CORPUS
CHRISTI CATHOLIC SECONDARY SCHOOL
Corpus Christi
Mathematics
MPM1D Exam Review
January 2016
Mrs. Pettipiece
MPM1D Exam Review 2016
EXAM REVIEW– JANUARY 2016
I.
NUMBER SENSE AND ALGEBRA
SUCCESS CRITERIA
A. I can add two mixed numbers
I can use two strategies:

add or subtract the whole parts first and the fraction part separately

convert them first into improper fractions, then add the fractions
B. I can add rational numbers expressions using BEDMAS
C. I can apply the exponent rules to powers with integer or rational bases
Exponent rules for a power with
integer base


(𝑎) = ⏟
(𝑎)(𝑎) ∙ … ∙ (𝑎)

If a < 0, then if n is even
(𝑎)𝑛 > 0 if n is odd (𝑎)𝑛 < 0
−(𝑎)𝑛 = − ⏟
(𝑎)(𝑎) ∙ … ∙ (𝑎)

(2)3 = (2)(2)(2)

(−2) = −2

𝑎 𝑛
𝑎
𝑎
𝑎
( ) = (⏟ )( ) ∙ … ∙ ( )
𝑏
𝑏 𝑏
𝑏

𝑛 𝑓𝑎𝑐𝑡𝑜𝑟𝑠
(−2)4 = 24
3
Examples
base
𝑛
𝑛 𝑓𝑎𝑐𝑡𝑜𝑟𝑠

Exponent rules for a power with rational
Examples
3
𝑎 𝑛
𝑎𝑛
𝑏
𝑏𝑛


( ) =

𝑎 𝑛
𝑎
𝑏
𝑏
𝑎

𝑎
− ( ) = − (⏟ )( ) ∙ … ∙ ( )
𝑛 𝑓𝑎𝑐𝑡𝑜𝑟𝑠
𝑏
𝑏
𝑛 𝑓𝑎𝑐𝑡𝑜𝑟𝑠
3 3
3
3
3
4
4
4
4
( ) = ( )( )( )
5 3
53
6
63
( ) =
5 2
5
5
6
6
6
−( ) = −( )( )
For all of the above b≠0
(𝑎)𝑛 × (𝑎)𝑚 = (𝑎)𝑛+𝑚
(𝑎)𝑛 ÷ (𝑎)𝑚 = (𝑎)𝑛−𝑚 if a≠0
(2)3 × (2)4 = (2)7
𝑎 𝑛
( )
𝑏
(3)5 ÷ (3)2 = (3)3
( ) ÷( ) = ( )
((𝑎)𝑛 )𝑚 = (𝑎)𝑛×𝑚
((2)3 )2 = (2)6
(𝑎)0 = 1
(5)0 = 1
𝑎 𝑛
𝑏
𝑚
𝑎 𝑛
((𝑏 ) )
𝑎 0
𝑏
𝑎 𝑚
𝑏
𝑎 𝑛+𝑚
,
𝑏
𝑎 𝑚
𝑏
𝑎 𝑛−𝑚
, 𝑤here
𝑏
× ( ) = ( )
=
𝑎 𝑛×𝑚
(𝑏 )
,
where b≠0
b≠0
2 3
2 2
2 5
( ) × ( ) = ( )
3
3
3
4 5
4 3
4 2
( ) ÷( ) = ( )
5
5
5
3
, 𝑤here b≠0
( ) = 1, , 𝑤here b≠0
3 2
3 6
(( ) ) = ( )
4
4
1 0
( ) =1
6
D. I can simplify polynomial expressions

I can simplify a sum or a difference of polynomials by adding or subtracting the coefficients of like
terms.

I can determine the product of a monomial and a polynomial by using the distributive property to
expand it.
a x ( b + c) = a x b + a x c
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MPM1D Exam Review 2016
EXAMPLES
1. Evaluate – decimal answers are not permitted.
2 2
a. (3)
(3 2 ) 4
c.
36
b. −𝑥 2 + 2𝑦 − 3 using x = -3 and y = 2
2. Simplify.
36a 5 b 6
(3a 2 b) 2
a. (3n 2 )( 4n 5 )
c.
b. 4𝑎 + 6 − 6𝑎 − 14
e. 3a(4a 2  6a  10)
c. (2 x  3 y )  (3x  y )  (5 x  4 y )
3. Solve. Express any fractional answers in lowest terms.
x
x
 5 
a. 3x  8  6  5x
5
2
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MPM1D Exam Review 2016
4. Write simplified algebraic expressions for the perimeter, P, and area A of the following
figures:
a.
3x
9x-2
4y + 6
b.
4y
6y
6y
4y
c. Find the value of y, if the perimeter of the trapezoid in b is 226 m.
5. A designer wants to determine the simplified expression for the area of 20 small and 18 large
rectangular wood pieces like the ones below.
(2a+ 10) cm
a cm
(a + 6) cm
2a cm
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MPM1D Exam Review 2016
II.
LINEAR RELATIONS
SUCCESS CRITERIA
A. I can identify if a relation is linear by observing one of the following:

