Semester Exam Review Sheet - triadk12.org Exam Review... · College Readiness Math Semester Exam Review Write the set using interval notation and graph the inequality on the number

College Readiness Math Semester Exam Review

Write the set using interval notation and graph the inequality on the number line.

1) {x| -6 < x < 9}

Use the order of operations to simplify the expression.

2)4 · (8 + 2) + 4 · 7

4 · (6 - 1)

Simplify the expression.

3) 7a - 4a - a - 13

List all the elements of set B that are of the indicated type.

4) B = {12, 8, -13, 0, 0

1, 16}

Rational Numbers, Irrational Numbers, Whole Numbers, Integers, Natural Numbers

Evaluate the expression for a = -5, b = 16 and c = 7.

5) b + 40

a

Write the set by listing its elements.

6) {a|a is an even integer greater than 4}

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.

7) The product of 6 and 1 less than a number

Solve the equation.

8)r + 6

3 =

r + 8

6

9) 0.07y + 0.1(5000 - y) = 0.47y

10) 13(8c - 2) = 6c - 2

Solve the problem.

11) Janet drove 272 km, and the trip took 4 hr. At what average rate was Janet traveling?

Provide an appropriate response.

12) 5x2 - 7 = 3x

Is this a linear equation?

Decide if the statement is true or false.

13) -8 is a solution of -9x + 4x = 40.

Solve the equation for the specified variable. Use the distributive property to factor as necessary.

14) -9s + 8p = tp - 8 for p

1

Solve the formula for the specified variable.

15) S = 2πrh + 2πr2 for h

Solve the equation.

16) 31s + 25 = -4s

Find the slope of the line and sketch the graph.

17) 2x + 3y = 10

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

Decide whether the pair of lines is parallel, perpendicular, or neither.

18) 3x - 4y = 4 and 8x + 6y = -6

Decide whether the relation is a function.

19) {(-4, 1), (-3, -6), (3, -8), (3, 4)}

Find the x- and y-intercepts. Then graph the equation.

20) 12y - 4x = -8

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

Find the midpoint of the segment with the given endpoints.

21) (8, 2) and (7, 7)

Find the slope of the line through the pair of points.

22) (7, -8) and (5, 2)

2

Find the equation in slope-intercept form of the line satisfying the conditions.

23) m = 2, passes through (5, -4)

Find an equation of the line passing through the two points. Write the equation in standard form.

24) (2, -9) and (0, 4)

Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form.

25) Through (-6, 5); parallel to -7x + 5y = 57

Solve the system of equations.

26) 7x + 7y + z = 1

x + 8y + 8z = 8

9x + y + 9z = 9

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

27) x = -27 + 7y

-6x - 8y = -38

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

28) -x + 6y = 53

-3x - 6y = -57

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree.

29) 18c6 - 4c5 + 3c4

Write the polynomial in descending powers of the variable. Give the coefficient of the highest degree.

30) -25 - x5 - 18x4 + 48x

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree.

31) 14x2

Apply the product rule for exponents, if possible.

32) (5x8y)(-7x-2y-4)

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all

variables represent nonzero numbers.

33)x7

x13

Add or subtract as indicated.

34) (5 + 7x5 + 8x7 + 9x6) + (9x6 - 5x5 + 5 + 7x7)

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero

real numbers.

35)-3w7

x

4

3

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero

numbers.

36) (3x-5)4(x2)-4

Divide.

37)x2 + 3x - 18

x + 6

Add or subtract as indicated.

38) (8x3 + 5x2 + 3) - (-3x3 + x - 8)

Find the product.

39) (9y - 7)(81y2 + 63y + 49)

40) (4x + 12)(x + 2)

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if

necessary.

41) (3p)-3

Find the product.

42) (r - 5)2

Divide.

43)12x7 - 12x4

-2x7

Find the product.

44) (10r - 3)(10r + 3)

Divide.

45)4y4 + 6y3 + 3y - 1

2y2 + 1

Add or subtract as indicated. Write the answer in lowest terms.

46)3

r +

9

r - 2

47)3

14x +

9

10x2

4

48)x

x2 - 16 -

5

x2 + 5x + 4

Perform the indicated operation and express in lowest terms.

49)z2 + 9z + 20

z2 + 11z + 28 ÷

z2 + 5z

z2 + 4z - 21

50)4p - 4

p ·

8p2

5p - 5

Solve the equation.

51) 1 + 1

x =

42

x2

52) 6

x - 6 = 1 +

8

x + 6

53)4x - 6

2x + 1 =

2x - 1

x + 3

Factor by grouping.

54) 20r2 + 15ry - 4xr - 3xy

55) 3a + 3x - a2 - ax

Factor the trinomial completely.

56) 6x2 + 13x + 6

Factor out the greatest common factor. Simplify the factors, if possible.

57) (x - 4)(x + 7) + (x - 4)(x + 3)

58) 9wx - 15wy - 12wz


59) 15z2 + 4z - 4

5

60) 3x3 + 6x2y - 24xy2

Factor the polynomial completely.

61) 25x2 - 4

62) 36y4 - 49

Find all solutions by factoring.

63) 3m2 - 10m = 0

Solve the equation.

64) 3x3 + 28x2 + 60x = 0

Factor by grouping.

65) 36r2 + 45ry - 4xr - 5xy


66) 12x2 + 17x + 6

67) x2 - x - 90

Factor out the greatest common factor. Simplify the factors, if possible.

