Mourning Sr. High

Advanced Topics Summer Assignment

Directions:

1. Show all of your work, neatly. You may print the assignment or

neatly complete all questions on well labeled pieces of paper.

3. Use this assignment to help prepare for the 2020-2021 school

year.

4. If you need help use Khan Academy, www.purplemath.com,

etc.

This assignment will be collected for a grade on

Tuesday, August 25, 2020.

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ Determine which numbers in the set are natural (N), whole (W), integer (Z), rational (Q), irrational (I). 1. !−9,− !

", 5, "

#, √2, 0, 1, −4, 2, 11+

2. {2.01, 0. 6/, −13, 0.010110111… , 1, −6} Plot the real numbers on the real number line. 3. − $

"

4. −5.2

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< 𝒐𝒓 >) between them. 5. $

%, "#

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 6 and 7:

a) Give a verbal description of the subset of real numbers represented by the inequality or interval.

b) Sketch the subset on the real number line. c) State whether the subset is bounded or unbounded.

6. −2 < 𝑥 < 2

a.

b.

c.

7. [4,∞)

a.

b.

c. In exercises 8 and 9 use inequality notation and interval notation to describe the set. 8. 𝑦 is non-negative

Inequality Interval

9. 𝑡 is at least 10 and at most 22

Inequality Interval

10. Evaluate the expression. |3 − 8|

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ 11. Evaluate the expression. |−1| − |−2| 12. Evaluate the expression. 5|−5| 13. Evaluate the expression. |'("|

'(",𝑥 < −2

In exercises 14 and 15 place the appropriate symbol (<,>, 𝒐𝒓 =) between the pair of real numbers. 14. |−4| |4| 15. −|−6| |−6| In exercises 16 and 17 find the distance between 𝒂 and 𝒃. 16. 𝑎 = 126, 𝑏 = 75 17. 𝑎 = − $

", 𝑏 = 0

In exercise 18, use absolute value notation to represent the situation. 18. The distance between 𝑥 and 5 is no more than 3.

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 19 and 20, identify the terms. Then, identify the coefficients of the variable terms of the expression. 19. 6𝑥! − 5𝑥 20. 3√3𝑥" + 1 In exercises 21 and 22, evaluate the expression for each value of 𝒙. (If not possible, state the reason.) 21. 𝑥" − 3𝑥 + 2 22. '()

'*)

In exercises 23 and 24, identify the rule(s) of Algebra illustrated by the statement. 23. )

+(%(ℎ + 6) = 1,ℎ ≠ −6

24. 𝑥(3𝑦) = (𝑥 ∙ 3)𝑦 = (3𝑥)𝑦 In exercises 25 and 26, perform the operation. (Write fractional answers in simplest form.) 25. "'

#− '

,

26. #'

)-∙ $%

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 27 – 30, evaluate each exponential expression. 27. #

!

#"

28. (2! ∙ 3")" 29. −2$ 30. %∙!

#!

"#!∙!#$

In exercises 31 – 32, evaluate the algebraic expression for the given value of 𝒙. 31. 6𝑥$, 𝑥 = 10 32. −3𝑥%, 𝑥 = −2 In exercises 33 – 36, use properties of exponents to simplify each expression. 33. 5𝑥%(𝑥") 34. 6𝑦"(2𝑦$)"

35. (−𝑧)!(3𝑧)%

36. 9'

#!

(#!: 9'

(:"

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 37 – 40, rewrite each expression with positive exponents. 37. (𝑥 + 5)$ 38. (2𝑥"))"

39. 9*#%+"

#:)!

40. 9(

#!

'#!: 9'

(:!

41. Evaluate the expression without using a calculator. ;",-

%

In exercises 42 – 43, use the properties of radicals to simplify each expression. 42. <√2& =

"

43. <√32𝑥#& = In exercises 44 – 45, simplify the radical expression. 44. √72𝑥! 45. 2√20𝑥" + 5√125𝑥"

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 46 – 47, rationalize the denominator. 46. .

√!

47. #

√.%)"

48. Rationalize the numerator. √#0√!

!

