Grade 9 Math Study Guide

State the 3 types of Polynomials and give an example.

- Monomial = 1 term. Example: -2x^2 - Binomal = 2 terms. Example: 2x^2+3x - Trinomial = 3 terms. Example: 2x^2-6x+4

Define Scale Diagram.

A diagram that is an enlargement or a reduction of another diagram.

Define Irrational Number.

A number that cannot be written as a fraction.

Define Dependent Variable.

A variable whose value is determined by the value of another (the independent) variable. y=2x then x is dependent variable.

Define Independent Variable.

A variable whose value is not determined by the value of another variable. y=2x then y is independent variable.

Which fraction is equivalent to -(-7/-21)? A) -1/3 B) 1/3 C) -(6/-18) D) -6/-18

A) -1/3

Which solution requires a reversal of the inequality? A) -2x > 6 B) 2x < 6 C) 2x > -6 D) 2x > 6

A) -2x > 6

Evaluate: 8 and 4/5 ÷ (-1 and 7/15). A) -6 B) -1/6 C) -968/75 D) -12 and 68/75

A) -6

What is the constant term in the expression 4y + 5z^2? A) 0 B) 2 C) 4 D) 5

A) 0

Which number is not a perfect square? A) 0.4 B) 0.25 C) 9/49 D) 81/16

A) 0.4

Music Downloads charges $20 per month plus $0.10 per song downloaded. Happy Tunes charges a flat rate of $30 per month. Find the number of downloads that results in equal cost from either company. A) 100 B) 75 C) 50 D) 25

A) 100

The formula for the area of plastic needed to make a toy ball is A = 4πr^2, where r is the radius of the ball. Determine, to the nearest square centimetre the area for a ball with a radius of 12 cm. A) 1810 cm2 B) 576 cm2 C) 452 cm2 D) 151 cm2

A) 1810 cm2

An aeronautical chart has a scale of 1:100 000. Two cities are 20.0 cm apart on the chart. What is the distance between the cities? A) 20 km B) 100 km C) 200 km D) 2000 km

A) 20 km

A scale model of a bridge used a scale of 1:72 and was 3.6 m long. How long is the bridge? A) 259.2 m B) 50.0 m C) 20.0 m D) 5.0 m

A) 259.2 m

Write as a single power: (2x2x2x2x2) x (2x2x2) ÷ (2x2x2x2). A) 2^4 B) 2^5 C) 2^6 D) 2^7

A) 2^4

The chord of a circle is 24 cm long. The radius of the circle is 13 cm. How far is the midpoint of the chord from the centre of the circle? A) 5 cm B) 11 cm C) 12 cm D) 13 cm

A) 5 cm

Wilma's back yard has a length equal to twice the width. She dug a garden with an area of 12 m2. The rest will be grass. Determine an expression for the area, A, in terms of the width, w. A) A = 2w^2 - 12 B) A = 2w^2 - 12w C) A = 2w - 12 D) A = w^2 - 12

A) A = 2w^2 - 12

A heating technician estimated that the cost, C, of fixing a furnace would be no more than $500. Which inequality represents this situation? A) C ≤ 500 B) C ≥ 500 C) C < 500 D) C > 500

A) C ≤ 500

How can you find the centre of a circle? A) Draw any two tangents, and determine where they intersect. B) Draw any two non-parallel tangents, and determine where they intersect. C) Draw any two chords and their perpendicular bisectors. Determine where the bisectors intersect. D) Draw any two non-parallel chords and their perpendicular bisectors. Determine where the bisectors intersect.

A) Draw any two tangents, and determine where they intersect.

Sandor is considering running for mayor. He surveyed the 50 members of the soccer club he belongs to and found that 32 would vote for him. If 12 000 votes are cast in the election, how many could he expect to get? A) Less than 7680, since his sample is likely biased in his favor. B) 7680 C) More than 7680, since his sample is likely biased in his favor. D) The sample is too small to make a prediction.

A) Less than 7680, since his sample is likely biased in his favor.

A real estate office employs 20 people. A decision must be made as to where to hold the Christmas dinner. What kind of sample would be most suitable? A) Survey the entire population. B) Randomly select 5 employees. C) Use a stratified sample of 5 employees. D) Ask the first 5 employees who enter the office on a given day.

A) Survey the entire population.

