MATHS Assignment - Foundations of Mathematics, Semester 1, XYZ Uni

This document presents a complete solution to a maths assignment, addressing various algebraic problems and equations. The assignment covers topics such as calculating weighted averages, simplifying expressions, evaluating equations, and solving for unknowns in different scenarios, including geometric problems involving trapeziums. The solution demonstrates step-by-step calculations and explanations, providing a comprehensive guide for students studying foundations of mathematics. The assignment includes multiple questions with detailed solutions, offering a valuable resource for understanding and mastering fundamental mathematical concepts. The document also includes references to relevant academic resources.

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

2
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)

3
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

4
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

5
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)

6
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)

7
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.