Ch1 Test Key

Algebra Fall, 2009

Test: Fundamental Rules of Algebra

Name: Mr. Hershman

Part I. (18 points) Solve each of the problems without a calculator, show all work, and provide verbal explanations to support your answers. 1. Evaluate

5(3x+2) 3÷4

+

2÷3 2(x−1)

Solution: The answer is

for x = 3. 147 2

= 73 21 .

2 pts

2. Respond to each statement in complete sentences. ?

(a) There is an associative property of subtraction: a − (b − c) = (a − b) − c Solution: No. Substitute a = 3, b = 2, c = 1, 3 − (2 − 1) 6= (3 − 2) − 1. 2 6= 0.

4 pts

(b) There is a commutative property of multiplication: cat = act Solution: Yes. For example if c = 3, a = 2, and t = 1, then 3 · 2 · 1 = 2 · 3 · 1 because 6 = 6. Multiplication can be done from left to right or right to left. It is commutative. 3. Justify each step shown below by the Associative, Commutative, or Distributive Property. You may also use Substitution or any of the Properties of Equality (such as the Addition Property of Equality). 4(x + 3) = 10 2÷3 4x + 12 = 10 2÷3

Given

3 · (4x + 12) = 10 2 20 4x + 12 = 3 16 4x = − 3 4 x=− 3

(1) (2) (3) (4) (5) (6)

4. Simplify 3x + 2x(3x + y) + 4(x − 2y) Solution: 3x + 2x(3x + y) + 4(x − 2y) 3x + 6x2 + 2xy + 4x − 8y 6x2 + 3x + 4x + 2xy − 8y 6x2 + 7x + 2xy − 8y

2 pts

2 pts

(7) (8) (9) (10)

Algebra/T1

– Page 2 of 2 –

Name:

?

5. Does 3x + 2x2 = 5x3 ? Clearly explain your answer Solution: No. Choose a value for x and compute, unless x = 0 or x = 1, it will not be true.

2 pts

6. What is the difference between (xy)2 and xy 2 ? Solution: In the first we multiply before applying the exponent, and in the second the exponent precedes the multiplication so (xy)2 = xy · xy and xy 2 = x · y 2 . Substitution would be an easy way to demonstrate the difference.

2 pts

7. 5 13 + 3 52 Solution:

2 pts

5

6 11 5 +3 =8 15 15 15

(11)

Which cannot be simplified. 8. What is 56 of 2 23 ? Solution:

2 pts

5 4 20 2 5 8 · = · = =2 6 3 3 3 9 9

(12)

9. Johnny waited 5 23 minutes longer than Shane. And Alexandra waited 3 14 minutes less than Shane. How many minutes longer did Johnny wait then Alexandra? Solution: Johnny waited 5 minutes longer than Alexandra.

3 11 8 +3 =8 12 12 12

(13)

2 pts