review grade 10 applied 2010

8/2/2019 Review Grade 10 Applied 2010

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Exam Review Grade 10 AppliedMFM1P1

Unit 1: Similar Triangles1. S imil ar T r iang les Two triangles are considered similar if:

a) .

b) .

Example: Why are the following triangles similar? Solve for x.

A

B C E F

D


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60E

D

F

xcm

15

cm

60C

A

B

12 cm

26 cm

22.54cm

13 cm

cm


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Example: A hunter whose eye level is 160 cm above the ground wants to know the height of the treethat contains his prey. He places a mirror face up on the ground 20m from the tree so that it is level.Then he moves away so that he can see the top of the tree reflected in the mirror. He measures hisdistance from the mirror to be 150cm. How tall is the tree?

2 . P ropo rt ions Aproportion is solving for an unknown quantity in a rate or ratioEx) Solve for x:2:5 = x:13

Ex) Sun Li bought 12 oranges for $6.48. How many oranges could she buy with $10.00?

Ex) Jennifers car uses 8 L of fuel for every 100 km. If she travels 535 km, how much fuel will her carneed?

20m150cm

160cm

A

B C

D

F E


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Unit 2: Trigonometry1. The Pythagorean Theorem The Pythagorean Theorem only applies to triangles.

The equation is: a2 + b2 = c2

Label the triangle below as a, b, or c:

Ex) Find the value of the unknown side:

2. Labe l ing Tr iangles Triangles are labeled based on the angle.

The three sides of a triangle are , and

Ex) Label the triangles below:

3. Tr igonometr ic Rat ios The trigonometric ratios are found on The trigonometric ratios are found

triangles The ratios are:

Ex) Find all the trigonometric ratios to three decimal places for the following triangle:

12 m

59

? 12 m

31

?


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4. Solving For S ides When solving the side lengths of a right triangle, determine first:

1. Can we use the2. If we cannot use the Pythagorean Theorem, label the triangle3. Circle all that is give and what is required to find4. Determine which ratio from the given information5. Setup your proportion and solve the unknown

Ex) Solve for the unknown side length

a) c) d)

5. Solving For Ang les When solving for angles we use the trigonometric ratio

This is found by using the button on the calculator

Ex) Using a calculator, find the angle given the following ratios:

a) 45.0=Hypotenuse

Oppositeb) sin A = 0.415 c) tan A = 4.12

Ex) Find the missing angle

12 m40

?

12 m40

?

10 m

x

5 m

12 m

x

412 m

x

4


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6. App li ca ti onsEx) In order to safely land, the angle that a plane approaches the runway should be no more than 10.

A plane is approaching Pearson airport to land. It is at an altitude of 850 m. It is a horizontal distance of5 km from the start of the runway. Is it safe for the plane to land?

Ex) Draw and label a diagram of the path of an airplane climbing at an angle of 11with the ground.Find, to the nearest foot, the ground distance the airplane has traveled when it has attained an altitudeof 400 feet.


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Unit 3: Equations of Lines1. Slope Slope is the same as the . An example of rate of change is speed

(km/h),

We calculate the slope as .

Ex) Calculate the slope of the graphs below:

Ex) Calculate the rate of change from the following table:

HoursWorked TotalEarnings0 0

1 8

2 16

3 24

2. Reading the Equation of a L ine When a line is in the form the variable m = and the

variable b =Ex) Fill in the table below:

Equation Slope y-intercept

Y = -2x + 3

4 -2

y = -1/2 x

2/3 4

0 5

-2 0

y = 2x - 5


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3. Graphing Equations We can graph the equation of a line using table of values or slope/y-intercept method:Ex) Graph y = (2/3)x 5 using the slope-y-intercept method:

4. F inding EquationsEx) Find the equation of the following: A race car had a head start of 0.5 km. It travels at a constantspeed of 220 km/h. Write an equation for the total distance travelled over time.

Ex) Find the equation of the following:


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5. Equations: Di fferent Casesi. Given the slope and y-intercept

Find the equation of a line with a slope of -1/2 and y-intercept of -5

ii. Given a Point and the Slope

Find the equation of the line with a slope of 3 and that passes through the point (-2, 1)

iii. Given Two Points

Find the equation of a line that passes through the points (1,2)and (5,8)


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Unit 4: Linear Systems1. Solving Linear Systems Graphical ly When two equations of lines are graphed, the represents the

solution of both lines

At this , both lines share the same value andvalue

Ex) You have a job that pays $5 for every pyramid you create. Your friend has a job that pays her aninitial fee of $4 plus $3 for every pyramid she builds. Graph the two jobs on the same graph.

