Download Mathematics - MADAR International School

Semester One Mid-Term Exam Guidelines
2016- 2017
Department: math
Grade: 7
Date of the Exam:
You will be assessed on the following skills:
Content
Topic
To define the Key words :
3.2
Simplifying and
evaluating
algebraic
expressions
Resources
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Terms: A number , a variable or a product of a number and one or
more variables. Terms are the parts of the expression that are
added or subtracted
Coefficient : The numerical factor that is multiplied by a variable
Variable : is a letter used to represent unknown numbers
Constant : is the term that does not have a variable .it is fixed
number
Like Terms : Terms that have exactly the same variables that are
raised to the same power
Evaluate : To find the value of the expression by substituting the
variable with its value
1. To identify the coefficient of the terms in algebraic
expression :
Example :
3xy2 + 2y – x - 30
a) Terms :
4 terms
C) Variables : xy2 , y , x
b) Coefficient: 3 , 2 , -1
d) Constant : - 30
2. To simplify the algebraic expressions by combining like
terms
Example 1 :
Terms
Like or unlike Terms. Why ?
2x , 3x
Like Terms ( changing the
coefficient or its sign are not
reasons to judge terms as
unlike terms )
2x2 , 2x3
Unlike terms ( changing the
power of the variable
X2 , y 2
Unlike terms ( changing the
variable changed the term)
Students must
study any related
worksheets ,notes
and assessments in
addition to
referring to the
following
resources :
Text book :
p. 66-67
Practice book :
p. 73-74
Example 2 :
Simplify the expression :
2n2 + 4n – 3n2 + 2n + 20
 (2n2– 3n2 ) + ( 4n + 2n ) + 20 : use the commutative and
associative property to combine the like terms
 (2-3 )n2 + ( 4 + 2) n + 20 : add/subtract the coefficients
,use the distributive property
 -1n2 + 6n + 20
 -n2 + 6n + 20
: rewrite ( -1n2) as (–n2)
:The expression has been simplified
Example 3 : using distributive property to simplify the
expressions
3. To evaluate algebraic expressions for a given value of the
variable
Example : evaluate the expressions for the given value of the
variable :
2m + 3m2 + 6
for m = 5
 2(5) + 3 ( 52 ) + 6
: substitute 5 for m
 2(5) + 3(25 ) + 6
multiply
: evaluate the exponent then
 10 + 75 + 6 = 91
: add the like terms
3.3
To define the Key words :
Text book :
Equations
 Solution: is the value of the variable that makes the
equation true
p. 68-69
 Equation : is the statement in which two expressions are
equal. The equation is either algebraic or numerical
 Conditional equation : is algebraic equation that is True
for some real numbers
 Identity Equation : equation that is true for all real
numbers
 Algebraic equations : equations that include variable/s
,and they are classified as open equation
Practice book :
p. 75-76
 Numerical equations : equations that include only
numbers, and they are classified as closed equation ,and its
either true or false
1. To write word sentences as equation
Translate the word sentences to mathematical expressions
Example :
a + ( -3 ) = 48
The sum of a number (a) and the
opposite of 3 is 48
m ÷ 4 = 20
The Quotient of a number m and 4 is 20
2x + 8 = 12
Twice a number (x) increased by 8 is 12
h= 3 + y
Hamad is 3 years older than Yara
2. To determine whether a given number is a solution to a
given equation
The value of the variable is considered to be a solution if
it makes the equation true
Example: tell whether ( -2 ) is a solution to the equation below :
3x +2 = 1
 3( -2 ) + 2 = 1
 -6 + 2 =
-4
 Does
-4 = 1 ?
 -4 ≠ 1
then
:
substitute the given value
: Simplify
No , then it is false equation
x = -2
is not a solution
3. To identify the properties of equality
To find equaivalent equation apply

Reflixive property of equality

Transitive property of equality

Symmetric property of equalty

Addition,subtraction, multiplication ,and division properties
3.4
One step addition
and subtraction
equations
1. To solve equations by using the addition and subtraction
properties of equality
Text book :
p. 70-71
Practice book :
p. 77-78
3.5
One step
multiplication and
division
Equations
2. To solve equations by using the multiplication and division
properties of equality
Text book :
Multiplication
equation
Practice book :
Steps
Division equation
p. 72-73
p. 79-80
2x = 4
Multiplication
Identify What
operation that is
being performed on
the variable
2x ÷ 2 = 4 ÷2
Divide by 2
Apply the division
property of equality
X=2
2(2) = 4 True
n ÷ 3 = - 12
Division
3
Isolate the variable
by applying the
inverse property of
equality
Simplify
Check by substituting
the value of the
variable
n
= 3 ( - 12 )
3
Multiply by 3
Apply the
multiplication
property of equality
n = -36
-36 ÷3 = -12 True
Sample questions :
1. Fill in the blanks with the right concept :
a) Equation that is true for all real numbers is called ……………………………..
b) The algebraic equation that is True for some real numbers …………………………………….
c) ………………….........have exactly the same variables that are raised to the same power
d) The value of the variable that makes the equation true is called ……………………………………..
2. List all the conditions that are needed for terms in expressions to be considered as “ like Terms
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
3. State the statement that clarify the following properties of equality .Support your answer with a
clear example
a) Symmetric property of equality
b) Transitive property of equality
4. Identify the number of terms, coefficients, variables, and the constant in each expression
a) 12x2y + 5 m2 - m
Number of terms
Coefficient
Variable/s :
Constant
5. Classify and Justify :
Classify the following equations as conditional and identity equations. Then Explain your answer
a) 5+ x = 13
b) X 2 = 2 X
6. Simplify the expressions .Then evaluate for x = 5 , m = 2
1) -7 + 5x2 + 2y2 - 2x2
2) 3( m + 7 ) + 6m – 15
7. Decide Whether the given value of the variable is a solution to the given equation .Write Yes or No
a) -n + 3 = 23
for
n = 26
b) -5( a + 3 ) = - 30
for
a= 3
8. Use the table below to classify the equations into open and closed equations.
Decide whether the open equations are True or false
Word phrases
Write the Equation
Open or
closed
A number divided by 7 is
20
5 less than 17 is (- 12)
Solve the following equations for (m).Then check your answer
a) m + 6.7 = - 8.3
b) 25 – m = 23
c)
m – 45 = 200
d) 5m = - 85
e)
m
= 4.5
22
If the Equation is closed decide if
its : True or false
9. Problem solving :
a) Dana is thinking of a number. If she subtracts twice her number from 200, the result is 60.
What is Dana's number?
b) Ahmad grouped his CDs into 5 categories .Each category includes 100 Cd.
1) Write an equation to represent the given situation :
2) Solve the equation to find how many CDs Ahmad has in each category .
3) Your friend suggested that Ahmad has 10 CDs in each category .Urge to proof that
your friend is mistaken
c) Create an equation in which :
1. Algebraic expression is equivalent to a numerical expression
2. You apply addition property of equality to isolate the variable
3. You Suggest a solution that makes your equation false
Additional resources :
http://www.mathwords.com/e/equation_rules.htm
http://www.mathantics.com/
https://www.youtube.com/watch?v=sP_lJyo1U00
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-one-step-add-subequations/e/one_step_equations