Download Simplify - Magoffin County Schools

Standard form is writing the polynomial from the highest exponent to the lowest exponent.
Degree of the polynomial is the highest exponent from all terms
a) Write each polynomial in standard form:
b) Give the degree of each polynomial
1. x + x2
2. 3n2 + 6 - 5n
3. 8 - 2x3 + 4x2
4. 2 + x2 + 4x
5. 6 + 7x
6. 7 - 8a2 + 6a3
7. y3 - 4y + 6 - y2
8. x2 + 4 - x
9. x2 = x4
10. 3m - 7m3 + 3
11. 5a + 7a4 - 6a2
12. 6x3 + x + x2
13. 6 + x2 - 4x
14. x3 - 8 + 6x
15. y2 - 7y - 3y3
16. x - 6x2 + 9
17. 6x + 8x3 - 2x2
18. 12x2 - 6x3 + 7 + x
Adding and Subtracting Polynomials
Add only like terms which have the same letter and exponent
Rewrite all like terms under each other
Change all the signs in parentheses after a subtraction sign only
Simplify:
1. 2y + (4y - 3)
2. 3k + (2k + 4)
3. 9m + (-2m - 7)
4. (2x2 - 1) + (3x2 + 7)
5. (5a2 + 3) + (-7a2 - 4)
6. (2y - 3) + (4y + 5)
7. (2x2 - 3x + 5) + (4x2 + 6x - 8)
8. (a2 - 2a + 1) +(a2 - 4)
9. (3x) - (2x)
10. 2k - (2k + 4)
11. 6x - (2x + 7)
12. (7x - 5) - (5x + 3)
1
13. (10 - 2k) - (7 - 3k)
14. (z2 – 3z + 10) – (z2 + 5z – 6)
15. (8p2 + 5) – (3p3 - 3p2 + 2p – 9)
16. (2a2 – 3a + 5) – (a2 -2a – 4)
17. (11m3 + 3m2 - m) - (-6m3 + 3m2 + 4m)
18. (3d3 - 10d2 + d + 1) + (5d3 + 2d2 - 3d – 6)
19. Find the perimeter of triangle ABC.
20. Find the perimeter of quadrilateral ABCD.
21. Find the sum of the perimeters of triangle
ABC and Quadrilateral ABCD.
22. Subtract the perimeter of Triangle ABC from
the perimeter of quadrilateral ABCD.
Find each sum or difference and write your answer in standard form:
1. (3x2 - 4) + (5x2 + 8)
2. (5x3 + 6x2) + (x3 - 12x)
3. (5x2 + 4x + 8) - (3x2 + x + 3)
4. (8x2 - 4x + 1) - (3x2 + 6x - 4)
5. (4y2 - 3y + 8) + (6y2 + 6y - 9)
6. (a3 + 8a2 + 6a) + (8a3 + 2a2 - 6a)
2
7. (7y3 + 2y - 7) - (2y3 + y + 3)
8. (n3 + n2 + n) - (2n3 + 3n2 - 2n)
9. (7y2 + 8y + 1) + (y2 - 5y - 3)
10. (9x2 + 3x + 4) + (2x2 - 9x
11. (3a + 4a3 - 8) + (a2 + 2a - 7)
12. (2x3 + 6x - 7) + (3x2 - 9x - 5)
13. (x3 + 3x2 - 4x) - (2x2 + 3x + 1)
14. (4x2 - 7x + 8) - (2x3 + 8x - 5)
15. (3c2 + 4c - 6) - (3c + 8)
16. (2y3 - 7y + 10) - (y3 + 6y - 7)
