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) (8x^{12} )/ y^{ 9} |
e) | f) (12n^{ 8 }y^{ 4 })/m^{ 2} |

g) 1 | h) 12m^{ 3} |
i) 1/mn^{2} |

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2) ** Evaluate these expressions** :

a) | b) | c) y^{ 5 }/ (11x^{ 8 }) |

d) |
e) | f) x^{3} |

g) –30 |
h) | i) 25 |

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3) __Multiply or divide these expressions and collect like terms__ :

a) 6x^{2} + x – 15 |
b) –12x^{2} + 4x + 8 |
c) 4x^{2} – 14x^{3} – 8x^{4} |
d) 5x^{3} – x^{2} – x |

e) 4x^{7}y + 2x^{ }^{–}^{2} y^{4} – 1 |
f) 2x^{2} –3x + 50 |
g) – x^{6} + 4x^{3} – x^{2} – x – 1 |

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4) __Solve these ____equations__ :

a)
- 4(
x + 7) + 12(x – 1) = 6- 4
x + 28 + 12x – 12 = 6- 16
x = – 10 therefore x = – 5/8 |
multiply through by – 6, the lcm of – 3 and 2 expand the brackets, collect like terms and solve for |

b)
- 14(2
x) + 10(3x) = 35x – 70- 28
x + 30x – 35x = – 70- 23
x = – 70 therefore x = –70/23 |
multiply through by 70, the lcm of 5, 7 and 2 expand the brackets, transpose 35 collect like terms and solve for |

c)
- 2
x – 5 = 2(8 – x)- 2
x – 5 = 16 – 2x- 4
x = 21 therefore x = 21/4 = 5.25 |
multiply through by 6 expand the brackets, transpose – 2 solve for |

d) 2x(x –7) + 3(x^{ 2} – 4x + 2) = 5(5 + 5x + x^{ 2})2 2 - – 51
x = 19 therefore x = –19/51 |
expand the brackets transpose variables,constants, collect like terms, solve for |

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 = 2

- then if

- so

- 5(2

- 10

- 57.5

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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) = 500

- 225 + 760 = 500

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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) +

- 700 +

- 260 = 1.2

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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 |

- 5

- 45 = 5

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e)

person | dist. | rate | time |

Ryan | 120x | 120k/h | x |

Norman | 130x | 130k/h | x |

- 120

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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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