Math 9 Final Examreview

Math 9 Final ExamReview

Exponents (Ch2)

Demonstrate the differences between the exponent and the base by building models of a given

power, such as 23 and 32. Draw 23 and 32

 Explain, using repeated multiplication, the difference between 103 and 310.

Express 45as a repeated multiplication.

Express (-5(-5)(-5)(-5) as a power.

 Explain the role of parentheses in powers by evaluating a (–2)4,(–24 ) and –24.

a0=

Evaluate 32, 83Evaluate: 94 + 32 x 43

Demonstrate an understanding of exponent laws (Ch.2)

Q/Examples of exponent laws

(a5)(a7)(x8) / (x5)(y7)3

(d5)6 (d4)(e5)6(-32)(-37)

(e3)(-32)3(-33)

Q/52 + 53

Q/ 43 – 42 x 52

Q/Solve for x:(x4)2 = 256

Q/Susan needs to wrap two gift boxes in the shape of cubes. She has a sheet of wrapping paper 140cm by 30cm. One box is 7cm by 7cm by 7cm. Each side of the other box has an area of 529cm2. Does she have enough wrapping paper to wrap both gift boxes?

Q/Evaluate:

Identify the error(s) in a given simplification of an expression involving powers.

Demonstrate an understanding of rational numbers (Ch.1)

Order 3/5, -0.666….,0.5, -5/8, 3/2 by placing them on a number line

-->Identify three rational numbers that is between -2/3 and -4/5

 Solve a given problem involving operations on rational numbers in fraction or decimal form

Q/Add/Subtract/Multiply/Divide Fractions:

3/8 – 2 ¾ -3 ¼ - (-2/7)(2/3)(-4/9) (3/4) / (5/6)

Q/Convert to decimal: 28/40Convert to fraction: 0.84

Q/If x = –1.25 and y = 2.5, evaluate 2y + 3x.

Q/What is the value of ?

Q/Margaret takes 1 ¼ h to complete her English assignment and 2/3 h to complete her math assignment. How much longer does it take Margaret to complete her English assignment than her math assignment? Answer in minutes.

 Identify the error in applying the order of operations in a given incorrect solution.

Q/Evaluate: 1.6 – (2.4 – 5.6) – (4)2 + (4)(-6)

7(3 – 8) - 24

Q/Evaluate

.

 Determine the square root of a given positive rational number that is a perfect square.

Q/What is the square root of 36?

 Identify the error made in a given calculation of a square root

Q/is 3.2 the square root of6.4?

 Determine an approximate square root of a given rational number that is not a perfect square,

using a calculator.

Q/What is the square root of 7rounded to the nearest hundredth.

Q/What is the perimeter of a square if the area is 144cm2

Shape and Space

(3-D Objects and 2-D Shapes) (Ch.4)

Determine the area of overlap in a given composite 3-D object

Determine the surface area of a given composite 3-D object

 Solve a given problem involving surface area.

Q/Calculate the surface area

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Similar Polygons (Ch.3)

Determine if the polygons in a given pre-sorted set are similar, and explain the reasoning.

 Draw a polygon similar to a given polygon, and explain why the two are similar.

Determine the scale factor for a given diagram drawn to scale (for enlargement and reduction)

Solve a given problem that involves the properties of similar triangles

Q/This kite is reduced by a scale factor of ¾. What will the side lengths of the reduced kite be?

Q/On a map, 3 cm represents 5 km. The distance between two towns is 90 km. What is the distance between the two towns on the map?

Q/The scale on a map of a region shows that 2 cm represents 5 km. City of Westwood Heights is 12 cm from the Town of Southgate on the map. How far apart are Westwood Heights and Southgate?

Q/ / John would like to determine the height of a maple tree. He is 1.5 m tall and his shadow is 4.0 m long. The shadow of the tree at the same time of day is 80.0 m long. What is the height of the tree?

Q/What is the length of CD?Q/What is the length of AB?

Linear Relations (Ch.5)

Match given equations of linear relations with their corresponding graphs.

Extend a given graph (extrapolate) to determine the value of an unknown element.

Interpolate the approximate value of one variable on a given graph, given the value of the other

variable.

Solve a given problem by graphing a linear relation and analyzing the graph.

Write an expression representing a given pictorial, oral or written pattern.

Ex. Write an equation for the following.

Ex. How many blocks will there be in the 45th figure?

Write a linear equation to represent a given context.

 Represent a given problem, using a linear equation.

Write a linear equation representing the pattern in a given table of values, and verify the

equation by substituting values from the table.

Ex. A company is holding a video game exhibition. Tickets cost $15 per person, and it has given away 10 free tickets. Write a linear relation for the money the company will earn if n people attend. Graph the linear relation. How much will the company make if 100 people attend? How many people attended if sales are $600?

Solve problems:

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• 2x = 9

• x = 6

3

• 2x - 5 = -20

• x/2+ 4 = -14

• 3x = -10 - 7x

• -2(x - 3) = -4

• -x + 6 = 2x – 12

• 4(2x - 8) = -2(3x + 10)

• 4a – 2 + 1 = 3a + 7 – 1

5 2 2

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Ex. The perimeter of a rectangle is 210m. It is 7 m longer than it is wide. How long is it?

Identify and correct an error in a given incorrect solution of a linear equation.

Model the solution of a given linear equation, using concrete or pictorial representations, and

record the process (algebra tiles)

Verify by substitution whether a given rational number is a solution to a given linear equation.