17. (3x - 7x2 - 3) + (x2 + 5x)
18. (3y3 + 8y2 - 3) + (2y - 5y2)
19. 5a2 + 7a - 11) + (a + 4 - 5x2)
20. (6 - 8x) + (7x3 + 2x + 15)
21. (2x - 10x2 + 7) - (x2 + 8)
22. (3x3 - 10x + 8) - (2x2 + 7x + 8)
23. (x2 - 3 + 7x) - (-2x3 + 3x2 - 7x)
24. (6x3 - 9 + 8x) - (2x2 + 6x - 11)
25. (9 - 5x3 - 6x2) + (x + 6x2 - 4)
26, (x + 3x2 - 4x3 + 6) - (x3 + 3x2 - x)
3
- 5)
Multiplication
1st Multiply the coefficients
2nd Add the exponents of the different letters
Simplify each expression:
1. a ∙ a ∙ a
2. y2 ∙ y ∙ y3 ∙ y
3. 2c2 ∙ c
4. b2 ∙ b3
5. r3
6. (-t2)(-t6)
7. (-x3)(-x3)
8. (2x)(3x2)
9. (3ab)(5a2b)
10. r2(3rs5)
11. (-2pq)(-p2q)
12. (-2xz)(4x2y)
13. x(xy)(x2y)
14. (2r)(3st)(rst)
15. 2x3(-3xy2)(-x3y4)
16. wz2(-w3yz)(yz2)
17. x ∙ xn
18. yn ∙ yn
19. a2 ∙ an
20. t2n ∙ tn
1. (2a)(3b)
2. (-4m)(-3n)
3. (6k)(-2m)
4. (3x)(-3z)(2)
5) (-2k)(-3p)
6. (-6a)( b)
7. (2c)(3.5d)
8. (-3p)((-4.1r)
9. (2a)2
10. (3m3)2
11. (7y)(y4)2
12. (5b3)(-2b)
13. (4p4)(-6p)2
14. (-3a2)(-2a3)
15. (5k4)(-3k2)
16. (2p)2(-4p3)
17. 4x2)3
18. (2y4)2
19. (-2d2)3
20. (-3x2)2
21. (2a2b3)(6ab2)
22. (-3x3y3)(-4xy2)
23. ( p3r3)(9p2r)
24. (2c)2(3b3)
25. (2a2)2
26. 2(a2)3
27. (-3x2)3
28. (2p2r3)(5pr2)2
r5
- 2
Multiply:
4
29. (-4b4)3
30. 3(-3x2y)(xy6)
31. (a2b3)(12x3y)
32. ( -6xy3)2
Simplify:
1. 2x(x + 3x2)
2. -4(-y + 2y2)
3. 2a(3a + 1)
`
5. 2(a2 + 5a - 1)
6. -2m(m3 - 3m - 4)
7. -3(f2 - 2f - 8)
8. 4p(p2 - 3p - 2)
9. –r(r3 - 9r + 6)
10. a(4 - a -5a2)
11. 2x(2x3 - 4x + 3)
12. 4a2(-a2 - 3a + 9)
13. 4x + 2(x + 1)
14. 4(a - 3) - 3a
15. -2p - 2(p - 3) + 6
16. 4(2a - b) - 3(a + b)
17, 4(m - 1) + 3(m + 5)
18. 4a(2b - a) - 3a(2b + a)
19. 4xy(4x2y - 3xy2 + 7y2)
20. -2rs(r3 - 3r2s + 5s2)
21. 3(x - y) - 2(x - y)
22. 2x(x - 3) + 5(x2 - 2x)
23. 7(2x - y) - 2(x - 3y)
24. 2a2b(3ab - 7a2b2)
Division
1st Divide the coefficients
2nd Subtract the exponents of the different letters (cancel common factors)
`
Divide:
1.
-6xy
2y
2.
abc
-ac
3.
5.
24z6
6z2
6.
27x7y
3x2
7. -18x6
-9x3
5
8cd
-4cd
4.
12wz
3z
8.
-21a6b8
-3ab3
9.
4x + 8
2
13.
20cd
4d
10.
6y - 12
3
14. 18gh
2g
11. -14b + 21
7
12, 3y4 + 6y3 + 12y2
3y
15.
40ry
10r
16.
y3y2
y2x2
20. 12c2d3
-2cd2
-12ab
2a
17, -12pq
-3q
18,
-15st2
5st
19.