2. Solving Linear Systems By Subst itut ion When solving the point of intersection by substitution, we write one equation into terms of one

variable then substitute it into the other equation.

Ex) Solve:x + y = 33x y = 1

3. Solving Linear Systems By El iminat ion When solving the point of intersection by elimination, we write both equations equal with one

variable.

Ex) Solve by elimination

2x + 3y = 125x - 3y = 2


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Unit 5 & 6: Quadratic RelationsLinear vs Quadratic A linear relation forms a graph with a .

A quadratic relation forms a graph with shape of a .

Below is a table of value, determine if this relation is linear, quadratic or neither:

Features of a Quadratic Graph A quadratic relation can be seen when a ball is thrown in the air and the height is measured

versus time. A sketch of this graph might look:

A quadratic relation can be seen when a duck flies into the water, catches a fish and flies backout:

Time (x) Distance(y ) FirstDifferences SecondDifference

The relation is because:

A linear relation has theequal and theequal to .

A quadratic relation has the

equal.

This parabola is facing and

the vertex is a .

This parabola is facing andthe vertex is a .


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Label the key features (vertex, axis of symmetry, x-intercept(s), y-intercept, maximum /minimum value) of the following quadratic relation:

Forms of A QuadraticStandard Form: y =ax 2 + bx + c The y-intercept is the last or c term. We can change factored into standard form by .

There are three methods of expanding: , , and

Example 1) Find the y-intercept, x-intercepts of the following quadratic:y = (x + 4)(x 5)

Method 1: Tiles Method 2: Table Method 3: Algebra (FOIL)

The y-intercept is:

The x-intercepts are: and

Example 2) Expand the following: y = 2x(3x 4)


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Factored Form: y =(x r)(x s) There are two methods of factoring: algebra tiles and algebra

Example: factor y = x2 + 3x + 2 using tiles

1. Product/Sum Form: Factor y = ax2 + bx + c In this case r x s = c and r + c = b

Find the x-intercepts of the following:

y = x2 + 6x + 8 y = x2 3x 18

2. Common Factoring: y = ax 2 + bx Let us factor: y = x2 + 3x

This can be written as:Based on this r x s =

r + s =The factored form is y = or

Factor as state the x and y intercepts of:

y = x2 + 6x y = 2x2 2x 60


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3. Difference of Squares: y = ax 2 b2 y = x2 4 can be written as y =

r x s =r + s = factored form

y = x2 16 y = 2x2 200

Solving for the roots (x-intercepts): 0 = ax2 + bx + cThe y value of the x-intercepts is 0.To find the roots, we factor, set the y = 0, and solve for each of the roots

Eg. Solve the following trinomial:

y = x2 3x -28y = (x 7)(x + 4)0 = (x 7)(x + 4)0 = (x 7) 0 = (x + 4)7 = x -4 = x

The roots are x = 7 and x = -4

Try these:a. y = x2 + 8x + 12 b. y = x2 5x - 24

Unit 7: Imperial Measure, Surface Area, & VolumeConverting Imperial Measure

Covert the following values into the indicated units of measure. Use the appropriateconversion factor to solve.

i) 3 ft = ______ m ii) ______ ft = 18 m(1ft = 0.3048 m)

ii) 24 ft2 = ________ m2 iv) ______ ft2 = 155m2

(1ft2 = 0.0929 m2)


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Surface Area and VolumeThe surface area represents the _______________________ the object has

The volume represents the ____________________ the object has

Cylinders

SA = 2 r 2 + 2 r hiii) Find the volume and surface area of a cylinder with a height of 1.2 m and a radius

of 80 cm.iv) Find the volume and surface area of a cylinder with a height of 18 cm and a

diameter of 10 cm.

Spheres

Surface Area = 4 r2

v) Find the volume and surface area of a sphere with a radius of 8 cm.vi) Find the volume and surface area of a sphere with a diameter of 10 ft.

Height = h

Radius = r

Volume = r2h

Radius=r

Volume = 3

3

4r

review grade 10 applied 2010

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