| GRADE 9 REVIEW |
These topics are covered in this review.
| A. Exponents and Radicals |
| B. Algebra: Multiplying and Dividing |
| C. Solving Equations |
| D. Solving Word Problems |
| Mathtub Index |
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A/ EXPONENTS AND RADICALS :
1) Simplify: (answers must have only positive exponents.)
| a) (– 5)(– ax2 )(– ax)2 | b) (y –1 z –1) –2 | c) ( x – z y – z ) 0 | d) (2x4y –3z 0) 3 |
| e) (121a 4 b – 2 c 0 d – 5 ) ÷ (– 11a 2 b 2 c 2 d 2 ) | f) (–72m 0 n 5 y 6) ÷ (– 6m 2 n –3 y 2 ) | ||
g)  |
h) ( 4m 5 n – 3 ) (3m – 2 n 3 ) | i) m – 1 n – 2 p 0 | |
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2) Simplify these expressions :
a)  |
b)  |
c)  |
d)  |
e)  |
f)  |
g)  |
h)  |
i)  |
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B/ ALGEBRA: MULTIPLYING AND DIVIDING
3) Multiply or divide these expressions and collect like terms :
| a) (2x – 3) (3x + 5) | b) – 4 (3x + 2)(x – 1) | c) x2 (4 – 2x)(1 + 4x) | |
| d) 2x (x2 – 3x + 1) – x (–3x2 – 5x + 3) | e) x 2 y 3 (4x 5 y – 2 + 2x – 4 y – x – 2 y – 3 ) | ||
| f) (2x – 4)2 + (x + 2)2 – 3(x – 5)(x + 2) | g)  | ||
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C/ SOLVING EQUATIONS:
4) Solve these equations :
a)  |
b)  |
c)  |
d) 2x(x –7) + 3(x 2 – 4x + 2) = 5(5 + 5x + x 2) |
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D/ SOLVING WORD PROBLEMS:
5) Solve these word problems with a chart for all and a diagram where needed :
a) I reached into my pocket and found $2.30 made up of nickels, dimes and quarters.
The number of nickels was twice the number of dimes,
and 4 times the number of quarters was equal to 3 times the number of nickels.
How many of each coin did I find?
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b) A grocer has 100 kg of almonds at $2.25/kg and 400 kg of cashews at $1.90/kg
that he wishes to sell as a mixture.
For what price per kilogram should the mixture sell?
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c) Another grocer has 200 kg of shelled pistachios which sell for $3.50/kg.
He decides to mix them with peanuts that sell for $1.00/kg to make a mixture
that will sell for $2.20/kg.
How many kilograms of peanuts should he add in order to break even?
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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?
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e) Montreal and Toronto are 600 km apart. Ryan starts from Toronto
heading towards Montreal, travelling at 120 km/hr.
At the same time that Norman leaves Montreal heading for Toronto.
Norman travels at 130 km/hr.
i) How long will it take them to meet? ii) How far from Toronto will they meet?
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f) The following data represent the dollar amounts
spent for textbooks during the present semester by
a sample of 35 students at McGill University.
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57, 34, 27, 41, 25, 18, 39, 33, 37, 39,
38, 47, 31, 42, 60, 58, 31, 47, 37, 16,
64, 34, 41, 43, 50, 46, 63, 51, 41, 30,
42, 37, 48, 28, 34
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i) using your calculator, find the mean, median and mode of this distribution.
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ii) Starting with $15 as the lower limit for the first class,
and using an interval of $10, organize the data into a
frequency table below and fill in the blanks.
| class | frequency | cumulative frequency | relative frequency % | midvalue | subtotal |
| total |
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iii) Find the estimated mean, the median and modal class.
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