21.
2a + 12
2
22.
18y + 6
-6
23. 9a - 18b
9
25.
4x5 - 8x3 + 12x2
4x2
26.
32c - 16b + 4a
4
27.
28. 28x2y2 - 21xy2 + 14xy
7xy
29.
9a2b2c2 - 15abc2
3abc
30. 35c3d2e + 50c4d3e2
5cde
31. 25u2 - 15u - 5
-5
32.
9 - 6t - 3t3
3
33.
8a3 - 4a2 + 2a
2a
35. x3y - 2x2y2 + xy2
xy
36.
2u3v + 4u2v2 + 6uv3
2uv
34.
12x2 - 9x3 + 6x4
3x
37. 8z2xy - 12x2zy + 16zx2y3 - 24z2x3y3
4zxy
24. -25xy2 - 15xy2
-5xy
6x3 - 9x2 - 3x
3x
38. 56a4b4c3 - 49a3b3c2 + 35ab2c2 - 28a2bc4
-7abc
Simplify:
1. 7(2x2)(4y2)
2. 2(2x - 5) + 3 - 2x
3. 12 - 3(2x + 5)
4. (-4x2y)2
4. (2x3y2)(-3xy)(5x5y2)
6. -12x2y3
2xy
6
7. 2xy2(7x - 6y + 8)
8. 3(x + 2y) - 4(2x + y)
10. (m4n5)  (2m2n2)
11.
13. 12x - 4(2x + 3)
14. (5x - 6y) - (8x + 7x)
15. (5x - 6y) + (8x + 7x)
16. 2(x + 7) + 2(3 - 4x)
17. -5x2(2x2 + 8x - 6)
18.
19. 5a2b(2ab2 - 3b)
20. 2(4x + 7) - 13
21. -3(x - 5) + 2(3x - 7)
25x2 + 15x - 5
5
9. (3z2y)3
12. -2x(5x2y)(2x3)2
25a - 15b + 5c
5
22. (6y2 - 5y + 8) + (y2 + 6y - 10)
23. (a3 + 7a2 - 6a) + (8a3 + 5a2 - 3a)
24. (5y3 + 3y - 7) - (4y3 + 2y + 3)
25. (3n3 + n2 + n) - (2n3 + 3n2 - 9n)
26. 3x - 6 + 9 + 2x
27. 4x2 - 3x + 2x2 - 7x
29. 4(x - 5) + 3(3 - 4x)
30.
25x3 + 20x2 + 15x2
5x2
7
28.
7 - (4x + 7)
31. (2x)2(-3y)3
Simplify:
1. From 4x + 2y subtract x - 4y
2. Subtract 5a - 7b from 3a - 9b
3. From 5x2 + 5x - 4 subtract x2 - 3x + 5
4. Subtract 7r2 + 3r - 8 from 10r2 - 3r - 7
5. From m2 + 5m - 7 subtract m2 - 3m -4
6. From 12x - 6y + 9z subtract -x - 3z + 6y
7. Subtract 2x2 - 3x + 7 from x2 + 6x - 12
8. Subtract 5x + 4y - 6z from 3x - y - 8z
9. 5(d + 3) - 10
10. 3(2 - 3c) + 5c
11. 7 + 2(7x - 5)
12. -2(x - 1) + 6
13. -4(3 - 6a) - 7a
14, 5 - 4(3c - 5)
15. 8 + (4x - 6)
16. 9 - (5t + 6)
17. 5x(2x - 3) + 9x
18. (6b + 4) - 2
19. –(6x - 7) + 14
20. 4 - (2 - 8a)
21. 12y - 3y(2y - 4)
22. 7x + 3(2x - 1) - 8
23. 7c - 4d - 2(4c - 3d)
24. 3a - 2a(5a - 1) + 5a2
25. 4(2x + 5) - 3(2 - 7x)
26. (3y - 6) - (8 - 9y)
8
27. (4a - 3b) - (5a - 2b)
28. (2c + 3d) + (-6d - 2c)
29. (a - 2b) + (2a + 5b)
Multiplying Polynomials - Stapling
1st Draw your 2 staples and multiply
2nd Draw a line and add your two new terms
3rd Multipy the first terms
4th Multiply the last terms
Multiply:
1. (x + 3)(2x - 5)
2. (3w + 4)(2w - 1)
3. (x + 4)(x + 3)
4. (a - 11)(a + 5)
5. (3x - 4)(x - 5)
6. (4x + 3)(x - 7)
7. (5x - 3)(4x + 2)
8. (3y + 7)(4y + 5)
9. (3x + 7)(x + 5)
10. (5x - 2)(x + 3)
11. (a - 6)(a + 8)
12. (2x + 1)(3x - 1)
13. (k + 4)(3k - 4)
14. (y - 4)(2y + 3)
15. (x + 7)(x + 5)
16. (2x + 1)(4x + 3)
17. (6x - 5)(3x + 1)
18. (n - 7)(n + 4)
9
19. (5n - 1)(n + 4)
20.
