QMI1500
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WORKINGS AND
SOLUTIONS
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Question 1
’
If x = 4, find the value of the sum &( ) (5 + 𝑥 &)
Solution
’ &
&( ) (5 + 4)
• Substitute x = 4 into this equation:
• When t = 0, you4- get (54 + 4)) = 5 + 1) = 5 + 1 = 5 •
When t = 1, you get (5 + ) = 5 + = 5 + 2 = 7
• When t= 2, you get (5 + 4.) = 5 + 16 = 5 + 4 = 9
• When t= 3, you get (5 + 4’) = 5 + 64 = 5 + 8 = 13
• The sum of all these gives 5 + 7 + 9 + 13 = 34
Question 2
Solve for x in the following equation
Solution
• Left Hand Side gives:
• Right Hand Side gives: - 1.
o Multiplying top and bottom by 2 gives Right
.
Hand Side gives: .
Now equate the left to the right and you get:
Since the denominators are equal, it means that we can
also equate the numerators. This gives 3x -3 = 2 -10x
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Manipulate the equation
to get 13x = 5 And
therefore x =
-’
Question 3
Find r if 4𝑟 + 3 − 2 = 3
Solution
Manipulate the equation to isolate the variable that you
are trying to solve for
4𝑟 + 3 = 3 + 2 = 5
.
Square both sides to give: 4𝑟 + 3 = 5. = 25
On the left: the square root and the power of 2 cancel
each other out. We are left with just 4r + 3
Equating both sides gives
4r + 3 = 25 More
manipulation gives: 4r =
25 – 3 = 22
Divide both sides by 4 and get r = ..
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Question 4
Find the value of the following expression:
Solution
• Convert the mixed fractions into improper fractions
(i.e. where the numerator is bigger than the
- -’
denominator) o becomes o becomes o
becomes
• Find common denominator o 8 and 4 already have
a common denominator between them which is 8.
Multiply this by 5 to get a common denominator
amongst all 3 – you get 40
• Adjust numerators accordingly before adding them
o Multiply 37 by 5, to get 185 o Multiply 13 by 10,
to get 130 o Multiply 6 by 6, to get 48 o Adding these
up gives a numerator of 103 (185 – 130 + 48)
• The new expression of -)2)’
• Simplifying this gives us 2 .’2)
Question 5
Simplify the following:
Solution
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EXAM PACK
100% TRUSTED
WORKINGS AND
SOLUTIONS
This work is original and free from plagiarism.
Any references or quotations are properly cited.
LearnedWriter upholds academic integrity and
discourages dishonest practices, including
plagiarism.
, lOMoAR cPSD| 49074884
Question 1
’
If x = 4, find the value of the sum &( ) (5 + 𝑥 &)
Solution
’ &
&( ) (5 + 4)
• Substitute x = 4 into this equation:
• When t = 0, you4- get (54 + 4)) = 5 + 1) = 5 + 1 = 5 •
When t = 1, you get (5 + ) = 5 + = 5 + 2 = 7
• When t= 2, you get (5 + 4.) = 5 + 16 = 5 + 4 = 9
• When t= 3, you get (5 + 4’) = 5 + 64 = 5 + 8 = 13
• The sum of all these gives 5 + 7 + 9 + 13 = 34
Question 2
Solve for x in the following equation
Solution
• Left Hand Side gives:
• Right Hand Side gives: - 1.
o Multiplying top and bottom by 2 gives Right
.
Hand Side gives: .
Now equate the left to the right and you get:
Since the denominators are equal, it means that we can
also equate the numerators. This gives 3x -3 = 2 -10x
Downloaded by Vincent master ()
, lOMoAR cPSD| 49074884
Manipulate the equation
to get 13x = 5 And
therefore x =
-’
Question 3
Find r if 4𝑟 + 3 − 2 = 3
Solution
Manipulate the equation to isolate the variable that you
are trying to solve for
4𝑟 + 3 = 3 + 2 = 5
.
Square both sides to give: 4𝑟 + 3 = 5. = 25
On the left: the square root and the power of 2 cancel
each other out. We are left with just 4r + 3
Equating both sides gives
4r + 3 = 25 More
manipulation gives: 4r =
25 – 3 = 22
Divide both sides by 4 and get r = ..
Downloaded by Vincent master ()
, lOMoAR cPSD| 49074884
Question 4
Find the value of the following expression:
Solution
• Convert the mixed fractions into improper fractions
(i.e. where the numerator is bigger than the
- -’
denominator) o becomes o becomes o
becomes
• Find common denominator o 8 and 4 already have
a common denominator between them which is 8.
Multiply this by 5 to get a common denominator
amongst all 3 – you get 40
• Adjust numerators accordingly before adding them
o Multiply 37 by 5, to get 185 o Multiply 13 by 10,
to get 130 o Multiply 6 by 6, to get 48 o Adding these
up gives a numerator of 103 (185 – 130 + 48)
• The new expression of -)2)’
• Simplifying this gives us 2 .’2)
Question 5
Simplify the following:
Solution
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