1. Add: (4cᶣ - 3cᶟ + 5c² + 15c-7) + (c⁵ + 10cᶟ +4c² -5c + 2) + (-7cᶣ +c² -5c - 5)
Group like terns together
C5-3c4+7c3+10c2+5c-10
2. Find the greatest common factor for the group of terms. -18a², 3aᶟ
3a2
3. Simplify by removing factors of 1. 3r²+3r ÷ 24r²+9r
4. Multiply: (b + g)(b² - bg + g²) Simplify your answer.
b3 – b2g +bg2 + b2g - bg2 +g3
b3 + g3
5. Identify the degree of each term of the polynomial and the degree of the polynomial.
-6xᶟ + 5x² + 5x + 3 give the degree of the first, second, third and fourth term and the degree of the polynomial.
It is a 3rd degree polynomial
1st term is 3rd degree
2nd term is 2nd degree
3rd term is 1st degree
4thterm is a constant
6. Solve: x² + 2x – 4 = 0 the solution is __it is prime____________.
7. Multiply: (-3x)²(2x²)²
36x6
8. Factor: 40 – 13r + r² or tell if the trinomial is not factorable.
R2-8r-5r+40
(r-5)(r-8)
9. Simplify by taking roots of the numerator and the denominator. Assume that all expressions under
radicals represent positive numbers. ᶟ√343x⁵ ÷ yᶟ or tell me that the root is not a real
X5/33431/3/y3
10. Add. Simplify if possible. 8z ÷ z² - 25 + z ÷ z – 5
11. Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the
function. F(x) = ¼(x + 1)² +3
Vertex= (-1,3)
Line of symmetry x= -1
Minimum point is (- 1, 3)
12. Divide and simplify 5x – 35 ÷ 6 + x-7 ÷ 10x
5x- +x-
6x- -
(6x- -)30x
150x2-21-175x
150x2 -175x-21
13. Rewrite the following expressions with positive exponents. (30xy) – 8/9
14. Divide: (42bᶟ + 9b² + 42b + 25) ÷ (6b + 3)
7b^2-2b+ 8
15. Multiply: (r + 1/4)(r + 1/3) Simplify your answer
r2
r2
multiply by 12
12r2+7r+1 factorize
(3r+1) (4r+1)
16. Convert to decimal notation. 8.49 · 10⁷
17. Jack usually mows his lawn in 5 hrs. Marilyn can mow the same yard in 3 hrs. How much time would it take them to mow the lawn together?
In one hour jack mows and Marilyn
Therefore both mow( )= =
Therefore both take 1
=1.875 hrs
18. If the sides of a square are lengthened by 7 cm, the area becomes 256 cm². Find the length of a side of the original square.
(x+7) (x+7) = 256
X2+14x+49=256
X2+14x-207=0
(X-9) (x+23)=0
Hence x= 9 , -23
Therefore the side of the square is 9 since distance measure can’t be negative
19. Factor completely: 7x⁸ - 42x⁷ + 49x⁶ (Type the answer in factored form)
7x6(x2-6x+7)
20. Solve: 5x² = 15 next, find the x-intercepts f(x) = 5x² = 15.
X2=3
X=
The x intercept is + , -
21. Use the quadratic form to solve the equation: x² - 5x = -10 (Give the solution set)
X2-5x+10=0
a=1
b=-5
c=10
The equation has no real roots since the square root of numbers less than one are not real
22. Simplify by removing factors of 1. t² - 81 ÷ (t + 9)²
(t- 9) (t+9)/ (t+9) (t+9)
(t-9) /(t+9)
23. Solve: 1/w = 9/w – ½
Multiply through by w
1=9-w/2
=8
Therefore w= 16
24. Express using a positive exponent: g-⁶ (that is a g with a negative 6 power)
25. Solve: a² + 3a – 10 = 0
a2+5a-2a-10=0
a(a+5)-2(a+5)=0
(a-2) (a+5)=0
The value of a = 2 ,-5
26. Find all numbers for which the rational expression is undefined. qᶟ - 6q ÷ q² - 16.
This is undefined only when the denominator is 0.
Therefore
Q=4
27. If a pro basketball player has a vertical leap of about 25 inches, what is his hang time? Use the hang-time function V = 48 T².
25=48T2 divide by 48
T2=25/48
T= =0.7217
28. Factor: s² + 16s + 64
S2+8s+8s+64
(s+8) (s+8)
29. Multiply: (3√6 - 6√3)(4√6 + 8√3)
72+72 -72 -144
30. Subtract the polynomials: (-11b² + 9b + 3) – (6b² + 3)
-11b2-6b2+9b-3+3
-17b2+9b
31. Use rational exponents to simplify: ⁵√x¹⁵
(X15)
X3
32. Find a polynomial for the perimeter and the area.
Perimeter is 2 (x+x+9)
= 2(2x+9)
= 4x + 18
The area is
=X(x+9)
=x2 +9x
33. Find the vertex, line of symmetry, the maximum or minimum value of the quadratic function,
and graph the function. F(x) = -2x² + 2x + 1. Find the x & y-coordinates of the vertex.