What is the value of 5 in the power 5^4 called? A) base B) power C) exponent D) coefficient

A) base

Solve: 1/4y+1/2=-3/4. A) y = -5 B) y = -1 C) y = 1 D) y = 5

A) y = -5

Solve: y+2/3=y-1/2. A) y = 7 B) y = 1 C) y = -1 D) y = -7

A) y = 7

Define Symmetry.

An object or image has symmetry if it is balanced and can fit onto itself either by reflection or rotation.

Define Rational Number.

Any number that can be written as a fraction.

The CF-104 Starfighter is a former Canadian Forces aircraft with a length of 16.6 m. A plastic model is made using a scale of 1:48. What is the length of the model, to the nearest tenth of a centimetre? A) 48.0 cm B) 34.6 cm C) 34.5 cm D) 2.9 cm

B) 34.6 cm

Express (3^5 x 3^2) ÷ (3^4 x 3) as a single power. A) 3^5 B) 3^4 C) 3^3 D) 3^2

B) 3^4

Evaluate: -1 and 7/9 x (-3 and 3/8). A) -6 B) -1/6 C) 1/6 D) 6

B) -1/6

Which fraction lies between -0.54 and -0.56? A) -27/50 B) -11/20 C) -13/25 D) 55/100

B) -11/20

What is the opposite of 3x - 2y? A) 3x + 2y B) -3x + 2y C) -3x - 2y D) 2x - 3y

B) -3x + 2y

Damian wrote the expression (4^5)^2 as a repeated multiplication. How many 4s did he need? A) 30 B) 10 C) 7 D) 4

B) 10

A rectangular prism measures 16 cm by 8 cm by 5 cm. It is cut so that the 16 cm side is cut in half. How does the surface area of the half prism compare to the surface area of the original prism? A) 1:2 B) 18:31 C) 1:3 D) 1:4

B) 18:31

A square has a side length of 2 cm. A hexagon has a perimeter 4 cm larger than the perimeter of the square. What is the side length of the hexagon? A) 6 cm B) 2 cm C) 1 cm D) 0.5 cm

B) 2 cm

Evaluate (8 - 5)^3 + 2^5 ÷ (-4^2). A) 11 B) 25 C) 29 D) 43

B) 25

Which multiplication is equivalent to 8x^2 - 4x? A) x(2x - 1) B) 4x(2x - 1) C) 4(2x - 1) D) 4x(2x^2 - 1)

B) 4x(2x - 1)

Andelko measured the largest chord on his slice of pizza, and found it was 20 cm long. From the midpoint of the chord to the outside of the pizza, the shortest distance was 2 cm. What was the diameter of the pizza? A) 60 cm B) 52 cm C) 48 cm D) 26 cm

B) 52 cm

A circle has a diameter of 20 cm. A chord with a length of 16 cm is drawn. What is the shortest distance from the midpoint of the chord to the circumference of the circle? A) 4 cm B) 6 cm C) 8 cm D) 10 cm

B) 6 cm

Fans at a hockey game are sitting in three cheering sections. Section A supports the home team with 120 fans. Section B supports the visiting team with 90 fans. Section C supports neither team in particular (they just like to watch hockey) with 150 fans. A stratified sample of 24 fans is to be surveyed to predict the outcome of the game. How many from Section A should be included? A) 6 B) 8 C) 10 D) 12

B) 8

A circle with a radius r is inscribed in a square. Find an expression for the total area outside the circle but inside the square, in terms of r. A) A = (π - 4)r^2 B) A = (4 - π)r^2 C) A = (π - 4)r D) A = (4 - π)r

B) A = (4 - π)r^2

Which statement is false? A) All equilateral triangles are similar. B) All isosceles triangles are similar. C) All regular hexagons are similar. D) All squares are similar.

B) All isosceles triangles are similar.

The main intersection in a small town has two-way stop signs. The town council is contemplating spending $10 000 to install a set of stoplights. Which sample would be most likely to be free from bias? A) Survey 100 drivers of cars that stop at the intersection. B) Randomly select 100 homes from those in the town. C) Survey 100 pedestrians trying to cross the street without the stop signs. D) Survey 100 members of the local bicycle club.

B) Randomly select 100 homes from those in the town.