(y + 9)(y - 11)
21. (4x - 7)(2x - 3)
22. (x2 + x - 1)(x + 1)
23. (x + 6)(2x2 - 6x - 8)
24. (3m2 - 7m + 8)(m - 2)
25. (x + 2)(2x2 - 3x + 2)
26. (a2 + a + 1)(a - 1)
27. (x - 2)(x2 + 4x + 4)
28.
(2n - 3)(n2 - 2n + 5)
29.
(3x + 1)(4x2 - 2x + 1)
30.
(2x2 - 5x + 2)(4x - 3)
31.
(2x2 - 9x + 11)(2x + 1)
32.
(x - 5)(x2 + 5x - 3)
33.
(2x2 + 5x - 4)(2x + 7)
10
34. (2x - 1)(x2 - 7x + 1)
35. (x - 5)(x2+ 2x + 5)
36. (x + 9)(x + 7)
37.
(3y - 7)(2y + 1)
38.
(x + 7)(x - 7)
39. (2x - 5)(2x + 5)
40. (3x + 5)2
41. (x - 10)2
42. (2x + 3)(x + 7)
43. (x + 12)(x - 12)
44.
(5x + 1)(5x - 1)
Simplify:
1. m2 + m - 6 + 3m -2
2. 5s + 2 - 5s - 7 + 4s
3. t4 + 3t3 - 2t4 + 3 + 2t3 - 1
4. 6x2 + 8x - 8 - 2x2 - 9x + 4
5. -3 + 16z2 - 8z3 + 5z2 + 11 + 4z
6. -7a - 3a2 + 8a + 12a2 - 9
7. 5x3 + 3x - 4 - 3x2 + 8x3 + 6 - 6x
8. 3y4 + 3y + 3y3 - y2 + y + y2
9. n2 + 3n + 4n2 + n3 - 3n3 + 2
10. 8r2 + 4r3 - 3r2 - r - 4r2
11. (4y3 - 2y2 + y) + (y3 - 2y2 + 44)
12. (4m2 + m - 3) + (2m2 + 7)
11
13. (6n2 + 4n + 3) - (3n2 - 5n + 1)
14. (5p3 + 2p2 - p + 4) - (2p3 - p2 + p - 1)
15. (4y2 + y - 5) + (3y2 - 5y + 6)
16. (8x2 - 4x + 2) - (5x2 - 3X + 4)
17. (4m2 - 3m + 3) - (2m2 - 3m - 3)
18. (5r3 - r2 - 5) + (-6r3 - r2 + 3)
x3
x
20. 12x2y
3xy
21.
23. (2a2)(5ab)
24. (5x2y3)2
25. (-4a2b)(7a5b3)
26. (2x)2(-5xy2)
28. 3x2(2x - 7)
29. -14x2y5
-7x2y2
30. 15x2 - 10x + 5
5
31. (-3ab)(4ab)
32. (2x)3
33. 3x2y(5x - 6y)
34.
