Grade 9 Academic Math Review

Linear Relations

100

In y=mx+b what variable represents the independent variable?

The independent variable is "x".

200

What is extrapolation?

The process of estimating a value outside the range of the data.

300

What is the general form of a line in STANDARD FORM?

Standard Form is Ax+By+C=0

400

What is the formula for a slope?

m=(y₂-y₁)/(x₂-x₁)

500

Solve for "j"  

3j - 10 = 11

j = 7

Algebra & Polynomials

100

What are the like terms in 3y,2x,−3x?

2x,-3x

200

Simplify the following. 3x−2x+4x

5x

300

Multiply the polynomial by the monomial --- (7y)(8x+4)

56xy+28y

400

John has change in his pocket consisting of quarters, loonies and toonies. The number of quarters is twice the number of loonies and the number of toonies is twice the number of quarters. Write an algebraic expression to represent the total number of coins he has, using only one variable.

Let x represent the number of loonies. Then, "x + 2x + 4x" 

500

Expand and simplify: 

5x(x³-3x)+x²(-2x+x²)

6x⁴-2x³-15x²

Geometry

100

How do you calculate the volume of a cylinder?

V= πr²h

200

Calculate the AREA of a sphere with a diameter of 10cm

A=314.15cm²

300

What is the measure of each angle in a regular 20-gon?

162^o

400

A triangle has sides with lengths of 6 centimetres, 8 centimetres, and 10 centimetres. Is it a right triangle? Explain your steps.

Yes, it satisfies Pythagorean Theorem

500

Brad is building a slide for his kids. If the ladder is 3 metres tall and he wants the bottom of the slide to be 4 metres from the ladder, how long does the slide need to be?

The slide needs to be 5 metres long.

Exponents

100

Simplify 3x(2x²)3x = ?

18x⁴

200

Simplify -- (3x²y³)/(3xy²)

2xy

300

Simplify the following: 

x³y⁷/xy⁵

xy²

400

Simplify the following: 

(4x²)³(x²y⁴)²/2x³y⁴

32x⁷y⁴

500

Evaluate for x=-3 

-x² - 4x 

3

Problem Solving

100

Mrs. Richard's class is on a ferry that is travelling 26 kilometres per hour. The students notice that they are passing right by a speed boat that is travelling in exactly the opposite direction at 74 kilometres per hour. How long will it be before the two vessels are 10 kilometres apart in minutes?

6 minutes

200

Michelle scored 5 points more than triple the number that Carolyn scored. Together they scored 45 points. How many points did each girls score? 

Carolyn: 10

Michelle: 35

300

Movies 2 Go rent DVDs for $2.50 and have no membership fee. Films "R" Us rent videos for $2 but have a membership fee of $10. At what number of rentals would the price be the same?

The number of rentals needed to be the same price would be 20.

400

A square based pyramid has a base side length of 15cm and a height of 16cm. What are the dimensions for a cylinder having the same volume and height as the pyramid?

r = 4.9cm and h = 16cm

500

A ladder is placed 5 meters from the wall and it reaches 12m up the wall. How long is the ladder?

13m