The student council is planning a special event for the last day of classes. A sample of students will be surveyed to determine whether they should have a sports day, band concert, movie presentation, or variety show. Which of these would be a stratified sample? A) Select 60 students from classes attended by the members of the council. B) Select a number of students from each grade, based on the total number in that grade at the school. C) Select the first 60 students who enter the cafeteria on a given day. D) Randomly tape 60 questionnaires on lockers around the school.

B) Select a number of students from each grade, based on the total number in that grade at the school.

Consider the number line representing x > 2. There would be an ___ circle at 2, and an arrow pointing to the ___. A) open, left B) open, right C) closed, left D) closed, right

B) open, right

The cost of making hamburgers for a class BBQ is $50 for the BBQ rental, plus $1.50 per hamburger. If sales are expected to be 60 hamburgers, how much must each hamburger be sold for such that the BBQ does not lose money? A) p > $2.34 B) p > $2.33 C) p > $1.50 D) p > $1.17

B) p > $2.33

Saskia sent emails to all 120 people in her address book asking them if they would like to fill out a questionnaire for a school project. What kind of a sample is this? A) systematic B) voluntary response C) stratified D) random

B) voluntary response

Solve: 1/3+2/9x=1. A) x = 1 B) x = 1/3 C) x = 0 D) x = -1

B) x = 1/3

Solve: 7 - 2y > 3. A) y < 5 B) y < 2 C) y > 2 D) y > 5

B) y < 2

Which value is greater than -2 and 3/8? A) -2.4 repeated B) -2.4 C) -2.3 repeated D) -2 and 4/9

C) -2.3 repeated

Evaluate: 36x^2 ÷ -9x. A) -4x2 B) 4x2 C) -4x D) 4x

C) -4x

Which is a specific solution for the inequality b + 2 < - 3? A) -1 B) -5 C) -6 D) No solutions are possible.

C) -6

Which value is closest to the square root of 2.5? A) 1.4 B) 1.5 C) 1.6 D) 5.0

C) 1.6

Deepa has won 3 out of every 8 games played at inter-school chess tournaments. During the round-robin playoffs, she will play 32 games. How many can she expect to win? A) 3 B) 8 C) 12 D) 16

C) 12

Ellen earns a salary of $200 per week, plus a commission of $30 for every cell phone that she sells. Last week, she made $750. How many cell phones did she sell? A) 5 B) 10 C) 15 D) 20

C) 15

The distance travelled by a model rocket, in metres, while the engine is firing can be calculated from the equation d = 25t^3, where t is the time in seconds. How far will it travel, to the nearest metre, during a burn of 4.5 s? A) 91 m B) 506 m C) 2278 m D) 1 423 828 m

C) 2278 m

Sally is paid $25 per day to harvest tomatoes, plus $0.50 per basket. She would like to earn at least $120 per day. Whic inequality represents this situation? A) 25 + 0.5n > 120 B) 25 + 0.5n < 120 C) 25 + 0.5n ≥ 120 D) 25 + 0.5n ≤ 120

C) 25 + 0.5n ≥ 120

A ship was sailing west. When it was due north of a radar station, it was 7 km from the station. It continued sailing west for 24 km. How far was it from the station at that time? A) 14 km B) 24 km C) 25 km D) 48 km

C) 25 km

Simplify: (-18b^2 + 27b) ÷ (-9b). A) 2b - 3 B) 2b + 3 C) 2b^2 - 3 D) 2b^2 + 3

C) 2b^3 - 3

Which expression is equivalent to (3 ÷ 7)^5? A) 3^5 ÷ 7 B) 3 ÷ 7^5 C) 3^5 ÷ 7^5 D) 15 ÷ 16 807

C) 3^5 ÷ 7^5

How many lines of symmetry are possible for a star? A) 1 B) 3 C) 5 D) 10

C) 5

Combine like terms to simplify 2xy + 3yx + 4xy^2. A) 9xy B) 6xy + 3yx C) 5xy + 4xy^2 D) There are no like terms to combine.

C) 5xy + 4xy^2

If 2/5 = x/15, what is the value of x? A) 4 B) 6 C) 10 D) 12

C) 6

Simplify: 2y(3y - 4) A) 6y^2 - 8 B) 6y - 8 C) 6y^2 - 8y D) -2y^2

C) 6y^2 - 8y

Use exponent rules to evaluate 81^5 ÷ 27^6 without using a calculator. A) 81 B) 27 C) 9 D) 3

C) 9

Which of the following would be best determined by sampling the entire population of a business that employs 800 people in a single building? A) Where should the company picnic be held? B) What colour should the main foyer be painted? C) Are all of the phones working properly? D) How many water coolers should be ordered for the building?

