Mathematics Assignment

This document contains solved assignments and study material for mathematics. It includes topics such as numbers, fractions, percentages, algebraic expressions, and equations.

mathematics
[DATE]
Grizli777

Question 1
Numbers to two decimal places
(a) 5.435 = 5.44
(b) 142.9247 =142.92
(c) 0.00968 = 0.01
Question 2
S. No. Fraction
(simplified forms)
Decimal
(two decimal places)
Percentage
(nearest whole percent)
(a) 18
25
0.72 72%
(b) 12
25
0.48 48%
(c) 13
20
0.65 65%
(d) 13
40
0.325 33%
Question 5
Weightage of the tasks is highlighted below.
Assessment Task Weighting Mark
Written Assignments 30% 40
50
Participation 30% 12
20
Exam 40% ?
100
The combined assessment marks that needs to be obtained by Kermit in order to get the
Credit (60% - 69%) score is calculated as shown below.
Let the exam mark obtained by Kermit is x.

Written assignments score = 30% of 40 = 40*30% = 12
Participation score = 30% of 12 = 12*30% = 3.6
Exam score = 40% of x = x*40% = 0.40x
The minimum percentage for Credit score = 60%
Total marks = 60% of {(30%* 50) + (30%*20) + (40%*100)} = 60% * 61 = 36.6
Hence,
Minimum marks for Credit score = 12 +3.6 +0.40x = 36.6
15.6+0.40 x=36.6
x=52.5
And
The maximum percentage for Credit score = 69%
Total marks = 69% of {(30%* 50) + (30%*20) + (40%*100)} = 69% * 61 = 42.09
Maximum marks for Credit score = 12 +3.6 +0.40x = 42.09
15.6+0.40 x=42.09
x=66.23
Therefore, it can be concluded that assessment marks that needs to be obtained by Kermit in
order to get the Credit (60% - 69%) score would fall between 53 and 67.
Question 8
(i) Three less than the product of eight and a number x
Here,
The first number = 8
The second number = x
Product of eight and a number x = 8x
The product is less than 3 = 8x – 3

Hence, the expression = 8x-3
(ii) The difference of twice a number x and 3, increased by negative four
The given number is x
Twice of number x = 2x
The difference twice a number x and 3 = 2x-3
The difference is increased by negative four = (2x-3) + (-4)
Hence, the expression= (2x-3) + (-4)
In simplified for = 2x-7
(iii) Algebraic expression as a sentence
( 4 + x ) −(5 ÷ y )
Here,
(4+ x ) would be written as “four increased by a number x”
(5 ÷ y)would be written as “five divided by y”
Hence,
( 4 + x )−(5 ÷ y )would be written as “four increased by a number x is decreased by a
number five divided by y”
Question 9
(a) Sum of three consecutive odd numbers = 249
Middle number = Prime number
Smallest of the three number =?
Variable: Let the first odd number is x.
The second odd number would be x+2

The third odd number would be (x+2) +2 =x+4
Now,
Equation:
The equation can be formed as
x + ( x+2 ) + ( x +4 ) =249
3 x+ 6=249
3 x=249−6
3 x=243
x= 243
3 =81
Hence, the three consecutive oddnumbers would be
x=81 , x+2=83 , x+4=85
The smallest of the three consecutive odd numberswould be 81.
(b) Perimeter of the hexagonal = 74 meters
Variable:
Length of shortest side is x meter.
Four shortest sides (each of same length) = x meters
Fifth side five meter longer than x = x+5
Sixth side = 2x-1
Now,
Equation:
Sum of all six sides would be the perimeter of the hexagonal. Hence,

x + x+ x +x + ( x+ 5 ) + ( 2 x −1 ) =74
4 x+ x +5+2 x−1=74
7 x +4=74
7 x=70
x=10
Length of each four shortest sides = x= 10 meters
Fifth side five meter longer than x = x+5 = 15 meters
Sixth side = 2x-1= 20-1 = 19 meters
Therefore,
Length of shortest side would be10 meters.
Question 10
Equation to make k as the subject
(a) k −3 j= j
k = j +3 j
k =4 j

(b) 4 k +8=6−2 j
4 k=6−2 j−8
4 k=−2−2 j