35. 9 - 3x + 15 - x
36. 8x - 5y - x + 9
37. 5 - (2x - 8)
38. 3(2x + 5) - 10
19.
27.
15x2y + 10xy
5xy
-6m3n2
-3mn
22.
6x - 9y + 12
3
-15a2b2
-5ab
Zero Exponents - anything raised to the zero power is 1
Negative Exponents moves the term to the opposite location in a fraction with a positive exponent
Top becomes bottom
Bottom becomes top
Find the value
1. 70
2. 4 ∙ 50
3. (3 + 5)0
4. 5-2
5. (3 ∙ 4)-2
6. 3-2
7. 2-4
8. 10-1
9. 10-2
10. 70 + 6
11. 70 + 6-2
12. x0
12
13. (1 + 3)0
14. 10-3
15. 9-1
16. 90 + 40
17. -3 ∙ 50
18. 8-2
19. 50 + 3-2
20. 5-3
Simplify:
1. 8x-3
2. (2x)-4
3. -10c-3
4. (-2x)-3
5.
6.
7.
8.
1
4x-3
1
(4x)-2
3
5x-3
4
(3a)-3
9. a4b-3
c2d-4
10. x2y-4
z-3
11.
2a-2b5
3c3d-4
12.
13. x-2x5
14. a3a-6
15.
n-4n-2
16. y-3y0
a-3
a2
19.
6n-2
8n-6
20.
-2c-6
4c-4
2a5b-8
3cd-4
24.
2x-3
4y-3z-1
17.
x4
x-2
18.
21.
5a4b-5
10c2d-2
22. 9x-2y-4
3z3
23.
26. y(2x)-4
27. -10c-2
25. 8x-5y4
13
3x-5
4y-2z-1
28. (-2x)-2
Simplfy:
1. 6x + (5x - 8)
2. 2x - (9x - 4)
3. -9 - (12 - 3x)
4. –(5x + 5) - 4x + 8x
5. 7(2x - 4) - (10 - 3x)
6. -6(5 + x) + (13x + 1)
7. –(12 - 4x) + 8(10 - x)
8. 7(2x + 2) - 9(-1 + 6x)
9. 4(-3x - 5) - (10 + 4x)
10. 6x + (14x - 5) + (17 - 3x)
11. –(2 - x) - 3(6 + 8x) - 12
12. (4x - 9) + 8(2x + 3) - 7x
13.
14. 2(x + 2) -5(x - 2) - 12x + 7
11 - (3x - 6) + 2(4x + 5) + x
15. –(5y - 6) + 4(3 + 5y)
16.
17. 2(7 + 6y) + 15(y - 1)
18. 5(-3y - 1) - (6 - 5y) + 8
19. 4(3 + 7y) + 6(2 - y)
20. 7x - 4(6 - x) + 12
(-9y + 5) - 8(-y - 2)
Simplify:
1. (y + 5)(y + 7)
2. (c - 3)(c - 7)
14
3. (x + 4)(x - 8)
4. (w + 3)(w - 9)
5, (x + 5)2
6. (2x - 1)(x + 8)
7. (11y + 9)(12y - 6)
8. (8x + 9y)(3x + 2y)
9. (2r + 7)(3r + 5)
10. (7 - 5x)(7 + 5x)
11. (2x - 3)2
12. (6a - 1)2
13.
15 - (7x - 6) + 5(4x + 7) + x
14. -3(x + 2) + 6(x - 2) - 10x + 7
15. –(7y - 6) + 8(3 + 3y)
16.
