Numeracy Assignment: Foundations of Mathematics, Semester 1

This homework assignment delves into fundamental numeracy concepts, encompassing indices, roots, and various interest calculations (simple, compound, semi-annually, and quarterly). The assignment explores the laws of indices, including their evaluation, and illustrates root laws with examples of square, cube, and fourth roots. Furthermore, it covers scientific notation and its application. The document also addresses time value of money problems, including calculating the time for an investment to double and determining compound interest rates. While the student demonstrates proficiency in NPV and interest calculations, they acknowledge a lack of understanding regarding linear relationships and probabilities. The assignment concludes with an analysis of data sets, histogram creation, and comments on distributed marks, followed by real-life examples of probability usage and related calculations. The document also includes a reflective log, self-assessing the student's confidence in various topics and identifying areas for improvement, such as linear equations and probability calculations.

NUMERACY 2

SECTION 1
QUESTION 1
A. Three laws of indices
1. First law: The first law of indices in which power or fractional value of same base digit are
supposed to add with each other. Further, summation value will be consider as the fractional and
of one digit where base are same.
2. Second law: In the second law, fractional or power values are subtracted when base value has
to divide with each other. The value which remains is considered for deriving output or make
proper solution.
3. Third law: As per the third law, when fractional value are two like on base and on the whole
bracket then both powers are multiplied each other. Example of third law of indices is shown
below:
B. Solution of the laws
1. First law:
8^6 8 8^5
= 8^6+5
-= 8^11
2. Second law:
8^ 5 / 8^3
= 8^5-3
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= 8^2
3. Third law:
(8^6)^2
= 8^6*2
= 8^12
C. Evaluation
1. First law: It can be evaluated from the first law that, all the values available of fractional on
same base and digit are to be added where power increases. It is highly necessary that, base must
be same or equal on which power is included.
2. Second law: Under this, due to dividing base of different fractional there are power are to be
deducted with each other. Here total values of power reduces in comparison to other both laws of
indices.
3. Third law: As per the last law, it can be reviewed that, fractional values multiplied and
enhance with the higher rate as compare to other laws. Output value of the respective law is the
highest due to having high fractional digits.
QUESTION 2
A. Three illustrations of root laws
1. Square root: √81 = 9 (9*9)
2. Cube root: 3√64 = 4 (4*4*4)
3. Fourth root: 4√1296 = 6 (6*6*6*6)
B. Evaluation
1. Square root: In the law of square root, there outcome and solution is fractional up to two
times of the origin digit. In short, origin value is multiplication with itself of the output.
2. Cube root: Second rule is cube root which is three times multiplication and then derives the
final output of the problem. In this, just before the root sign digit “3” is mentioned which
indicate that it is cube root.
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3. Fourth root: According to the fourth root, specific digit is multiplied itself up to the four
times and then assessed answer. In addition to this, digit “4” is always marked before the symbol
of root which reflects that it is fourth root in the nature.
C. Scientific notation
The term of mathematics under which a big or large amount is to be written in short and
small number is called as scientific notation. Very basic trick used is that, after the first digit all
are converted into zero and then write in different way which is mentioned below. Further,
scientific notation of 6,80,000 is such as follows:
680000 = 6.8 * 10^5
Weeks 1-2
3

QUESTION 3
A. Simple interest
B. Annually compound interest
C. Semi-annually compound interest
D. Quarterly compound interest
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QUESTION 4
A. Time taken to become investment amount double
It can be said that amount invested worth of 80000 GBP will become double and reach at
1,60,000 within 15 years 8 months.
When making calculation of this with the help of rule of 72 it will be double in 16 years
(72 / 4.5).
B. Calculation of compound interest rate
Interest rate in the current case is 2% where investor generate 9751.96 GBP from the
investment worth of 8000 GBP up to 10 years.
Weeks 3-4
5

QUESTION 5
In order to not having knowledge about the linear relationship concept and problems, it is
not possible for me to determine solution of it. Only one thing I know about this is that, linear
concept of mathematics shows relation among two or more variables but not in appropriate ways.
Along with this, it is clearly stated under the below table of skills audit that, I cannot do and
perform any kind of simplification of the linear equation and determine relationship of the
variables. Due to such all the responsible factors and causes, questions of the linear equation are
not performed or analysed.
Week 5
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QUESTION 6
A) Calculation of NPV of the project
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B) Advise to the ATOB Trading Limited
Net present value shows that project will provide up to which level of profit and return of
the initial investment. Positive NPV of the project will be accepted while negative will be
rejected by the company. At the present scenario, NPV of the project is negative which is worth
of -9631 which indicates that, it will not generate profit at the end of year. Hence, it can be
advised to the ATOB Trading Limited firm that, it needs to avoid and not undertake the project
within workplace.
Week 6
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QUESTION 7
A) Producing tally of the data set
B) Drawing histogram of the above data set
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