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STPM Coursework

STPM 2018 Term 1 Mathematics (T) Coursework Sample

STPM 2018 Term 1 Mathematics (T) Coursework PBS Assignment

A complex number is an extension of a real number and it can be represented in Cartesian and polar forms. In this assignment, you are required to explore the powers and roots of complex numbers.

(a) Let z =1+i. Find z^n, where n = 2, 3, 4, …, and represent the complex numbers on an Argand diagram. (b) Rewrite z=1+i in polar form and repeat task (a). (c) Comment on the methods used in (a) and (b).

2 Let z=r(cos pi/5+isin pi/5). Find z^n, where n = 2, 3, 4, …, with a value of r in each of the following cases: (a) 0 (b) r>1. Represent the complex numbers on an Argand diagram and comment on your results.

3. Find the n complex numbers which satisfy the equation z^n=a+bi, for n>3 and represent them on an Argand diagram in each of the following cases: (a) a<>0, b=0, (b) a=0, b<>0, (c) a<>0, b<>0. State the conjugate pairs of the roots, if any.

Please check with your teacher for all the requirements. All sample below are for reference only.

Question 1 (a)

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70 comments.

Nice work! Thank you!

You are welcome

Nice work and it’s very important to all …. Thank and Regards.

How to plot the argand diagram using computer? Can you please teach me??

thank you so much

how to draw the Argand diagram for Q3C in details?

it helps me a lot ! thanks!

Sir, I am curious about what program did you used to plot the graph? May you share it with us? Thank in advance Sir.

may i know roughly how to draw the graphs for question 3?

Um sir. May I know which app or software you use to plot those Argand diagrams?

Sir,do the points in 2 a and 2b need to connect together?

It depends on your teacher.

Sir, can I ask the methodology and results is seperated?

thanks! definitely a great reference

You are welcome.

Sir,how to do methodology?? Tq

Please check with your school teacher for methodology. This page shows the result only.

How to plot the graph in 1B question?

Thank you soooo much! This is the only website that I can refer from and it is very useful 🙂 I’ll search for this website again for the next coming sem math t assignment 🙂 Really appreciate your effort to upload the answer T T

Hi ,can I know how to use geogebra

https://wiki.geogebra.org/en/Manual

sorry sir can i know about how to plot question 1 in spiral shape?

You can use geogebra or use paper. It depends on your school teacher

sorry sir can i ask about how to plot question 1 in spiral shape

How to write introduction and methodology?

Please check with your school teacher for methodology and intro. This page shows the result only.

great guidelines for the candidates ! thanks!

sir lee may i ask how to put methodology in our assignment?

Sir,may I know how to write a methodology?

how to write methodology?

z^n=(-1)^k(2)^2k n=4k (-1)^k(2)^2k(1+i) n=4k+1

please guide me about where does the solution come from? (-1)^k(2)^2k?

anyway im from penang

From observation.

It is like 2=x, if you call x=2, or 2=2x, if you call x=1. It depends on how you define it. you can write any expression if your teacher wants it.

thank you very much!!

Sir, can you teach how to do the viva?

Sir graph for ques 1a can be in spiral shape?

Yes. You can

Sir how to do 1)b) repeat the task?

Redo the power 2, 3, 4, 5

Sir can i know how to connect those points become an exponential spiral?

Using Computer? Or manual?

May i know is the 3c’s argond diagram same as the 3b? *hand drawing

The roots are different

Sir how to plot the graph and draw the diagrams?

You can use geogebra to draw it. Download it and install in your computer or phone

Semester 2 coursework answer when published???

It will be published if they are available

When can i get semester 3 coursework results??

Hi sir, can I know what is the conjugate pair for 3(a) when n=6

Conjugate for x+yi is x-yi. If you have the first complex root is 2+3i, then the second root will be 2-3i

math is too difficult to me even I do more exercise , how I should do to master every chapter

Please find a good teacher to guide you

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Exploring The Structure For STPM Maths T 2024

29 November 2023

7 minutes to read

• 01. Topics Covered In Term 1: Algebra and Geometry
• 02. Topics Covered In  Term 2: Calculus
• 03. Topics Covered In Term 3: Statistics
• 04. Latest Exam Format For The STPM Mathematics T Written Test
• 05. Overview Guideline For STPM Mathematics T Coursework

Do you know what's one of the most effective ways to solve a big problem?

