Algebra I Honors Quarter 4 Exam Review

10-1 Pythagorean Theorem Determine which of the following sets of lengths can be the side lengths of a right triangle.

1. 12, 60, 61 2. 15, 36, 39 3. 12, 35, 38 No Yes No

10-2 Simplifying Radicals Simplify each radical expression.

4. 192s2 5. 3 150b8 6. 20x2y3

8s 3 15b4 6 2xy 5y

7. 3x3

64x2 8. 2 24

48t 4 9. 3xy17

507x5y9

3x8

2t 2

y4

13x2

10. 4 10 i 2 90 11. 3 5c i 7 15c2 12. −6 15n5 i 2 75

240 105c 3c −180n2 5n

13. 27

14. 58x

15. 3 615

2 77

10x4x

3 105

10-3 Operations with Radical Expressions

16. 52 −1

17. 37 − 3

18. −26 + 11

5 2 + 5 3 7 + 3 3

4 2 6 − 2 11

5

19. 12 + 4 75 − 36 20. 18 + 3 72 + 4 21. 2 700 − 3 20 + 5 28

22 3 − 6 21 2 + 2 30 7 − 6 5

22. (3 11 + 7)2 23. (2 + 10)(4 − 12) 24. (3+ 6)(5 − 12) 106 + 6 77 8 − 4 3 + 4 10 − 2 30 15 + 5 6 − 6 3 − 6 2

11-1 Simplifying Rational Expressions Simplify each expression. State any excluded values.

25. n2 + 7n +12n2 + 6n + 8

26. c2 − 6c + 8c2 + c − 6

27. w2 + 7w

w2 − 49

n + 3n + 2

; n ≠ −4,−2 c − 4c + 3

; n ≠ −3,2 ww − 7

; w ≠ −7,7

11-2 Multiplying and Dividing Rational Expressions Multiply. State any excluded values. Be sure to distribute. Do NOT leave as multiplication problems.

28.

6y2

5i2

y + 3 29.

2xx +1

ix −13

30.

m − 4m + 4

im

m −1

12y2

5y +15; y ≠ −3 2x2 − 2x

3x + 3; x ≠ −1 m2 − 4m

m2 + 3m − 4; m ≠ −4,1

Multiply. Do NOT distribute. Factor and simplify, but leave the parenthesis.

31.

4c2c + 2

ic2 + 3c + 2c −1

32.

b2 + 4b + 42b2 − 8

i3b − 64b

33.

t 2 − t −12t +1

it +1t + 3

2c(c + 2)c −1

3(b + 2)8b

t − 4

Divide. Do NOT distribute. Factor and simplify, but leave the parenthesis.

34. x2 + 6x + 8x2 + x − 2

÷ x + 42x + 4

35. 2n2 − 5n − 34n2 −12n − 7

÷ 4n + 52n − 7

2(x + 2)x −1

n − 34n + 5

36.

4b −1b2 + 2b +112b − 3b2 −1

37.

g + 23g −1g2 + 2g6g + 2

38.

c + 4c2 + 5c + 63c2 +12c2c2 + 5c − 3

b −13(b +1)

2(3g +1)g(3g −1)

2c −13c(c + 2)

11-3 Dividing Polynomials Divide. (Write your remainder as a fraction, using the divisor as the denominator.)

39. (−4q2 − 22q +12)÷ (2q +1) 40. (2w3 + 3w −15)÷ (w −1)

−2q −10 + 222q +1

2w2 + 2w + 5 − 10w −1

11-4 Adding and Subtracting Rational Expressions Add or subtract. (Do NOT distribute the denominators. Simplify and leave them with parenthesis.)

41. 3b − 3

− bb − 3

42. 5c2c + 7

+ c − 282c + 7

43. 12 − b

− 42 − b

-1 6c − 282c + 7

− 32 − b

or 3b − 2

44. aa + 3

− 4a + 5

45. 9m + 2

+ 8m − 7

46. pp + 3

+ p + 54

(a + 4)(a − 3)(a + 3)(a + 5)

or a2 + a −12(a + 3)(a + 5)

17m − 47(m + 2)(m − 7)

p2 +12p +154(p + 3)

11-5 Solving Rational Equations

47. dd + 3

= 2dd − 3

−1 48. yy + 2

− 1y= 1

-1 − 23