In a table of values, the first differences are constant.

The degree of the equation that represents the relation is 1.

The graph is a line.
B. I can write a linear relation in:
C.

Slope intercept form:
y = mx + b, where m is the slope and b is the y - intercept

Standard form: Ax + By + Cz = 0
I can determine whether a linear relation is a partial or a direct variation by examining its table
of values, its graph or its equation
Direct variation
Partial variation
(0, 0) is an ordered pair in the table of value
(0, 0) is not an ordered pair in the table of value
The initial value is 0, so the graph passes through (0, 0)
The initial value is some number b, so the graph
passes through (0, b)
The equation looks line y = mx
The equation looks line y = mx + b
D. I can identify a solution to a linear relation as being

an ordered pair that appears in the table of value

a pair (x, y) that lies on the line representing the linear relation

a pair (x, y) that makes a true statement in the equation of the relation
E. I can determine the rate of change of a linear relation by doing one of the following:

calculate the first differences in a table in which the x - values increase or decrease by 1

calculate the slope,
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
, using any two points on a graph of the relation. The rate of change has
the same value as the slope.
𝑚=
∆𝑦
∆𝑥
=
𝑦2 −𝑦1
𝑥2 −𝑥1
F. I can determine the solution to an equation by isolating the variable in the following way:

if the variable appears on one side perform the inverses of the operations one at a time, in their
opposite order, until the variable is isolated

if the variable appears on both sides, use inverse operations to group the variable on one side,
then solve as indicated by the first bullet
G. I can solve an equation for one variable in terms of another variable by following the next steps:

if the variable appears on one side perform the inverses of the operations one at a time, in their
opposite order, until the variable is isolated
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MPM1D Exam Review 2016
EXAMPLES
6. Identify the following as either linear or nonlinear.
a.
y  5 x 2  3
d.
b. y  7  5 x
c.
TABLE A
x
y
0
25
1
36
2
49
3
64
4
81
1st Differences
7. A prototype rocket is launched from a hill 500m above the sea level. It rises at 40 m/s
a. Write an equation for the relation between the
height of the rocket and the time
b. Graph the relation
c. Identify the relation as a direct or partial variation
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MPM1D Exam Review 2016
8. Gord bought a new phone for $750 in 2012. This graph shows its value over the first three
years.
a. How much does the value of the
phone go down every year?
Axis Title
Value of Iphone over years Iphone value
c) Write an equation for the relation
between the phone's value and its
age.
$800
$700
$600
$500
$400
$300
$200
$100
$0
2011
2012
2013
2014
2015
2016
Axis Title
d) Use your equation to determine the value of the phone after in 2015 years.
9. This graph shows how Maria is snowboarding down
the hill.
a. On which segment is Maria go fastest? Why?
b. On which segment will she go slowest. Why?
c. Prove your answers to part a and b mathematically.
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MPM1D Exam Review 2016
III.
ANALYTIC GEOMETRY
SUCCESS CRITERIA
1. I can identify the steepness and direction of a line by analyzing its slope

The greater the magnitude of the m-value, the steeper the line

A line rising to the right has a positive slope

A line falling to the right has a negative slope

A horizontal line has a slope of 0 and its equation has the form y = b where b is the value of the y intercept

A vertical line has an undefined slope and its equation has the form x = a, where a is the value of the
x - intercept
2. I can graph an equation in the form Ax + By + C = 0 or Ax + By = D by rewriting it in the from
y = mx + b using inverse operations to solve for y
3. I can locate two points on most lines by plotting the y - intercept and locating the second point
using the rise and run of the slope. Then I can draw the line.
𝒓𝒊𝒔𝒆
4. I can calculate the slope, 𝒓𝒖𝒏 , using any two points on a graph of the relation. 𝑚 =
𝑦2 −𝑦1
𝑥2 −𝑥1
5. I can find a point on a line if given the slope and another point on the same line by substituting both
points and the given slope into the formula and use inverse operations to solve for the unknown
coordinate
6. I can determine the equation of a line in the form y = mx + b if you know two points on the line or
one point and the slope:

if the slope is not given and you know two points on the line use them to calculate the slope

substitute the slope and the point (x, y) of a point on the line into y = mx + b and solve for b.

