Chapter 11 and 12 Quiz Review
Divide. Identify the divisor, dividend, quotient, and remainder if any.
1. (12𝑟 4 − 30𝑟 2 − 72𝑟) ÷ (-6r)
2. (8𝑞 + 𝑞 2 + 7) ÷ (7 + 𝑞)
3. (4𝑤 4 + 3𝑤 − 7) ÷ (2𝑤 − 1)
Simplify. Find the excluded values.
4.
5.
6.
3𝑐+33
𝑐+11
𝑣+2
𝑣 2 −4
8𝑥 3 −52𝑥 2 +84𝑥
8𝑥 3 −48𝑥 2 +72𝑥
Solve. Check for extraneous solutions.
7. √3𝑥 + 4 = 16
8. √9𝑥 − 30 = √4𝑥 + 5
9. √𝑥 − 8 − 4 = −2
10. √3 − 𝑥 = 𝑥 + 1
Find the unknown lengths of the right triangle. Write your answer in simplest radical form.
11.
x√2 𝑖𝑛
x 𝑖𝑛
2x − 5 𝑖𝑛
12. A right triangle has sides a=x, b=x+2 and c=14. Find the value of each side.
13. The average late payment fee F (in dollars) on a credit card account during the period 1994-2003 can be
12+1.6𝑥 2
modeled by 𝐹 = 1+0.04𝑥2 where x is the number of years since 1994. Rewrite the model so that it has only
whole number coefficients. Then simplify the model and approximate the average late payment fee in 2003.
Simplify the expression.
14. √15 + 5√3 − 2√27
2
15. (3 − 2√7)
16.
5
+
√7
2
√14
121
17. √
16𝑚2
4𝑥 2
3
18. 6√
1
2
19. (2 − 4√3)
80𝑥 5
20. √ 15𝑥
Solutions.
1. −𝟐𝒓𝟑 + 𝟓𝒓 + 𝟏𝟐 divisor: -6r, dividend: 𝟏𝟐𝒓𝟒 − 𝟑𝟎𝒓𝟐 − 𝟕𝟐𝒓, quotient: −𝟐𝒓𝟑 + 𝟓𝒓 + 𝟏𝟐; no remainder
2. q+1; divisor: q+7; dividend: 𝒒𝟐 + 𝟖𝒒 + 𝟕, quotient: q+1; no remainder
𝟏
𝟕
3. 𝟐𝒘𝟑 + 𝒘𝟐 + 𝟐 𝒘 + 𝟒 +
𝟐𝟏
𝟒
𝟐𝒘−𝟏
(we will learn to simplify the last term next week); divisor: 2w-1; dividend:
𝟒𝒘𝟒 + 𝟑𝒘 − 𝟕; remainder is 21/4
4. 3; c≠11
5.
6.
𝟏
v≠-2, 2
𝒗−𝟐
𝟐𝒙−𝟕
x≠0,3
𝟐𝒙−𝟔
7. {48}
8. {12}
9. {7}
10.
−𝟑∓√𝟏𝟕
𝟐
11. Sides are 5 in, 5 in, and 𝟓√𝟐
12. 𝒂 = −𝟏 + √𝟗𝟕, 𝒃 = 𝟏 + √𝟗𝟕, 𝒄 = 𝟏𝟒
13.
𝟒𝟎𝒙𝟐 +𝟑𝟎𝟎
𝒙𝟐 +𝟐𝟓
14. √𝟏𝟓 − √𝟑
15. 𝟑𝟕 − 𝟏𝟐√𝟕
16.
17.
𝟓√𝟕+√𝟏𝟒
𝟓√𝟕
√𝟏𝟒
or
+
𝟕
𝟏𝟒
𝟕
𝟏𝟏
𝟒𝒎
18. 𝟒𝒙√𝟑
𝟏
19. 𝟒𝟖 𝟒 − 𝟒√𝟑
20.
𝟒𝒙𝟐 √𝟑
𝟑