By breaking it into smaller problems.

As Form 6 students, you might be taken aback when you're told that there are a total of 18 chapters to cover for your STPM Maths T subject, for instance.

But what if I told you that you have three semesters to learn them and only be tested on 6 topics each semester? It does take some burden off your shoulders, right?

In this article, we will discuss the STPM Maths T syllabus for each term and the latest examination format for this subject.

Topics Covered In Term 1: Algebra and Geometry

Throughout the three semesters, you will learn a total of 18 chapters (6 chapters per semester).

Here are the six chapters that you will study during your first semester.

• Chapter 1: Functions [28 teaching period] 

In this chapter, you will be taught polynomial and rational functions, exponential and logarithmic functions, as well as trigonometric functions.

• Chapter 2: Sequences and Series [18 teaching period] 

In this chapter, you will be taught on core principles and formulas of sequences and series as well as binomial expansions.

• Chapter 3: Matrices [16 teaching period] 

In this chapter, you will learn about various operations revolving matrices as well as different systems of linear equations.

• Chapter 4: Complex Numbers [12 teaching period] 

In this chapter, you will learn about what are real and imaginary parts of complex numbers, how to present an Argand diagram, perform elementary operations for complex numbers and also apply de Moivre’s theorem.

• Chapter 5: Analytic Geometry [14 teaching period] 

In this chapter, you will master the methods to transform a given equation of a conic into the standard form and find the vertex, focus and directrix of a parabola, ellipse and hyperbola.

• Chapter 6: Vectors [20 teaching period] 

In this chapter, you will learn about vectors in two and three dimensions as well as various elements of vector geometry.

Learn more about the advantages that you can gain when you learn and master STPM Maths T as a Form Six student.

Topics Covered In  Term 2: Calculus

Now, let's move on to the second semester.

Here is the breakdown of sub-topics that will be covered in the following six chapters under the theme of calculus.

• Chapter 7: Limits and Continuity [12 teaching period] 

In this chapter, you will learn how to determine the existence and values of the lefthand limit, right-hand limit and limit of a function; the continuity of a function at a point and on an interval; and also apply the intermediate value theorem.

• Chapter 8: Differentiation [28 teaching period] 

In this chapter, you will learn to master sub-topics like derivatives and different applications of differentiations.

Furthermore, you'll learn how to perform implicit differentiation, determine the stationary points, extremum points and points of inflexion; find the equations of tangents and normals to curves, including parametric curves and many more.

• Chapter 9: Integration [28 teaching period] 

In this chapter, you will be taught about different sub-topics like indefinite integrals, and definite integrals.

You will learn how to integrate rational functions by means of decomposition into partial fractions, perform integration by parts; calculate the area of a region bounded by a curve (including a parametric curve) and many more.

• Chapter 10: Differential Equations [ 14 teaching period] 

In this chapter, you will learn about first-order differential equations with separable variables, first-order linear differential equations utilizing an integrating factor and how to use a boundary condition to find a particular solution.

At the end of this chapter, you will master the skill to solve problems that are related to science and technology which can be modelled by differential equations.

• Chapter 11: Maclaurin Series [12 teaching period] 

In this chapter, you will learn how to determine the Maclaurin series for a function and the interval of convergence.

You will also learn the difference between standard series and power series as well as how to use series expansions to find the limit of a function.

• Chapter 12: Numerical Methods [14 teaching period] 

In this chapter, you will learn about the numerical solution of equations and numerical integration.

Some of the learning outcomes under the subtopic of numerical solution of equations include locating the root of an equation approximately using graphical considerations and searching for a sign change and many more.

Under numerical integration, you will learn how to use the trapezium rule and sketch graphs to determine whether the trapezium rule gives an overestimation or an underestimation in simple cases.

Dive deep into these tips to score well for your STPM Maths T papers .

Topics Covered In Term 3: Statistics

We've arrived at our final semester for your STPM Maths T syllabus.