C) Are all of the phones working properly?

Which statement is true? A) The inscribed angle subtended by an arc measuring one-quarter of a circle measures 90°. B) The central angle subtended by an arc measuring one-half of a circle measures 90°. C) The inscribed angle subtended by a diameter of a circle measures 90°. D) The central angle subtended by a diameter of a circle measures 90°.

C) The inscribed angle subtended by a diameter of a circle measures 90°.

Solve: 2(x + 3) = 8. A) x = -1 B) x = 0 C) x = 1 D) x = 2

C) x = 1

State the coefficient, degree and constant term of 3x^2-2x+5.

Coefficient = 3 and -2. Degree = 2. Constant term = 5.

What is the coefficient in the expression -2(-7)^3? A) 7 B) 2 C) -1 D) -2

D) -2

Evaluate -2.56 - (-3.68). A) -6.24 B) 6.24 C) -1.12 D) 1.12

D) 1.12

A jar contains an unknown number of jelly beans of various colours, but none are blue. Alison added 24 blue beans, and mixed up the beans in the jar. She extracted a random sample of 30 beans and found that 4 of them were blue. Estimate the number of other coloured jelly beans in the jar. A) 24 B) 30 C) 96 D) 156

D) 156

A motorcycle of length 2.4 m was represented in a drawing with a length of 4.8 cm. What was the scale? A) 1:0.2 B) 1:2 C) 1:20 D) 1:50

D) 1:50

A number pattern starts with the number 3. Each number is 5 more than the previous number. What is the fifth number? A) 14 B) 17 C) 18 D) 23

D) 23

Jixuan has 64 centimetre cubes. He used all of them to build a rectangular prism. What is the maximum surface area that he could construct? A) 96 cm2 B) 136 cm2 C) 160 cm2 D) 258 cm2

D) 258 cm2

A metre stick casts a shadow 72 cm long at the same time that a flagpole casts a shadow 24 m long. How tall is the flagpole, to the nearest metre? A) 300 cm B) 17 m C) 30 m D) 33 m

D) 33 m

Divide: (12xy + 8xz) ÷ (4x). A) 12y + 8z B) 3x^2y + 2x^2z C) 3xy + 2xz D) 3y + 2z

D) 3y + 2z

What is the product of 2z and 3.2z? A) 1.6 B) 1.6z^2 C) 6.4z D) 6.4z^2

D) 6.4z^2

Which polynomial is of degree 2? A) 3 - ab B) a^2 + b C) 2a^2 + 3b^2 D) All of the above.

D) All of the above.

Describe the line symmetry of the letter H. A) No line symmetry B) Two oblique lines of symmetry C) One vertical, one horizontal, and two oblique lines of symmetry D) One vertical and one horizontal line of symmetry

D) One vertical and one horizontal line of symmetry

Radi needed to survey 50 students at his school for a math assignment. Each of the students has a locker numbered from 1 to 600. Radi programmed his graphing calculator to randomly generate 50 integers from 1 to 600 and used them to select the students to be interviewed. What kind of a sample is this? A) stratified B) systematic C) convenience D) random

D) random

Which expression is a binomial? A) 2x B) x^2 C) xy D) x + y

D) x + y

Solve: 0.2(6x + 1) = 0.4(2x - 0.5) A) x = 1 B) x = 0.4 C) x = -0.4 D) x = -1

D) x = -1

Solve: 3(x - 1) ≤ 4x - 2 A) x ≤ - 5 B) x ≥ - 5 C) x ≤ - 1 D) x ≥ - 1

D) x ≥ - 1

Simplify (3x^2 +2x - 4) - (2x^2 - 3x + 1). A) x^2 - 5x - 5 B) 5x^2 + 5x - 5 C) 5x^2 - x - 3 D) x^2 + 5x - 5

D) x^2 + 5x - 5

Solve: 1.2z + 3.6 = -0.8z + 4.4 A) z = 4.0 B) z = 2.0 C) z = 1.0 D) z = 0.4

D) z = 0.4

Define Order of Rotation.

The number of times that a shape or design fits onto itself in one complete turn.

Define Interpolation.

To estimate a value that lies between 2 data points on a graph.

Define Extrapolation.

To predict or infer an unknown value from known values.