17. -7(7 + 2y) + 5(y - 5)
18. 7(6y - 12) - (8 - 5y) - 23
19. (5y3 - 2y2 + y) - (y3 - 7y2 + 15)
20. (4m2 + m - 3) - (2m2 + 13)
21. (4n2 + 5n + 9) + (3n2 - 6n + 1)
22. (2p3 + 5p2 - p + 4) + (2p3 - p2 + p - 1)
23. (2y2 + y - 5) - (5y2 - 8y + 7)
24. (8x2 - 4x + 2) + (2x2 - 7x + 14)
25. (4m2 - 3m + 3) + (6m2 - 2m - 1)
26. (5r3 - r2 - 5) - (-6r3 - r2 + 3)
15
(-5y + 7) - 4(-y - 2)
x7
x2
28. 12x5y
2xy
29.
31. (7a2)(5ab)
32. (4x5y2)2
33. (-3a2b)(8a6b4)
34. (-3x)2(-2xy5)
36. 4x2(x - 8)
37. -28x2y4
-7xy2
38. 18x2 - 12x + 6
6
27.
35.
12x2y + 16xy
4xy
-63m4n3
-3mn
30.
10x - 5y + 15
5
Scientific Notation
.
x 10a
1st Have only one digit to the left of the decimal point all numbers are to the right and
the rest of the digits go after the decimal point to the right
2nd The exponent represents the number of times you moved the decimal point
If a is negative the number is a small decimal
If a is positive the number is a big number
1.
23, 000,000,000
2. .0000000000067
3.
458,000,000
4.
20,000,000
5. .00000098
6.
32,000,000,000,000
7. .00000000009
8. 210,000,000
9.
.00000000054
10. 9,000,000
11. .0000000012
12. .00000000000034
13. 68,500,000
14. 4,800,000,000
15. .0000000041
16. .00000805
17.
18. .00000065
19.
20. 7,800,000,000
21. .0000000091
23. .0000098
24. 34,000,000,000
.000000000005
22. 500,000,000
7,650,000,000,000,000
16
Write in standard form:
1. 2.3 x 106
2. 3.76 x 109
3. 3.5 x 10-6
4. 5.0 x 10-5
5. 4 x 10-4
6. 7.09 x 1012
7. 5.3 x 108
8. 2.16 x 107
9. 8.5 x 10-8
10 . 5.0 x 10-8
11. 7.9 x 10-6
12. 5.9 x 1010
13 . 1.35 x 107
14. 6.6 x 107
15. 3.9 x 10-7
16.
8.3 x 10-7
17. 7.3 x 10-5
18. 7.9 x 109
19.
7.3 x 108
20. 1.7 x 1012
21. 2.5 x 10-8
22.
5.23 x 10-3
23. 4.32 x 10-7
24. 7 x 1010
Multiplication –
1st
2nd
3rd
1.
Division -
Multiply the numbers
1st Divide the numbers
Add the exponents and rewrite it
2nd subtract the exponents and rewrite it
Rewrite as scientific notation
3rd Rewrite as scientific notation
(2 x 103)(4x104)
2. (6 x 105 )(7 x 10 6)
3. (5.5 x 107)(4.2 x 104)
4. (3.45 x 107) x (6.25 x 105)
5. (2.33 x 106) x (8.19 x 103)
6. 3.5 x 108 )x( 6.6 x 104)
7. (4 x 106)  (2 x 104)
8. (9 x 108)  (2 x 10 6)
9. (3 x 107)  (8 x 104)
10. (6.8 x 103) x (4.54 x 106)
11. (2.9 x 108) / (1.3 x 10 6)
12. (4.8 x 106)÷(1.2 x 103) .
17
14. (4.8 x 106)×(1.2 x 103)
15. 7.5 x 107 )x( 2.6 x 109)
17. (6.8 x 105 )(4.2 x 10 4)
18. (7.5 x 104)(4.9 x 106)
19. (6.5 x 108) x (6.8 x 106)
20. (7.33 x 109) x (8.9 x 109)
21. 2.5 x 108 )x( 8.6 x 107)
22. (4.3 x 108)  (3X103)
23. (9.5 x 1010)  (5 x 10 5)
24. (2 x 1012)  (8 x 105)
25. (5.8 x 104) x (6.54 x 104)
26. (6.9 x 108) / (1.7 x 10 8)
27. (6.0 x 108)÷(1.2 x 103) .
