This is the summer math packet for students entering Algebra 3 and Trig next
year. Unless you register within two weeks of the beginning of the school year
you are responsible for understanding how to do these problems before school
starts in fall. This will be collected the first day back and graded and there will be
a test over the material the first week of school.
If you have questions about how to work the problems, google for video clips that
cover the individual topics. If you are still confused email me, and we can get
together before school starts to figure out the problems. They should all be
review but I know you learned some of the concepts a long time ago.
I hope you have a wonderful summer!
Denise Kendrick ([email protected])
1. Classify the number –48 as rational or irrational.
2. Classify the number
29 as rational or irrational.
3. Classify the number as rational or irrational.
5.3787719
4. Classify the number 15 as rational or irrational.
4
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5. Classify the real number as rational or irrational.
8.642642642
6. Approximate the number 7.3737 to three decimal places by rounding.
7. Simplify by using the order of operations.
39 – 17 + 44
8. Simplify by using the order of operations.
2+9 • 6–2
9. Simplify by using the order of operations.
–8 • (8 + 8) + 5 • (5 – 4 ÷ 2)
10. Simplify the following using the order of operations.
2x – (–7y) + 4z
11. Simplify.
−92
(−3)(2)
12. Expand.
−10(6r − 3s)
13. Add the fractions and simplify.
4 1
+
5 9
14. Subtract the fractions and simplify.
9 1
−
8 9
15. Multiply the fractions and reduce to lowest terms.
3 6
⋅
7 7
16. Divide the fractions and reduce to lowest terms.
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1 5
÷
6 18
17. Approximate the number 3.205811 to three decimal places by rounding
18. Simplify by using the order of operations.
–2 • (–4 + 3) + 3 • (–4 − 2 ÷ 2)
19. Subtract the fractions and simplify.
5s 9s
−
–3 2
20. Evaluate the algebraic expression for the specified values.
x –µ
for x = 380, µ = 140, s = 10
s
21. Simplify r4 ⋅ r7 using properties of exponents. Express in terms of positive exponents.
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22. Simplify (4s4)2 using properties of exponents. Express in terms of positive exponents.
23. Simplify 8z–4z8
24. Simplify (2e–3f 8)–2 using properties of exponents. Express in terms of positive
exponents.
25.
( 6hk )
5
( −3hk )
4
Simplify
26. Express 22,800,000 in scientific notation.
27. Express 0.00077878 in scientific notation
28. Write 8.7 × 102 as a decimal.
29. Write 8.5 × 10–5 as a decimal.
30. Simplify –4q8q–6 using properties of exponents. Express in terms of positive exponents.
32. Name the coefficient(s), variable(s), and degree of the monomial 5x9.
33. Name the coefficient(s), variable(s), and degree of the monomial 4x3z5.
34. Determine whether –6 is a polynomial or not. If it is, state the degree.
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35. Determine whether –3x7 + 12 is a polynomial. If it is, state its degree.
36. Determine whether –4x7y2 – 15 is a polynomial. If it is, state the degree.
37. Subtract the polynomials and express your answer as a single polynomial in standard
form,
8z9 – 2(z9 – 10y + 4)
38. Add the polynomials and express your answer as a single polynomial in standard form.
(–5r3 – 4sz4 + 5y + 2) + (–7r3 – 8sz4 – 7y + 3)
39. Subtract the polynomials and express your answer as a single polynomial in standard
form.
(6q4 – 9ab10 + 9x – 5) – (–9q4 + 6ab10 – 9x + 3)
40. Multiply the monomial by the trinomial and express your answer as a single polynomial
in standard form.
8m6(5m8 – 10n7 – 5)
41. Multiply the binomial by the trinomial and express your answer as a single polynomial in
standard form.
(6m – 9)(4m2 – 8m + 8)
42. Multiply the binomials using the FOIL method and express your answer as a single
poylnomial in standard form.
(x + 1)(x + 9)
43. Mulitply the binomials using the FOIL method and express your answer as a single
polynomial in standard form.
(z + 1)(z – 3)
44. Multiply the binomials using the FOIL method and express your answer as a single
polynomial in standard form.
(r – 8)(r – 9)
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45. Multiply the binomials using the FOIL method and express your answer as a single
polynomial in standard form.
(2s + 4)(3s – 6)
46. Name the coefficient(s), variable(s), and degree of the monomial –5r9s2.
47. Add the polynomials and express your answer as a single polynomial in standard form.
(2x9 + 2yx9 + 3wx2 – 3x) + (4x9 – 12yx9 + 5wx2 + 14x)
48. Multiply the binomials using the FOIL method and espress your answer as a single
polynomial in standard form.
(7z + 3)(z + 8)
49. Factor the common terms out of the polynomial 35z + 7
50. Factor the common term out of the polynomial e12 – 8e.
51. Factor the common term out of the polynomial 5x9 – 15x.
52. Factor the common term out of the polynomial 2t9 + 8t8 – 10t7
53. Factor the polynomial completely
x2 + 2x – 63
54. Factor the binomial completely
k2 – 81
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55. Factor the trinomial completely.
x2 + 4xy – 21y2
56. Factor 4b6 – 16b5 – 180b4 into a product of three polynomials.
57. Factor r3 – 25r into a product of three polynomials.
58. Factor the common term out of the polynomial 57t3 – 57t2 + 39t
59. Factor the binomial n2 – 1 completely.
60. Factor d3 – 64d into a product of three polynomials.
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