Vertex = (0.5 , 1.5)
X coordinates for the vertex is 0.5
The area isLine of symmetry is x=0.5
Maximum value is (0.5, 1.5)
the value f(1/2) = 3/2 is maximum
34. Multiply: (9x + 5)(5x² + 4x + 6)
BODMAS
45x3 + 61x2 +74x+30
35. Multiply and simplify. Assume variables represent nonzero real numbers. y¹⁸ · y°
Y0=1
Therefore y18x1 =y18
36. Factor completely: 9w² - 16
The area is
3w(3w-4)+3w(3w-4)
(3w-4) (3w+4)
37. Use rational exponents to write x⅕ · y⅓ · z⅟9 as a single radical expression.
The area is
38. Simplify by factoring. Assume that all expressions under radicals represent nonnegative
numbers. √48a²b
161/2*31/2 a1b1/2=4a(3b)1/2
39. Multiply and simplify. 16x² ÷ 2x² -12x + 18 · 2x – 6 ÷ 4x
BODMAS
8x2-12x+36x-(2/3x)
8x2+24x-(2/3x)=(24x3+72x2-2)/3x
40. For the following equation, state the value of the discriminant and then describe the nature of the
solutions. 5x² -5x + 6 = 0 State the value of the discriminant, and then tell me if it has one solution, two imaginary solutions or two real solutions.
The area is
+++++++*+++++++++++
The discriminant
b2-4ac=25-120=-95
41. Solve: b² - 6b -40 = 0
B2-10b+4b-40=0
(b+4)(b-10)
B=-4,10
42. Find the x-intercepts of the graph of the equation y = x² - 3x – 10.
X2-3x-10=0
X2-5x+2x-10=0
(x-5)(x+2)
5 ,-2
43. Factor completely. 100b² + 160bt + 64t²
4(5b+4t)2
44. Solve: 6xᶣ - 11x² + 3 = 0
6x4-9x2-2x2+3=0
(3x2-1)(2x2-3)=0
X2=1/3 ,x2=3/2
45. Rationalize the denominator. Assume that all radicals under radicals represent positive numbers. √u - √v ÷ √u + √v
(√u - √v)( √u -√v)/ (√u + √v) (√u - √v)
(U+v-√2uv)/(u+v)
46. Factor the trinomial. cᶟ - 2c² - 63c
C(c+7)(c-9)
47. Perform the indicated operations and simplify. V – 1 ÷ v – 8 – v + 1 ÷ v + 8 + v – 120 ÷ v² - 64.
BODMAS
v-(1/v)-8-v+(1/v)+8+v-(120/v2)-64
v-64-(120/v2)=(v3-64v2-120)/v2
48. Find the variation constant and an equation of variation where y varies directly as x and y = 80
when x = 10. The variation constant of K = ? The equation of variation is y = ?
Y=kx
80=10k
K=8
Y=8k
49. Find the following ²⁰√(-5)²⁰
(-5)20/20=-5
50. Evaluate the polynomial for x = 3. 3x² - 5x + 4.
3*32-5*3+4=16
51. Add. (2x² - 3xy + y² ) + (-8x² - 7xy - y²) + (x² + xy – 4y²)
The area is
2x2-8x2+x2-3xy-7xy+xy+y2-y2-4y2
-5x2-9xy-4y2
52. Subtract. Simplify if possible. 3 - z ÷ z – 2 – 5z – 6 ÷ 2 – z
3-2-(6/2)-(z/z)-6z=-3-6z
53. Multiply and simplify by factoring. Assume that all expressions under radicals represent non-
negative numbers. ᶟ√y⁷ ᶟ√81y⁸
(81 y15)1/3=y5ᶟ√81
54. What does it mean to refer to a 20 inch T.V. set or a 25 inch T.V. set? Such units refer to the
diagonal of the screen. A 15 inch R.V, set also has a width of 12 inches. What is it’s height?
Hyp2=opp2+height2
t
Heght=9
55. Solve: (x + 16)(x – 15)(x + 14) > 0
-16<x<-14 or x>15.
56. Subtract. Simplify by collecting by like radical terms if possible. 8√20 - 5√5
√5(8√4-5)=11√5
57. Solve: √7x + 46 = x + 4
√7x =x-42
7x=1764-84x+x2=0
X2-91x+1764=0
X2-28x-63x+1764=0
(X-28)(X-63)=0
X=28, 63
58. Solve for x. 4x(x – 5) – 5x(x – 4) = -1
4x2-5x2-20x+20x=-1
X2=1
X=1
59. Simplify: ᶟ√-1 ÷ 25
-1/25
60. Use the FOIL method to find the product. (2x² - 9)(x⁹ - 1)
61. Find the following. Assume that variables can represent any real number. √(a + 7)²
(a+7)2/2=a+7
62. Factor completely. 4r² + 49 – 28r
(2r-7)2
63. Rewrite with a rational exponent. ⁷√21 = . 14√212
64. Divide and simplify. t⁸ ÷ t¹¹ =
1/t3
65. with a quadratic equation in the variable x having the given numbers as solutions. Type the
equation in standard form, ax² + bx + c = 0. Solution 10, only solution.
(x-10)(x-10)=x2-20x+100
Therefore the equation is x2-20x+100=0
66. In a right triangle, find the length of the side not given. B = 1, c = √10. The length of the third
side is what?
A2+b2=c2
A2=10-1=9
A=3