Ex. Jarome has an equal number of nickels, dimes, and quarters. He has $4.40 in coins. How many nickels does he have? A.33 B. 30 C. 11 D. 10

Solve and graph:

3 + 4x < 56 4 – 2x

Translate a given problem into a single variable linear inequality, using the symbols ≥, >,

or ≤.

Ex. Jose decides to take up squash. The local racquet club costs $152 for the season and charges $5 each time he uses the court. Jose does not want to spend more than $400. Write an inequality for the situation.

Determine if a given rational number is a possible solution of a given linear inequality.

Ex. Can Jose play 5 times? 56 times?

Polynomials (Ch.6)

Identify the variables, degree, number of terms and coefficients, including the constant term,of a given simplified polynomial expression.

Ex. 4x2y6z – 10y3– 7

Ex. Simplified, what is the coefficient and constant

-5x + 6 – 4x – 8 + x

Match equivalent polynomial expressions given in simplified form;

Ex. 4x –3x2 + 2 isequivalent to -3x2+ 4x + 2.

Ex. 10x - 7xy + ____y2 + 9y2 + ___xy = ___x + xy + 12y2

Identify the error(s) in a given simplification of a given polynomial expression.

Model addition and subtraction of two given polynomial expressions concretely or pictorially, and record the process symbolically.

Ex. What is the area?

(-7x2 - 4x - 2) + (3x2 - 6x + 8) (-x2 - 2x + 4) - (5x2 - 4x - 2)

Identify like terms in a given polynomial expression.

Ex. 4x2 , 3x, 4x3, 8y, 2x, 9y, 8x3, x2

Model multiplication and division of a given polynomial expression by a given monomial concretely orpictorially, and record the process symbolically.

Identify the error(s) in a given simplification of a given polynomial expression.

Circle Geometry (Ch.9)

Solve problems and justify the solution strategy,using the following circle properties:

• the perpendicular from the centre of a circle to achord bisects the chord

• the measure of the central angle is equal to twicethe measure of the inscribed angle subtended bythe same arc

• the inscribed angles subtended by the same arc arecongruent

• a tangent to a circle is perpendicular to the radiusat the point of tangency.

Ex. Angle R =Ex. Value of h

Symmetry (Ch.8)

Classify a given set of 2-D shapes or designs according to the number of lines of symmetry.

Complete a 2-D shape or design, given one half of the shape or design and a line of symmetry.

Determine if a given 2-D shape or design has rotation symmetry about the point at its centre,

and, if it does, state the order and angle of rotation.

Rotate a given 2-D shape about a vertex, and draw the resulting image.

Identify a line of symmetry or the order and angle of rotation symmetry in a given tessellation.

Identify the type of symmetry that arises from a given transformation on a Cartesian plane.

Complete, concretely or pictorially, a given transformation of a 2-D shape on a Cartesian

plane; record the coordinates; and describe the type of symmetry that results.

Identify and describe the types of symmetry created in a given piece of artwork.

Determine whether or not two given 2-D shapes on a Cartesian plane are related by either

rotation or line symmetry.

Draw, on a Cartesian plane, the translation image of a given shape, using a given translation

rule such as R2, U3; label each vertex and its corresponding ordered pair; and

describe why the translation does not result in line or rotation symmetry.

Create or provide a piece of artwork that demonstrates line and rotation symmetry, and

identify the line(s) of symmetry and the order and angle of rotation.

Ex. Rotate the little dipper 90cw, 180ccw, 270cw around the origin.

Ex. Reflect the little dipper in the x-axis; y-axis.

Ex. Plot triangle ABC with points A(2,5), B(-2,2), C(6,-2)

D(2,1). If the triangle ABC rotates 90 degrees clockwise around point D (2,1), then the coordinates of C' will be:

A) (6,-2)B) (1,-3)C) (-1,-3)D) (-2,6)

Probability and Data Analysis (Ch7 and Ch10)

Describe the effect of:

• bias •use of language • ethics • cost • time and timing • privacy• cultural sensitivity

on the collection of data.

Analyze a given case study of data collection; and identify potential problems related to bias,use of language, ethics, cost, time and timing, privacy or cultural sensitivity.

Provide examples to illustrate how bias, use of language, ethics, cost, time and timing, privacyor cultural sensitivity may influence data.

Select and defend the choice of using either apopulation or a sample of a population to answer aquestion.

Identify whether a given situation represents the use of a sample or a population.

Provide an example of a situation in which a population may be used to answer a question, andjustify the choice.

Provide an example of a question where a limitation precludes the use of a population; anddescribe the limitation, eg., too costly, not enough time, limited resources.

Identify and critique a given example in which a generalization from a sample of a populationmay or may not be valid for the population.

Provide an example to demonstrate the significance of sample size in interpreting data.

Demonstrate an understanding of the role ofprobability in society.

Provide an example from print and electronic media, e.g., newspapers, the Internet, whereprobability is used.

Identify the assumptions associated with a given probability, and explain the limitations ofeach assumption.

Explain how a single probability can be used to support opposing positions.

Explain, using examples, how decisions may be based on a combination of theoreticalprobability, experimental probability and subjective judgment.

REVIEW QUESTIONS:

p.150 #1-18; p.360 #1-16; p.498 #1-16 All Chapter Reviews and Chapter Self-Test for Ch. 1-10

Practice Tests:

(note: this link is on Mr.Semaka’s homework website)

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