Maths Assignment Solutions and Past Papers

This maths assignment provides detailed solutions to various math problems and past papers from a university-level course. It covers topics such as weighted assessments, algebraic equations, and geometric shapes. The assignment is divided into questions (Q1-Q10) with corresponding answers and explanations.

Running head: MATHS ASSIGNMENT
Maths Assignment
Name of Student
Name of University
Author Note

1
MATHS ASSIGNMENT
Table of Contents
Q1....................................................................................................................................................2
Q2....................................................................................................................................................2
a)..................................................................................................................................................2
b)..................................................................................................................................................3
Q3....................................................................................................................................................3
Q8....................................................................................................................................................4
a)..................................................................................................................................................4
b)..................................................................................................................................................4
c)..................................................................................................................................................4
Q9....................................................................................................................................................4
a)..................................................................................................................................................4
b)..................................................................................................................................................5
Q10..................................................................................................................................................5
a)..................................................................................................................................................5
b)..................................................................................................................................................6
References........................................................................................................................................7

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MATHS ASSIGNMENT
Q1.
It is given that for the maths semester, written assessment has 50% weightage, class tests
have 20% weightage and the final exam has 30% weightage.
Ron had scored 30 out of 50 in his written assessment. This means that he scored 60% in written
assessment. He scored 120 out of 150 in the class tests which is 80%.
Ron must score 50% overall to pass the semester. Let “x” be the total marks. Then Ron must
score 0.5x to pass.
Ron has already scored 60% of 0.5x in written assessments, 80% of 0.2x in class tests (Blitzer,
Mayne, and Pietro, 2017).
The marks already obtained by Ron= 0.6*0.5x + 0.8*0.2x = 0.3x+0.16x = 0.46x
Therefore, in order to pass he needs to score 0.5x-0.46x=0.04x
The final tests are conducted on a total of 100 marks and hold 30% weightage.
Let z% of 100 be the marks that Ron needs to score in the exam to pass.
Then, z% of 0.3x should equal 0.04x.
Then, z
100 * 0.3 x =0.04x  z = 40
3 = 13.33
Therefore z % of 100 = z = 13.33
Therefore, Ron should score 13.33 or more out of 100 in his exam to pass this semester.
(Answer)

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MATHS ASSIGNMENT
Q2.
a)
4 y +5 x −2 x−7 y +3 x + y
= ( 4 +1−7 ) y + ( 5+3−2 ) x
= −2 y +6 x
= 2(3 x− y ) (Answer)
b)
3 xy +4 x2−2 x2 y +7 xy −5 x2 +8 x2 y−7 x y2
= (7+3) xy−(5−4)x2 +(8−2) x2 y−7 x y2
=10 xy−x2 +6 x2 y−7 x y2
=x ( 10 y −x+ 6 xy −7 y2 )
=x ( 10 y −7 y2−x +6 xy )
=xy ¿ (Answer)
Q3.
Given that a= 4 and b=-10
2 b2−25 a
=2 (−10 )2−25 ( 4 )
=200-100

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MATHS ASSIGNMENT
=100 (Answer)
Q8.
a)
The algebraic equation expressing, “A dozen more than four lots of y”.
Answer: 12+4 y
b)
The algebraic equation expressing, “Double the quotient of y and ten, then plus seven times
x.”
Answer: 2 y
10 + 7 x
c)
Find twenty five less than product of three and x, then add to the difference of y and 4x.
Answer: ( y−4 x )+ (3 x−25)
Q9.
a)
It is given that sum of 3 numbers who are consecutive to one another is 33.
Let the largest of these 3 numbers by x. The numbers are x, x-1 and x-2. It is also mentioned that
one of these 3 numbers is a prime number which is obvious and unnecessary for our purposes.
Then x + ( x−1 ) + ( x−2 ) =33
Therefore 3 x−3=33

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MATHS ASSIGNMENT
That is, ( x−1 )=11
Then x equals 12. This means that the required numbers are 12, 11 and 10.The largest number
is 12. (Answer)
b)
It is given that the shortest side of a trapezium is x metres. Its longest side is 3x metres.
The parallel side of the longest is said to be equal to 2x+1 metres and the remaining side in x+2
metres.
The perimeter of the trapezium is given to be 38 metres. The perimeter is calculated by
the formula:
P= a + b + c + d, where a, b, c, d are sides of the trapezium (Kaufmann and Schwitters, 2014).
Then based off the given information,
38 = x + 3x + (2x + 1) + (x + 2)
Then,
7x + 3 = 38
 7x = 35
 x = 5
Then the parallel sides of the trapezium are 15 metres and 11 metres. The other sides are 5
metres and 7 metres. The shortest side is 5 metres. (Answer)

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MATHS ASSIGNMENT
Q10.
a)
T+4u=5
 T= 5 – 4u (Answer)
b)
3t-2u= 4u+7
 3t = 4u +2u +7
 3t = 6u +7
 t = 6
3 u + 7
3
 t = 2u + 7
3 (Answer)

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MATHS ASSIGNMENT
References
Blitzer, R., Mayne, M.C. and Pietro, J., 2017. College algebra. Pearson.
Kaufmann, J. and Schwitters, K., 2014. Elementary algebra. Nelson Education.