GRADE 9 REVIEW SOLUTIONS

A/ EXPONENTS AND RADICALS :

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

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2) Evaluate these expressions :

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

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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

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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 2 expand 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 2 expand the brackets, transpose 35x collect 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 6 expand the brackets, transpose – 2x and – 5, collect like terms solve for x.
d) 2x(x –7) + 3(x 2 – 4x + 2) = 5(5 + 5x + x 2) 2x² – 14x + 3x² – 12x + 6 = 25 + 25x + 5x² 2x² + 3x² – 5x² – 14x – 12x – 25x = 25 – 6 – 51x = 19 therefore x = –19/51	expand the brackets transpose 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.

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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.

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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.

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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.

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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.

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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.

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