1) Simplify: (answers must have only positive exponents.)

 a) 5a 3 x 4 b) y 2 z 2 c) 1 d) (8x12 )/ y 9 e) f) (12n 8 y 4 )/m 2 g) 1 h) 12m 3 i) 1/mn2

.

2) Evaluate these expressions :

 a) b) c) y 5 / (11x 8 ) d) e) f) x3 g) –30 h) i) 25

.

3) Multiply or divide these expressions and collect like terms :

 a) 6x2 + x – 15 b) –12x2 + 4x + 8 c) 4x2 – 14x3 – 8x4 d) 5x3 – x2 – x e) 4x7y + 2x –2 y4 – 1 f) 2x2 –3x + 50 g) – x6 + 4x3 – x2 – x – 1

.

4) Solve these equations :

 a) 4(x + 7) + 12(x – 1) = 6 4x + 28 + 12x – 12 = 6 16x = – 10 therefore x = – 5/8 multiply through by – 6, the lcm of – 3 and 2expand the brackets,collect like terms and solve for x. b) 14(2x) + 10(3x) = 35x – 70 28x + 30x – 35x = – 70 23x = – 70 therefore x = –70/23 multiply through by 70, the lcm of 5, 7 and 2expand the brackets, transpose 35xcollect like terms and solve for x. c) 2x – 5 = 2(8 – x) 2x – 5 = 16 – 2x 4x = 21 therefore x = 21/4 = 5.25 multiply through by 6expand the brackets,transpose – 2x and – 5, collect like termssolve for x. d) 2x(x –7) + 3(x 2 – 4x + 2) = 5(5 + 5x + x 2)2x² – 14x + 3x² – 12x + 6 = 25 + 25x + 5x²2x² + 3x² – 5x² – 14x – 12x – 25x = 25 – 6 – 51x = 19 therefore x = –19/51 expand the bracketstranspose variables,constants, collect like terms,solve for x.

5) Solve these word problems with a chart for all and a diagram where needed :

a)
 coin number value nickels 2x 5(2x) dimes x 10x quarters 3x/2 25(3x/2)

since # of nickels = 2x
then if q is the # of quarters, 4q = 3(2x)
so q = 3(2x)/4 = 3x/2
5(2x) + 10x + 25(3x/2) = 230
10x + 10x + 37.5x = 230
57.5x = 230, which makes x = 230/57.5 = 4
There are 8 nickels, 4 dimes and 6 quarters.

.

b)

 item amount unit price value almonds 100kg 2.25 2.25(100) cashews 400kg 1.90 1.90(400) mixture 500kg x 500x

2.25(100) + 1.90(400) = 500x
225 + 760 = 500x becomes 985 = 500x, therefore x = \$1.97
The mixture should sell for \$1.97/kg.

.

c)

 item amount unit price value pistachios 200kg 3.50 3.50(200) peanuts x 1.00 x mixture 200 + x 2.20 2.20(200+x)

3.50(200) + x = 2.20(200+x)
700 + x = 440 + 2.20x
260 = 1.2x x = kg.
He will use kg. of peanuts.

.

d) Mike's father's age is now 5 times Mike's age. Five years ago, Mike's father was 10 times as old as he was then. How old are they now?

 person age now age 5 yrs. ago Father 5x 5x – 5 Mike x x – 5

5x 5 = 10(x 5) 5x 5 = 10x 50
45 = 5x x = 9
Mike is 9 years old and his dad is 45.

.

e)

 person dist. rate time Ryan 120x 120k/h x Norman 130x 130k/h x

120x + 130x = 600 250x = 600
x = 2.4 hours. d = 2.4 (120) = 288 km
They meet after 2.4 hours at a distance of 288 km from Toronto.

.

f)

 class \$ frequency cumulative frequency relative frequency % midvalue subtotal [15, 25[ 2 2 5.7 % 20 40 [25, 35[ 10 12 28.6 % 30 300 [35, 45[ 12 24 34.3 % 40 480 [45, 55[ 6 30 17.1 % 50 300 [55, 65[ 5 35 14.3 % 60 175 total 35 35 100 % 1,295

mean = 37
[35, 45[ both median and modal class.

.

(all content of the MathRoom Lessons © Tammy the Tutor; 2004 - ).