SOLUTIONS  P MATH 10 REVIEW FOR TEST #1

Exponents — radicals —polynomials

This review assumes that students have already thoroughly reviewed the content of the three papers and gone over their hand-in assignments.  A package of review material is available.

 

I Exponents

 

Rewrite using a positive exponent:

 

2-5 = 1/25

Write as a power of 10

1 000 000 = 106

 10-2 or 1/102

Find the product:

35a15

Find the quotient (use positive exponents):

9/w12

Simplify as far as possible:

1/76

 

1/a8

5/6

 

1

125/27

Simplify:

A5/B5

-27p3q6

 

II Radicals

 

 

2ึ3

 

 

7ึ5/10

7ึ2

 

2a2bึ7b

2x3y4 3ึ7x

 

1/32                     

3ึ2

 

8ึ10 + 16ึ35

 

 

54 + 16ึ15

 

-360

 

III Polynomials

 

 

12xy – 5xy + 2xy = 9xy

17a – 24b – 22a + 19b = -5a-5b

(3a – 2b) – (5a + b) = -2a – 3b

-20p3q4

 

 

8ab

(3y2 – y – 6) – (2y2 + 5y –7) =

 

5(a+7b) =  5a + 35b

 

 

3x(9y – 3c + 3) = 27xy – 9xc + 9x

 

3x(2x-3) + 2x(x+4) = 8x2 – x

 

 

(x+7)(x–2) = x2 + 5x – 14

 

 

=  -4a + 2a2b2 + 3a3

 

Special products:

(x+2y)2 = x2 + 4xy + 4y2

(2x – 7)2 = 4x2 – 28x + 49

(2x + 3)(2x – 3) = 4x2 – 9

 

 

–5(3a + 5)2 =

 

-5(9a2 + 30a + 25) =

 

-45a2 – 150a – 125

 

 

 

Long Division—do the following by long division and check by multiplying: