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)
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multiply through by 6, the lcm of 3 and 2 expand the brackets, collect like terms and solve for x. |
b)
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multiply through by 70, the lcm of 5, 7 and 2 expand the brackets, transpose 35x collect like terms and solve for x. |
c)
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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
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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) |
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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 |
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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) |
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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 |
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e)
person | dist. | rate | time |
Ryan | 120x | 120k/h | x |
Norman | 130x | 130k/h | x |
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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 |
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