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 |

**Click on a topic and go to work.**

the **solutions** are in a **separate file** you can open

in a new window from the MathTub Index.

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**A**/ __EXPONENTS AND RADICALS__ :

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

a) (– 5)(– ax^{2} )(– ax)^{2} |
b) (y^{ –1} z^{ –1})^{ –2} |
c) ( x^{ – }^{z} y^{ – }^{z} )^{ 0} |
d) (2x^{4}y^{ –3}z^{ 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) x^{2} (4 – 2x)(1 + 4x) | |

d) 2x (x^{2} – 3x + 1) – x (–3x^{2} – 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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