use the values of m and b to write the equation of the line
7. I can determine if two lines are parallel or perpendicular

the slopes of parallel lines are equal m1 = m2

the slopes of perpendicular lines are negative reciprocals 𝑚1 =
1
−𝑚2
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MPM1D Exam Review 2016
EXAMPLES
10. For each determine the slope and y-intercept:
a. The equation y  
2
x  4.
5
b.
m = _____
b = _____
m = _____ b = _____
11. Express each of the following in the form y = mx + b.
a) 3 x  4 y  16  0
b) 
1
1
x  y  12
2
5
12. A line passes through the points A (1, –3) and B (2, 4). Find:
a. The slope of the line AB.
b. The equation of the line in the form y = mx + b.
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MPM1D Exam Review 2016
c. The slope of a line parallel to AB.
d. The slope of a line perpendicular to AB.
13. A stress test evaluates the health of a patient's heart. While riding on a stationary bike or
running on a treadmill, a patient has his or her heart rate measured by a technician and compared
with a safe maximum heart rate. This safe heart rate is based on the patient's age as shown in the
graph.
a. What does the y-intercept represent in this
situation? What is the value of the y-intercept?
b. What does the slope of the graph represent? What
is the slope?
c. Determine the equation for the line.
d. Ellen is 14 years old. Using your equation, determine her maximum safe heart rate.
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MPM1D Exam Review 2016
14. Draw a line through point A(2, -5) with a slope of 
1
.
4
10
8
6
4
2
-10 -8 -6 -4 -2
2
4
6
8 10
-2
-4
-6
-8
-10
15. Evan and his sister Sarah shovel driveways during the winter. They charge $10 for a double
driveway and $5 for a single driveway. This past winter, Evan earned $225 and Sarah earned
$230.
a. Write equations for both Evan and Sarah to represent the relationship between the amounts
earned shoveling single and double driveways.
b. Isolate the variable used for single driveways in both equations.
c. If the both shoveled 10 double driveways, how many single driveways did each shoved?
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MPM1D Exam Review 2016
IV.
MEASUREMENT AND GEOMETRY
SUCCESS CRITERIA
1. I can find the sum of angles in a polygon using the formula 180o x (n-2), where n is the number of
sides of the polygon.
2. I can find the interior angles of a regular polygon for the given sum of interior by dividing the
sum by 180o and add 2.
3. I can determine the exterior angles of a regular polygon knowing that the sum of all exterior
angles is 360o.
4. I can identify all quadrilaterals and their properties (see lesson and anchor charts)
5. I can identify the measure of an exterior angle of a triangle by adding the measures of two
interior angles opposite it.
6. I can identify the length of a midsegment in a triangle by calculating half the length of the side
opposite it
7. I can find the minimum perimeter of a rectangle with a given area, knowing that it's a
square.
8. I can find the maximum area of a rectangle with a given perimeter, knowing that it's a
square.
EXAMPLES
16. The measure of ACB is 39o. What are the values of x
and y? Give reasons!
17. Determine the value of x.
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MPM1D Exam Review 2016
18. Find the values of the indicated measures. Give reasons for each step!
73
c
53
a = ________
a
b = ________
b
c = ________
40
19. What is the measure of each of the other 2 angles labeled x ?
90
90
x
x
90
20. A stop sign has a shape of a regular octagon.
Determine the measure of each of the interior angles on a stop sign.
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MPM1D Exam Review 2016
21. An ironing board is designed so the board is always parallel to the floor as it is raised and lowered. In
the diagram, the two triangles are isosceles and AEB = 88o. Determine ALL the angles in CED. State
the rules that apply.
22. In the given diagram, determine the values of r and w. Explain
you arrived at each step in your solution.
how
23. A rectangular flower bed with an area of 800 m2 is attached to the side of a building.
Determine the minimum length of edge stone needed to enclose the three open sides.
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MPM1D Exam Review 2016
24. Calculate the surface area and the volume of the following regular pyramid.
25. What is the measure of the interior and the exterior angles of a regular heptagon?
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