
Find the number.
15. Helen paid a total of $138.03 for a new coat. The tax rate was 7%. Find the
listed price of the coat.
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16. Solve each inequality and graph the solution on the number line.
a. 9𝑥 − 4 ≤ 4𝑥 + 1.
b. 4(𝑥 + 3) > 3𝑥 + 17.
17. Complete the ordered pairs for the equations:
a. 𝑦 = −3𝑥 + 5
(0,
), (
, 0), (−2,
b. 2𝑥 − 𝑦 = 9
(0,
), (
, 0), (3,
)
)
18. Find the slope of a line that passes through each pair of points.
a. (3, 5) 𝑎𝑛𝑑 (6, −9)
b. (−7, −2) 𝑎𝑛𝑑 (−3, 8)
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19. Graph the linear equation and give the x- and y-intercepts.
3
a. 𝑦 = 5 𝑥 − 3
b. 4𝑥 − 3𝑦 = 12
20. Find the value of the polynomial −𝑥 2 + 5𝑥 − 4 when 𝑥 = −3.
21. Add or subtract as indicated.
a. (4𝑦 4 − 5𝑦 3 + 3𝑦 2 − 𝑦 ) + (3𝑦 3 − 𝑦 2 + 2)
b. (−7𝑥 2 − 6𝑥 + 9 ) − ( 5𝑥 2 − 4𝑥)
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Test 3: Sections: 5.2-5.6, 5.8, 6.1, 6.2
22. Simplify each expression. Leave answers with positive exponents. Assume
that all variables represent non-zero numbers.
a. 𝑥 3  4𝑦 8  (−3𝑥 5 𝑦 2 )3
b.
c.
(𝑤 −4  𝑥 8 )
−2
𝑤5𝑥 3
𝑚−4  𝑛8
(
𝑚−6 𝑛5
−1
)
23. Find each product.
a. (𝟑𝒙𝟐 – 𝟕𝒙)(𝟐𝒙𝟐 + 𝟐𝒙 + 𝟒)
b. (3𝑤 – 7𝑥)(3𝑤 + 7𝑥)
c. (9𝑝 + 4𝑟)2
d. (5𝑥 2 − 2𝑦)2
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24. Divide.
a.
6𝑥 4 −12𝑥 3 + 2𝑥 2 −5𝑥
2𝑥
b. (15𝑚12 − 12𝑚9 + 9𝑚8 − 6𝑚6 + 3𝑚3 ) ÷ (−𝑚3 )
25. Write each number in scientific notation.
a. 56890
b. 0.00652
26. Write each number without exponents.
a. 6.78 × 105
b. 3.5 × 10−4
27. Simplify. Write the answer in scientific notation: (3.5 × 103 )(4.8 × 104 )
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28. Factor completely.
a. 8𝑥 6 𝑦 5 + 24𝑥 3 𝑦 7 − 12𝑥 2 𝑦 2
b. 7𝑥 2 − 7𝑥𝑦 − 5𝑥 + 5𝑦
c. 5𝑚3 𝑛 − 10𝑚2 𝑛2 − 20𝑚𝑛3
d. 𝑥 2 − 5𝑥 − 6
e. 8𝑚2 − 10𝑚 − 3
f. 108𝑤 3 + 36𝑤 2 + 3𝑤
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Test 4: Sections: 6.3-6.6, 7.1
29. Factor completely.
a. 9𝑥 2 + 𝑦 2
b.
𝑥2
16
−
𝑦2
25
c. 4𝑥 2 + 12𝑥𝑦 + 9𝑦 2
d. 9𝑤 2 − 30𝑤 + 25
30. Solve each equation.
a. 9𝑥 2 – 36 = 0
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b. (4𝑤 + 3)(2𝑤 – 5) = 0
c. 𝑤 2 − 9𝑤 = −20
d. 𝑝(6𝑝 + 5) = 4
31. Find the values for which the rational expression is undefined.
a.
b.
3𝑥−1
𝑥 2 −2𝑥−8
(𝑤−6)2
𝑤(2𝑤+7)
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32. Find the value for each rational expression when 𝑥 = 2.
a.
b.
5𝑥+3
(𝑥−2)(2𝑥+3)
1− 2𝑥
2𝑥 − 1
33. Write each rational expression in lowest terms.
a.
b.
c.
4𝑥 2 − 9
6 − 4𝑥
(𝑥 + 2)2
𝑥 2− 4
4𝑥 2 + 8𝑥𝑦 − 5𝑦 2
10𝑥 2 − 3𝑥𝑦 − 𝑦 2
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Test 5: Sections: 7.2-7.4, 8.1-8.5
34. Simplify. Write the answers in the lowest terms.
a.
b.
c.
d.
𝑥 2 −1
𝑥2
∙
5
𝑥2
𝑦+3
𝑦 2 − 𝑦−2
7
𝑚
+
6
𝑥+3
+ 6𝑥 + 5
÷
2
𝑦 2 + 4𝑦 + 3
5
2𝑚
−
3
𝑥+3
35. Find all square roots.
a. 64
b. 169
c.
16
49
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36. Find each square root.
a. √121
b. −√144
c.
√
4
81
37. Two legs of a right triangle measure 5 cm and 12 cm. Find the measure of the
triangle’s hypotenuse.
38. The diagonal of a rectangular garden measures 37 feet. The width of the garden
is 12 feet. Find the length of the garden.
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39. Simplify.
a.
b.
√
28𝑥 2
49
27√15
9√3
c. −√14 ∙ √7
d. 3√50 + 2√32 − √8
e. 2√5 ∙ (3√2 − 4√5)
f. √98𝑥 2 𝑦 3 𝑧 4
40. Rationalize each denominator.
a.
b.
10
√5
4
√3𝑥
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