13. (4.3 x 105)(2 x 107)
16.
(2.8 x 103)(7X109)
1. 1. Which expression is
equivalent to
?
1)
2)
3)
4)
2. The expression
equivalent to
1)
2)
3)
4)
4. The product of
is
1)
2)
3)
4)
and
5. The expression
equivalent to
1)
2)
3)
4)
7. The product of
is
1)
2)
3)
4)
and
8. The product of
1)
2)
3)
4)
18
3. Which expression represents
in simplest form?
1)
2)
3)
4)
is
is
and
is
6. The product of
1)
2)
3)
4)
and
9. What is the product of
and
?
1)
2)
3)
4)
is
10. The expression
11. What is the product of
is
equivalent to
1)
2)
3)
4)
and
?
1)
12. The product of
1)
2)
3)
4)
and x is
2)
3)
4)
13. What is half of ?
1)
2)
3)
4)
14. What is one-third of
1)
2)
3)
4)
?
15. The quotient of
,is
1)
4)
16. The expression
is equivalent to
1)
2)
3)
,
1)
4)
4)
19. The expression
17. When
is
is divided by
, the quotient is
2)
3)
20. Which expression
represents
3)
is
equivalent to
1)
2)
in simplest
2)
3)
23. The expression
represents
1)
is
equivalent to
3)
4)
1)
4)
21. Which expression
2)
4)
22. The expression
in simplest
in simplest
form?
form?
1)
4)
3)
3)
18. Which expression
form?
1)
2)
represents
equivalent to
1)
2)
4)
2)
2)
3)
19
4)
24. Simplify:
3)
25. Which expression is
equivalent to
?
1)
2)
3)
4)
26, Expressed in simplest form,
is equivalent to
1)
2)
3)
4)
28. The expression
equivalent to
1)
2)
3)
4)
is
31. The expression
is
equivalent to
1)
2)
3)
4)
1. The expression
equivalent to
1) x0
2) 2
2x 2  x 2
3) x2
is
29. The product of
is
1)
2)
3)
4)
32. The expression
is
30. If
is
, then
equivalent to
1)
2)
3) 1000
4) 0
is
equivalent to
1)
2)
3)
4)
33. The expression
equivalent to
1)
2)
3)
4)
2. Which expression is equivalent to
-3x(x - 4) - 2x(x + 3)?
4) -2x4
and
27. The expression
equivalent to
1)
2)
3)
4)
1) -x2 - 1
2) -x2 + 18x
3) -5x2 - 6x
4) -5x2 + 6x
20
3. The sum of
and
can be expressed as
1)
2)
3)
4)
is
4. The sum of
is
1)
2)
3)
4)
7. What is the sum of
and
1)
2)
3)
4)
and
5. The sum of
is
1)
2)
3)
4)
and
8. The sum of
and
1)
2)
3)
4)
?
10. The expression
11. The expression
equivalent to
1)
2)
3)
4)
13. 13. When
from
1)
2)
3)
4)
9. What is the sum of
and
1)
2)
3)
4)
is
is
is subtracted
, the difference is
6. What is the sum of
and
?
1)
2)
3)
4)
?
12. The expression
is
equivalent to
1)
2)
3)
4)
is
equivalent to
1)
2)
3)
4)
14. When
is subtracted
from
, the difference is
1) 0
2)
3)
4)
21
15. When
subtracted from
difference is
1)
2)
3)
4)
is
, the
16. When
subtracted from
result is
1)
2)
3)
4)
19. Subtract
.
22. If
from
1)
2)
3)
4)
is
, the
from
is subtracted
, the result is
25. What is the product of
and ?
1)
2)
3)
4)
17. When
subtracted from
result is
1)
2)
3)
4)
is
20. When
subtracted from
result will be
1)
2)
3)
4)
is
23. When
subtracted from
result is
1)
2)
3)
4)
, the
, the
is
, the
26. What is the product of
and
?
