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Algebra and Trigonometry

Review Exercises

Algebra and TrigonometryReview Exercises

Review Exercises

Real Numbers: Algebra Essentials

For the following exercises, perform the given operations.

1.

(532)26

2.

64÷(28)+14÷7

3.

252+6÷2

For the following exercises, solve the equation.

4.

5x+9=−11

5.

2y+42=64

For the following exercises, simplify the expression.

6.

9(y+2)÷32+1

7.

3m(4+7)m

For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.

8.

11

9.

0

10.

56

11.

11

Exponents and Scientific Notation

For the following exercises, simplify the expression.

12.

2224

13.

4543

14.

(a2b3)4

15.

6a2a02a−4

16.

(xy)4y32x5

17.

4−2x3y−32x0

18.

(2x2y)−2

19.

(16a3b2)(4ab−1)−2

20.

Write the number in standard notation: 2.1314×10−6

21.

Write the number in scientific notation: 16,340,000

Radicals and Rational Expressions

For the following exercises, find the principal square root.

22.

121

23.

196

24.

361

25.

75

26.

162

27.

3225

28.

8081

29.

491250

30.

24+2

31.

43+63

32.

125135

33.

5−243

34.

32503−8

Polynomials

For the following exercises, perform the given operations and simplify.

35.

(3x3+2x1)+(4x22x+7)

36.

(2y+1)(2y22y5)

37.

(2x2+3x6)+(3x24x+9)

38.

(6a2+3a+10)(6a2−3a+5)

39.

(k+3)(k6)

40.

(2h+1)(3h2)

41.

(x+1)(x2+1)

42.

(m2)(m2+2m3)

43.

(a+2b)(3ab)

44.

(x+y)(xy)

Factoring Polynomials

For the following exercises, find the greatest common factor.

45.

81p+9pq27p2q2

46.

12x2y+4xy2−18xy

47.

88a3b+4a2b144a2

For the following exercises, factor the polynomial.

48.

2x29x18

49.

8a2+30a27

50.

d25d66

51.

x2+10x+25

52.

y26y+9

53.

4h212hk+9k2

54.

361x2121

55.

p3+216

56.

8x3125

57.

64q327p3

58.

4x(x1)14+3(x1)34

59.

3p(p+3)13−8(p+3)43

60.

4r(2r1)235(2r1)13

Rational Expressions

For the following exercises, simplify the expression.

61.

x2x12x28x+16

62.

4y2254y220y+25

63.

2a2a32a26a85a219a410a213a3

64.

d4d29d3d216

65.

m2+5m+62m25m3÷2m2+3m94m24m3

66.

4d27d26d217d+10÷8d2+6d+16d2+7d10

67.

10x+6y

68.

12a2+2a+13a2−1

69.

1d+2c6c+12ddc

70.

3x7y2x

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