68) (x - 8)(x + 3) + (x - 8)(x + 3)

Factor the polynomial.

69) 49x2 - 126xy + 81y2


70) 6z2 + 5z - 6

71) 2x3 + 2x2y - 40xy2

Factor the polynomial completely.

72) 36x2 - 25

73) 49x2 + 9

Find all solutions by factoring.

74) 7m2 - 9m = 0

Solve the equation.

75) 3x3 + 28x2 + 60x = 0

6

Find the vertical asymptotes and then state the domain.

76) f(x) = 4

x + 7

77) f(x) = x2 - 81

x2 - 6x - 27

Express the rational expression in lowest terms.

78)27m5p2

9m10p

79)y2 + 7y + 12

y2 + 8y + 15

Perform the indicated operation and express in lowest terms.

80)4p - 4

p ·

4p2

5p - 5

81)k2 + 13k + 40

k2 + 14k + 48 ·

k2 + 6k

k2 + 9k + 20

82)z2 + 5z + 6

z2 + 7z + 10 ÷

z2 + 3z

z2 - 2z - 35

83) 5

11x +

5

11x

Add or subtract as indicated. Write the answer in lowest terms.

84)3

r +

6

r - 2

85)x

x2 - 16 -

4

x2 + 5x + 4

Simplify the complex fraction.

86)

x

5

7

x + 5

87)

4 + 2

x

x

3 +

1

6

7

Without actually solving the equation, identify the vertical asymptotes and state the domain.

88)12

x - 1 -

2

x + 3 = 0

Solve the equation.

89) 1 + 1

x =

72

x2

90)2

x - 3 +

3

x =

-9

x2 - 3x

91)x

2x + 2 =

-2x

4x + 4 +

2x - 3

x + 1

92)2

7x +

1

2x = -

1

14

Solve the problem.

93) If m varies directly as p, and m = 24 when p = 3, find m when p is 6.

94) If x varies inversely as y2, and x = 3 when y = 8, find x when y = 4.

95) The intensity of a radio signal from the radio station varies inversely as the square of the distance from the

station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the intensity be at a distance of

11 miles? Round your answer to the nearest unit.

8

Answer KeyTestname: SEMESTER EXAM REVIEW SHEET

1) (-6, 9)

2)17

5

3) 2a - 13

4) 12, -13, 0, 0

1, 16

5) -4

6) {6, 8, 10, ...}

7) 6(x - 1)

8) {-4}

9) {1000}

10)12

49

11) 68 km/hr

12) No

13) True

14) p = 9s - 8

8 - t or p =

-9s + 8

t - 8

15) h = S - 2πr2

2πr

16) - 5

7

17) Slope: - 2

3

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

18) Perpendicular

19) Not a function

9


20) (2, 0); 0, - 2

3

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

21)15

2,

9

2

22) - 5

23) y = 2x - 14

24) 13x + 2y = 8

25) y = 7

5x +

67

5

26) {(0, 0, 1)}

27) {(1, 4)}

28) {(1, 9)}

29) Trinomial; 6

30) -x5 - 18x4 + 48x - 25

31) Monomial; 2

32) 12x14y3

33)1

x6

34) 15x7 + 18x6 + 2x5 + 10

35)81w28

x4

36)34

x28

37) x - 3

38) -x3 + 9x2 - 2x + 9

39) 729y3 - 343

40) 4x2 + 20x + 24

41)1

27p3

42) r2 - 10r + 25

43) -6 + 6

x3

10


44) 100r2 - 9

45) 2y2 + 3y - 1

46)12r - 6

r(r - 2)

47)3(5x + 21)

70x2

48)x2 - 4x + 20

(x - 4)(x + 4)(x + 1)

49)z - 3

z

50)32p

5

51) {-7, 6}

52) {10, -12}

53)17

6

54) (4r + 3y)(5r - x)

55) (a + x)(3 - a)

56) (3x + 2)(2x + 3)

57) 2(x - 4)(x + 5)

58) 3w(3x - 5y - 4z)

59) (3z + 2)(5z - 2)

60) 3x(x - 2y)(x + 4y)

61) (5x + 2)(5x - 2)

62) (6y2 + 7)(6y2 - 7)

63)10

3, 0

64) -6, - 10

3, 0

65) (4r + 5y)(9r - x)

66) (4x + 3)(3x + 2)

67) (x + 9)(x - 10)

68) 2(x - 8)(x + 3)

69) (7x - 9y)2

70) (2z + 3)(3z - 2)

71) 2x(x - 4y)(x + 5y)

72) (6x + 5)(6x - 5)

73) Prime

74) 9

7, 0

75) -6, - 10

3, 0

76) -7

77) -3, 9

11


78)3p

m5

79)y + 4

y + 5

80)16p

5

81)k

k + 4

82)z - 7

z

83)10

11x

84) 9r - 6

r(r - 2)

85)x2 - 3x + 16

(x - 4)(x + 4)(x + 1)

86)x(x + 5)

35

87)12

x

88) 1, -3

89) {-9, 8}

90) ∅

91) {3}

92) {-11}

93) 48

94) 12

95) 264 units

12

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Semester Exam Review Sheet - triadk12.org Exam Review... · College Readiness Math Semester Exam Review Write the set using interval notation and graph the inequality on the number