1)
2)
3)
4)
22
18. If
from
1)
2)
3)
4)
is subtracted
, the difference is
21. When
subtracted from
result is
1)
2)
3)
4)
24. If
from
1)
2)
3)
4)
is
, the
is subtracted
, the result is
27. What is the product of
and
?
1)
2)
3)
4)
28. What is the product of
and
?
1)
2)
3)
4)
29. The expression
equivalent to
1)
2)
3)
4)
31. The expression
is equivalent
to
1)
2)
3) 3
4)
32. When
, the result is
1)
2)
3)
4)
34. When
divided by
1)
2)
3)
4)
is
, the quotient is
simplest form?
1)
2)
3)
4)
is divided by
35. The expression
33. What is
by ?
1)
2)
3)
4)
36. If
is
divided
, the expression
is equivalent to
1)
2) 2
3)
4) 4
38. Which polynomial is the
in
30. The expression
equivalent to
1)
2)
3)
4)
1)
2)
3)
4)
37. Which expression
represents
is
quotient of
?
1)
2)
3)
4)
23
39. Express in simplest form:
4 40. Which value of x makes the 41. For which value of x is the
expression
undefined?
1)
2)
3) 3
4) 0
expression
undefined?
1) 0
2) 2
3)
4) 4
42. For which value of x is the
expression
undefined?
1)
2) 2
3) 7
4) 0
43. For which value of m is the
44. For which value of x is the
45. For which value of x is the
expression
expression
expression
1)
2)
3)
4)
undefined?
1)
2) 2
3) 3
4) 0
1
0
3
-3
46. For which value of x is the
expression
1) 1
2)
3) 5
4)
undefined?
undefined?
undefined?
1)
2) 2
3) 0
4) 6
47. Which value of n makes the 48. For which value of x will the
expression
undefined?
1) 1
2) 0
3)
fraction
1)
2) 2
3) 0
4)
4)
24
be undefined?
49. For which value or values
of n is the expression
undefined?
1) 1, only
2)
, only
3) 1 and
4) 0
52. The algebraic expression
is undefined when x is
1)
2)
3)
4)
0
2
3
9
50. For which value of x is
51. The function
is
undefined when the value of x is
1) 0 or 3
2)
3) 3, only
4)
undefined?
1)
2) 0
3) 3
4) 4
53. Which value of x makes
the expression
54. For which set of values of x
is the algebraic expression
undefined?
undefined?
1)
2) 2
3) 3
4)
1)
2)
3)
4)
1. What is the product of
2. What is the product of 12 and
3. What is the product of
and
notation?
1)
2)
3)
4)
expressed in scientific
notation?
1)
2)
3)
4)
, and
in scientific notation?
1)
2)
3)
4)
written in scientific
25
,
expressed
5. The quotient of
4. What is the quotient of
and
1)
2)
3)
4)
and
expressed in scientific
notation is
1) 4,000
2) 40,000
3)
4)
?
7. What is the value of
in
scientific notation?
1)
2)
3)
4)
10. In 1995, the federal
government paid off one-third of its
debt. If the original amount of the
debt was $4,920,000,000,000,
which expression represents the
amount that was not paid off?
1)
2)
3)
4)
8. If the mass of a proton is
6. If
is divided by
, the result is
1) 1
2) 0.01
3)
4)
9. If the number of molecules in 1
gram, what is the mass
of 1,000 protons?
1)
g
2)
g
3)
g
4)
g
mole of a substance is
,
then the number of molecules in
100 moles is
1)
2)
3)
4)
11. Two objects are
12. The distance from Earth to
the imaginary planet Med is
miles. If a spaceship is
capable of traveling 1,420 miles
per hour, how many days will it
take the spaceship to reach the
planet Med? Round your answer
to the nearest day.
centimeters apart. A message
from one object travels to the other
at a rate of
centimeters
per second. How many seconds
does it take the message to travel
from one object to the other?
1)
2)
3)
4)
26