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
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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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C) Comment on distributed marks
Average value of the marks = ∑FX / ∑F
= 1735 / 25
= 69.4
It can be said from the above table that, average marks which gained and obtained by the
students of class are like 69.4 out of total 100 marks. Under this specific average value total 7
students rely among 25 available pupils.
Week 7
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QUESTION 8
A) 4 real-life examples where probabilities can be used
In the life of particular person, there are probabilities are supportive tool in order to
identify risk associated with specific criteria and event. On the basis of that, individual able to
know that how much level of chances or probability is there of risk and prevention. 4 examples
in which such concept used in the life are described below:
1. Planning of weather: In order to derive that there will be hail or rain or snow in the
upcoming times the probability tools and techniques are taken into account.
2. Sports strategies: There are several kinds of techniques used in the sports by athletes
and coaches and to derive the best and effective strategy they use concept of
probabilities.
3. Insurance options: For making analysis of various insurance policies and determine
most profitable the probability is taken into account in the real life.
4. Games and recreational activities: At the last, probability uses by people in terms of
select specific game or action which are recreational and become profitable.
B) Value of X
Value of probability remains always one or 100% and at the current case, total is 0.60 or
60% for the three numbers. Calculation for X probability is such as follows:
Numbers 1+2+3+4+5 = probability 1
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X+0.20+0.10+X+0.30 = 1
0.60X = 1
X = 1-0.60
X = 0.40
Further the X value will be divided in two parts for two numbers like 1 and 4.
Probabilities of 1 and 4 will be like 0.20 and 0.20 respectively (0.40/2).
C) Number of times for 4
5 sided spinner takes total 100 times where equal distribution will be done for all the
numbers. Hence, times of 4 number will be 20 and simplification of it is as below:
4 number = 0.20 probability * 100 times
4 number = 20 times
D) Symmetry characteristics in context to the probabilities
1. Median or middle value of the data set and arithmetic mean or average value of the whole
available data.
2. Symmetry probability distribution is unimodal where median and average values are
coincided by mode.
3. All the central moments or values come under odd nature are equal to zero due to having
negative terms.
4. For the symmetry model of probability distribution, every values of skewness are
considered equal to zero.
Week 8
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SECTION 2
TASK 1: Two illustrations of real life
1. In order to purchase a new production equipment at the operation department of my
company I use the NPV calculation because of having two options. With the help of NPV
I am able to select the viable project which has the higher value after completion of its
estimated life.
2. Apart from this, at the time of making investment in the bank, I had use the concept of
simple interest rate which is given by them. Further, by taking support of simple interest
rate calculation I get the fair value or amount of interest.
TASK 3: Reflective log
It can be said from the above self-assessment that, I am confident in order to make or
derive solution of Net present value of the project, powers or fractional values, simple interest
etc. Along with this, I can easily determine the interest amount of investment in case of
compound rather than simple. I have full confidence in terms of making calculation of different
laws and rules of the root as well as powers. When any kind of problems are given to me related
to the NPV and simple interest rate then I can easily resolve. The reason is that, for such both the
topics I am the most confident.
In the above mentioned those concepts are introduced in which I am the most and proper
confident but some areas are there like probabilities and linear equation, high improvement is
required. Under the probabilities section, I have little knowledge but to perform calculation I am
not sure. Further, I cannot make computation of exchange rate probabilities. Moreover, I have
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not any idea regarding to the linear equation and relationship by which it is not possible to make
calculations of it. Further, probabilities and linear equation are those areas in which enhancement
and improvement is required in me.
It can be evaluated or reviewed from the current project of numeracy 2 that, consistent
contribution as well as involvement in the class is highly necessary. It will help to learn all the
things and perform calculations in proper ways. Further, to take experience and practice
independent study and is required.
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