Download Section A: Fill in the blanks (12 marks)

MPM 1D1 – Unit #5 Test – More Algebra
Name: ___________
Short Answer – Write an equation to represent each sentence.
______________1. Five more than a number is 21.
______________ 2. A number decreased by 11 is 15.
______________ 3. Four times a number, added to 6, is 14.
______________ 4. A number divided by 3 is 18
______________ 5.The sum of two consecutive numbers is 303.
Multiple Choice - Identify the best answer by circling the letter.
1. The total cost, C, in dollars, of running an advertisement in a newspaper is $12, plus a
charge of $5.00 per day: where n represents the number of days. Which equation represents
the cost of running an ad?
a) C = 12n + 5
b) C = 12 + 5n
c) C = (12 + 5)n
d) C = 12 + 5 + n
c) 7 = 6y – 2
d) 6 = 6y
2. The equation 7 = 4y + 2(y – 1) is the same as:
a) 7 = 6y – 1
b) 7 = 8y2 – 4y
3. Darrick and Sabrina are each asked to solve an equation.
Who correctly solved his or her equation?
a) Darrick only
b) Sabrina only
c) Both Darrick and Sabrina
d) Neither of them
4. What equation represents the area of the garden below if the total area of the garden is 375 m 2.
Remember area of a rectangle is equal to the length times the width.
a) 25(10 + x) = 375
b) 2(25) + 2(10 + x) = 375
c) 25(10) + 10x = 375
d) 25(10) + x = 375
5. The perimeter of an equilateral triangle is 45 cm. Which equation gives the length of one side?
a)
x
 45
3
c) 3x  45
b) 45x  4
d)
x
3
45
6. By what number would you divide both sides to solve the equation 6 x  12 ?
a) 2
b) 3
c) 6
d) 12
7. Which is the correct solution for 2 x  5  15 ?
a) x = 5
b) x = 15
c) x = 10
d) x = 20
8. By what number would you multiply both sides to solve the equation
a) 2
b) 4
c) -2
x
 2 ?
2
d) - 4
9. y  2 is the correct solution for which equation?
a) 2 y  5  1
b) 3 y  1  5
c) y  3  5
d) 4 y  8  4
10. The perimeter of a rectangle is 36m. If the length is three times the width, what is the length?
a) 4.5 m
11. The expression
a) 6x + 10
b) 18 m
c) 13.5 m
d) 9 m
3x  5
is also equal to:
2
b) 4x
c)
4x
2
d)
3x 5

2 2
Modified True / False
Indicate whether the statement is true or false. If false, change the identified word or phrase to make
the statement true.
____
12.
To solve an equation means to find a number for the variable that makes both sides of
the equation have the same value.
_________________________
____
13.
The algebraic expression
represents two more than a number
_________________________
____
14.
represents the statement two less than five times a number
_________________________
____
15.
x = 2 is the solution for x – 2 = 4. _________________________
___
16.
a = 3 is the solution for 2a + 3 = 9. _________________________
Short Answer – Place your answer in the space provided.
1. Solve each equation using the algebraic rules studied in class. You must show your
algebraic thinking.
a) 4x – 7 = 9
b) 2(4y – 1) = -10
c) - x = -5
d) 0 = 20 – 5x – 5 + 8x
e)
m  3 m 1

4
3
f) 5(m – 2) = 2(m - 2) – 9
g)
1
(x – 2) = 5
3
2. The solution to the equation 7x – 2(x + 5) = 1 – 2(4 – 3x) is x = -3.
Using LS = RS and substitution, verify that this answer is correct.
7x – 2(x + 5) = 1 – 2(4 – 3x) ; where x = -3
3. Rearrange each formula to isolate for the indicated variable.
a) y = mx + b
(for m)
b) P = 2(l + w)
(for w)
c) V = l w h
(for h)
4. The sum of two consecutive numbers is -167. What are the numbers?
5. Rebecca is 7 years older than Jessica. The sum of their ages is 39.
How old are they?
6. The side length or a rectangle is 6 cm longer than the width. If the perimeter of the
rectangle is 48 cm, how long is each side?
7. The formula F 
9
C  32 relates temperature in degrees Fahrenheit to temperature in degrees Celsius.
5
a) Rearrange the formula to isolate C.
b) When the temperature is 0 o F , what is it in Celsius, to the nearest tenth of a degree?
c) On the warmest summer day, the temperature was 100̊F. What was the equivalent temperature in
Celsius, to the nearest tenth of a degree?
Bonus:
Find the perimeter of the shape below.
MPM 1D Unit #5 – Equations
Category
Level 4
Assessment Rubric
Level 3
Name:_______________________ Date:______________
Level 2
Level 1
Below Level 1
Know./
Underst.
Demonstrates a solid and thorough
understanding of Equations (opposite
operations, simple equations, equations
with variables on both sides, equations
involving fractions, rearranging
formulas, word problems and
equations). Able to solve problems
with no errors.
Demonstrates good
understanding of
Equations. Able to
solve the problem with a
minor error(s)
Application
Has a thorough understanding of how
to use the concepts (Equations) to form
a solution.
Has good understanding of
how to use the concepts
(above) to form a solution.
Has some understanding of
how to use the concepts
(above) to form a solution.
Demonstrates a solid understanding of
the connection between the questions
required solution and its interpretation.
Demonstrates good
understanding of the
connection between the
questions required solution
and its interpretation.
Demonstrates a moderate
understanding of the
connection between the
questions required solution and
its interpretation.
Communication
Provides a thorough, clear and
insightful explanation/justification.
Solutions are well formed, with
completeness, accuracy and proper
mathematical form
Provides a complete, clear,
and logical explanation,
missing small details.
Solutions are complete but
some proper form is
missing
Provides a partial
explanation/justification that
shows some clarity and logical
thought. Solutions are somewhat
complete, but disorganized.
Provides a limited or
inaccurate
explanation/justification
that lacks clarity or logical
thought. Solutions are
incomplete, scattered and
disorganized.
Needs to provide some
explanation/justification.
Thinking
Shows flexibility and insight when
carrying out the plan, by trying and
adapting one or more strategies to solve
the problem. (when necessary)
Carries out a plan
effectively by using an
appropriate strategy and
solving the problem.
Carries out the plan to some
extent using a strategy, and
develops a limited and/or
incorrect solution
Uses a strategy and attempts
to solve the problem but
does not arrive at a solution.
Needs to demonstrate a
strategy that could be used
to solve this problem.
Demonstrates moderate
understanding of Equations.
Able to solve the problem with
some errors.
Demonstrates a limited or
inaccurate understanding
of Equations needed to
solve the problems.
Has limited understanding
of how to use the concepts
(above) to form a solution.
Demonstrates little
understanding of the
connection between the
questions required solution
and its interpretation.
Needs to demonstrate an
understanding of
Equations. No attempt
made at solving the
problem, or the attempt has
little or no validity.
Needs to show
understanding of how to use
the concepts answer
question.
Demonstrates an
insufficient connection
between the questions
required solution and its
interpretation.