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# 5N1833 Mathematics QQI Level 5 Assignment Example Ireland

Mathematics is a difficult subject to understand, especially when you are not very good at it. This is why we have created this sample for anyone who needs maths help and wants to do well in their QQI Level 5 assignment. We will be going over some of the common mistakes people make when they try and solve problems and give examples of how you should complete your assignments.

The goal of this assignment is to equip the learner with a deep understanding and application for mathematical skills, tools, techniques. These are applied across many different contexts so they can be used on any type or size problem that crops up!

## Learning Outcomes Of (5N1833) Mathematics QQI Level 5 Course

By the end of this course, learners will be able to:

### Modelling Using Mathematics

Modeling is the act of representing or simulating a real-world system, process, or object by means of abstraction. Mathematics can be used to model many different things in our world including physical systems, social systems, and economic systems.

Some of the questions on the assessment may include:

1. Explain the difference between the mathematical model and physical model, and the difference between them.

2. Explain the modeling process in graphical form

3. Solve simple mathematical models, including identifying situations that require mathematical modeling, and using appropriate mathematical skills and processes.

4. Apply simple mathematical models to explain and predict behavior

### Statistics And Probability

Students are often required to study statistics and probability in mathematics. These mathematical concepts can be studied on their own or as part of a wider course, such as calculus, linear algebra, or differential equations. Statistics is the branch of mathematics that deals with collecting and analyzing data about one’s experiments in order to make conclusions about the population from which the sample was drawn. Probability is a branch of pure mathematics that studies random phenomena by considering all possible outcomes without reference to their likelihoods.

Some of the questions on the assessment may include:

1. Discuss statistical concepts, including discrete and continuous variables, sampling, variance, and skewness

2. Present information in a series of graphs and tables, using pie charts, trend graphs, correlation graphs (+/-), cumulative frequency curves, histograms, and frequency tables with discrete and continuous variables

3. By calculating the mean, mode, median, weighted average, range, interquartile range, and standard deviation, calculate the statistics used to measure and compare the average and dispersion of grouped data

4. Use the basic principles of counting, permutation, and combination to calculate the number of possible results for tests that are not repeated

5. Demonstrate an understanding of relative frequency and probability through the use of information technology simulations

6. Solve the simple probability problem of one or two events, including where two events are mutually exclusive and where two events are independent.

7. Discuss the results of the investigation, including the interpretation of the results and possible distortions as well as the reasons for the results of the investigation.

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### Functions And Graphs

In mathematics, functions and graphs are used to solve problems. Graphs help illustrate the relationship between two variables such as distance and time. Functions show a relation between input and output with specific conditions for both.

Some of the questions on the assessment may include:

1. Describe the properties of basic mathematical functions, including linear, quadratic, exponential, logarithmic, and trigonometric functions

2. Define the inverse of the function

3. Draw linear and quadratic functions, show the relationship between domain and range

4. Derive the inverse of the function from the algebraic expression of the function

5. Use a series of formulas to calculate the straight-line equation, including the distance between two points, slope, parallel line, and perpendicular line

6. Solve the problem of maximum and minimum limits given by linear inequalities from the graphs of linear inequalities and half-planes

7. Analyze linear and quadratic function graphs of important attributes, including domain and range, maximum and minimum, increment and decrement intervals, periodicity

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### Calculus

Calculus is a branch of mathematics that deals with limits, derivatives, and integrals. Calculus is used in the sciences (physics, biology), engineering (mechanics, electrical engineering), and economics to find rates of change.

Some of the questions on the assessment may include:

1. Summarize the key concepts of calculus, including limit, differentiation, and integration

2. Explain the basic theorem of calculus

3. Calculate the average rate of change of the related variables x and y of various standard functions y=f(x)

4. Use derivative tables to differentiate simple standard functions

5. Use the product rule, quotient rule, and chain rule to calculate the derivative of a compound function

6. Integral standard integrals, polynomials, trigonometric functions, and exponential functions

7. Use integral to calculate the area between the curve and the x-axis

8. Apply differentiation to solve simple rate-of-change models, including maximum and minimum

9. Application integration to solve simple and practical real-life problems.

### Complex Numbers

A complex number is a number that can be expressed in the form of a + bi, where “a” and “b” are real numbers. Complex numbers are typically used to describe positions on the plane or in space. The imaginary unit, denoted by “i”, is defined as the square root of negative one (-1). Complex numbers are often written with an arrow over each term (e.g., 4+3i) or with a bar above them (4 + 3√-1 i), although this notation has mostly fallen out of use outside computer science since it does not distinguish between pure imaginary and complex conjugate quantities.

Some of the questions on the assessment may include:

1. Explain the meaning of plurals

2. Represent complex numbers on the Argand graph to include distinguishing modulus and parameters

3. Solve quadratic equations with complex roots

4. Perform mathematical functions on complex numbers, including addition, subtraction, multiplication, division, conjugation, modulus, and drawing on Argand diagrams

5. Apply de Moivre’s theorem to find the power of Z and the cube root of 1.

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### Trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It has applications in many fields, including astronomy, engineering, surveying, navigation, physics, and trigonometric functions in calculus.

Some of the questions on the assessment may include:

1. Explore the application of trigonometric functions in daily life.

2. Define the sine, cosine and tangent functions related to the unit circle

3. Use appropriate trigonometric formulas and terminology to solve practical and simple problems, including the ratio of sine, cosine, and tangent of a right-angled triangle, triangle area=1/2absin C, sine rule, cosine rule

4. Analyze the functions y=sinx, y=cosx, y=tanx, and y=asinbx from the graph drawn by determining the period and amplitude.

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