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Chapter 1…. In a NUTSHELL!
1.1: Real Numbers
Classify each set of numbers as a type (natural numbers, whole numbers, integers, rational
numbers irrational numbers, real numbers…).
1. 1, 2, 3…
2. 0, 1, 2, 3, 4…
3. -3, -2, -1, 0, 1, 2
4. 2, 5.7218743829
5.
3 , 1.64, 
6. 4, 5, 6, 7, 8…
7.
8. 5
7
1.2: Polynomials
Evaluate the expression.


9. 54
10. (-2)5
2 
11.  
3 
13. 2 3  2 5
14. (3y)2(3y)3
15. 3872180
3
12. -42
3 
16. 2 
5 
3
`
Perform the indicated operationsand simplify.

17. (-3x + 2) - (4x - 3)
18. (1.4x3 – 1.2x2 + 3.2) – (-0.8x3 – 2.1x – 1.8)

19. (3x2)(2x3)
20. 2(3m – 1) – 3(-4m + 2n)
22. x  2x [x  (1 x)]
21. 2x[3x[2x – (3 – x)] + (x + 1)(2x – 3 )]
1.3: Factoring Polynomials
Factor the polynomial.

23. 2m2 – 11m – 6
24. 4a2 – b 2
25. x4 - 16y2
26. 2x3 + 6x + x2 + 3
27. ax2 – (1 + ab)xy + by2
1.4: Rational Expressions
Simplify the expression.
28.
28x 2
7x 3
29.
4 x 12
3x  9
30.
x2  x  2
x 2  3x  2
31.
x2  4
2x 2  x  6
Perform the indicated operations and simplify.



6x 3
8
 2
32.
32 3x
33.

k 2  
2k  3 k 2  6k  8

k 2  k  6 k 2  2k  8

34.

x
y

ax  ay by  bx
Chapter 1…. In a NUTSHELL!
1 1

x y
35.
1
1
xy
1.5: Integral Exponents

Simplify the expression, writing your answer using positive exponents only.
36. (2x-2y2)3
a 2b 2 2 1
38.  1 2  

3a b  

2u 2v 3 
37. 

 3uv 
1.6: Solving Equations
Solve the given equation.

39. 3x= 12

40. 0.4 – 0.3p = 0.1(p + 4)
41.
m 2 2 m3
 
m
m m3
1.7: Rational Exponents and Radicals
Write the expression in simplest radical form.
42.
16
3
43.
x3y5
4
1.8: Quadratic Equations

44. 16x 2 y 3

Solve using the quadratic 
formula.
45. 2x2 – x – 6 = 0

46. 4x= -2x2 + 3
47. 2.1x2 – 4.7x – 6.2 = 0
1.9: Inequalities
Find the values of x that satisfy the inequalities.
48. 6  x  2  4

49. (2x – 3)(x – 1)  0

50.

x 2
2
x 1
Chapter 1…. In a NUTSHELL!








1. Natural, real
2. Whole, real
3. Integers, real
4. Rational, real
5. Irrational, real
6. Natural, real
7. Irrational, real
8. Natural, real
9. 625
10. -32
11. 8/27
12. -16
13. 256
14. 243y5
15. 1
16. -54/125
17. -7x + 5
18. 22x3 – 12x2 + 21x + 50
19. 6x5
20. 2(9m – 3n – 1)
21. 22x3 - 20x2 - 6x
22. –x – 1
23. (2m + 1)(m – 6)
24. (2a – b) (2a – b)
25. (x2 – 4y)(x2 + 4y)
26. (2x + 1)(x2 + 3)
27. (x – by)(ax – y)
28. 4/x
29. 4/3
x 1
30.
x 1
x 2
31.
2x  3
1
32. x
2
k 1
33.
k 2
bx  ay
34.
ab(x  y)
yx
35.
xy 1
8y 6
36. 6
x
3
37.
2uv 2
38. 9a2b8
39. x= 4
40. p= 0
41. -3= 3; which is impossible. No solution.
42. 4 3 /3
43.
x 3 y 5 /2
44. 4xy y

3
45.  or 2
2

1
 46. 1  2 10
47.  0.93 or 3.17

48. (-4, 6)
3
49. x  1 or x 

2

50. x  0 or 1  x