In exercises 49 – 51, simplify the expression. 49. 32)!/# 50. ?√32 51. (𝑥 − 1)./!(𝑥 − 1)"/! In exercise 52

a) Write the polynomial in standard form b) Identify the degree and leading coefficient of the polynomial c) State whether the polynomial is a monomial, binomial or trinomial

52. 14𝑥 − .

"𝑥#

a) b) c)

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 53 – 54, add or subtract the polynomial. Write the result in standard form. 53. (6𝑥 + 5) − (8𝑥 + 15) 54. (𝑡! − 1) + (6𝑡! − 5𝑡) In exercises 55 – 57, multiply each polynomial. 55. (𝑥 + 7)(𝑥 + 5) 56. (3𝑥 − 5)(2𝑥 + 1) 57. (𝑥" − 𝑥 + 2)(𝑥" + 𝑥 + 1) In exercises 58 – 60, find the special product. 58. (𝑥 + 10)(𝑥 − 10) 59. (2𝑥 + 3)" 60. (2𝑥 − 𝑦)!

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 61 – 64, completely factor the expression. 61. 6𝑥" − 54 62. 1 − 4𝑥 + 4𝑥" 63. 2𝑥" + 4𝑥 − 2𝑥! 64. 2𝑥! + 𝑥" − 8𝑥 − 4 In exercises 65 – 67, find the domain of the expression. 65. .

!)*

66. √𝑥 − 7 67. .

√*)!

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 68 – 69, simplify the rational expression. 68. .#*

!

.$*

69. *!)*)"

.$)!*)*!

70. Find the distance between the points (1, 4), (−5,−1). 71. Find the midpoint of the line segment joining the points (6, −3), (6, 5) 72. Find the length of each side of the triangle and show that these lengths verify the

Pythagorean Theorem.

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 73 – 74, solve each system by graphing. 73.

74.

In exercises 75 – 76, sketch the graph of each function. 75. 𝑦 = (𝑥 − 3)" − 4

76. 𝑦 = −2(𝑥 − 4)" − 3

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 77 – 79, sketch the graph of each line. 77. 𝑦 = −2

78. 𝑥 = 2

79. 5𝑥 + 2𝑦 = 0

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 80 – 82, sketch the graph of each linear inequality. 80. 𝑦 > "

#𝑥 − 2

81. 𝑥 + 4𝑦 ≥ −4

82. 𝑥 > 5

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 83 – 84, write the slope-intercept equation of each line. 83. 5𝑥 − 𝑦 = 33 84.

In exercise 85, write the point-slope form of the equation of the line through the given point with the given slope. 85. 𝑡ℎ𝑟𝑜𝑢𝑔ℎ:(4, −4);𝑚 = −2 In exercises 86 - 87, write the point-slope form of the equation of the line through the given points. 86. 𝑡ℎ𝑟𝑜𝑢𝑔ℎ:(4, −4)𝑎𝑛𝑑(−2, 4) 87. 𝑡ℎ𝑟𝑜𝑢𝑔ℎ:(−2,−4)𝑎𝑛𝑑(0, −4)

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________ In exercises 88 - 89, write the slope-intercept form of the line described. 88. 𝑡ℎ𝑟𝑜𝑢𝑔ℎ:(4, 1)𝑎𝑛𝑑𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑡𝑜𝑦 = #

2𝑥 − 3

89. 𝑡ℎ𝑟𝑜𝑢𝑔ℎ:(3, 3)𝑎𝑛𝑑𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟𝑡𝑜𝑦 = − !

-𝑥 + 2

In exercises 90 - 91, solve the system by the method of substitution.

90. U 𝑥 − 𝑦 = 26𝑥 − 5𝑦 = 16

91. U2𝑥 − 𝑦 + 2 = 04𝑥 + 𝑦 − 5 = 0

In exercise 92 - 93, solve the system by the method of elimination. 92. U𝑥 + 2𝑦 = 6

𝑥 − 2𝑦 = 2

93. U5𝑥 + 3𝑦 = 63𝑥 − 𝑦 = 5

Advanced Topics Name ____________________________________ Summer Assignment Date_________________ Period________

In exercises 94 - 95, determine if the ordered triple is a solution of the system of equations.

94. (0, 3, 1) 95. (−1, 0, 5)