Similarly, you will be taught 6 chapters.

• Chapter 13: Data Description

In this chapter, you will study discrete, continuous, ungrouped and grouped data, and expand on the concepts of mode, median and interquartile range based on what you have learned during your SPM studies.

You will also learn more about the appropriate measures of central tendency and measures of dispersion and apply the Pearson coefficient of skewness .

• Chapter 14: Probability

Apart from learning about the addition and multiplication principle of various probability operations, you will also learn how to calculate conditional probabilities and identify independent events in this chapter.

• Chapter 15: Probability Distributions

In this chapter, you will study the properties and direct application of discrete random variables, continuous random variables, binomial distribution, Poisson distribution and normal distribution.

• Chapter 16: Sampling and Estimation

In this chapter, some of the major learning outcomes that you will master include learning the differences between a population and a sample, and between a parameter and a statistic as well as determining and interpreting a confidence interval for the population mean based on a sample from a normally distributed population with known variance.

• Chapter 17: Hypothesis Testing

In this chapter, you will learn how to explain what a hypothesis and alternative hypothesis are, as well as the significance level of a test. You will also master the ability to carry out various hypothesis tests for different samples.

• Chapter 18: Chi-Squared Tests

In this chapter, you will learn how to use the chi-squared distribution tables and identify the chi-squared statistic.

From there, you will get to apply the goodness of fit test and test of independence for different problems.

Latest Exam Format For The STPM Mathematics T Written Test

After reviewing all the topics that will be covered for your STPM Maths T subject, let's now look at the examination structure for your assessments.

Every semester, candidates will sit for one written test. It is a central assessment and the test duration is 1 hour and 30 minutes. 

There are two sections for each STPM Maths T written test.

For Section A, candidates have to answer 6 questions of variable marks. The total mark for section A is 45 marks.

For Section B, candidates can choose from two question options. The total mark for section B is 15 marks.

The full mark for each written test is therefore 60 marks, which will be rounded up to 26.67% in terms of weightage to calculate the overall grade for your STPM Maths T subject.

Don't forget to look through these amazing learning resources for your STPM Maths T papers .

Enhance Your STPM Maths T Revision Journey With A Superprof Tutor

Since you'll be preparing for a written test that involves different topics each semester, it could be an overwhelming process.

Instead of going through the revision journey all by yourself, why not study the STPM Maths T subject under the guidance of an experienced Maths tutor?

With Superprof, you can find a reliable Maths tutor who can help you strengthen your comprehension of all the taught topics for each semester consistently.

That way, you don't have to worry about the lack of preparation or the lack of practice before sitting for the actual exam. You can also master the marking rubrics of your STPM Maths T papers .

Not only that, you also get to enjoy a flexible learning experience because you can opt to learn from a home tutor or online tutor with the help of Superprof.

Visit the Superprof Malaysia homepage to kickstart your STPM Maths T revision journey today.

Overview Guideline For STPM Mathematics T Coursework

Apart from your written test, you will also need to complete three assignments (coursework) throughout the three terms.

Unlike your written test, your coursework assessment will be graded by your subject teacher. Each semester, you will be given a different assignment task (based on the taught topics that semester).

You need to come out with a written report and undergo a viva session to receive your grade.

What Should Be Included In Your Complete Written Report Each Semester

Read the following information carefully as you prepare your report.

Don't forget to print out and complete the declaration statement and attach it to your report before the final submission.

The total mark allocation for your report is 40 marks.

• Introduction

Include the title of the report and describe the problem in your introduction.

• Methodology

Write down the application of appropriate methods to address the given problem. You should also list the collection of relevant data and information under this section.

You should include mathematical calculations and the final results with mathematical reasoning. Based on that, you should also interpret your results systematically.

You should discuss and summarise the outcomes of your assignment report.

Things To Take Note For Each Viva (Presentation) Session

The complete mark for your viva session is 20 marks.

• Understanding of the assignment

You need to provide complete and accurate explanations alongside critical discussion using appropriate terminology based on your assignment report.

• Communication

You should present the relevant explanations and examples clearly and effectively.

Important tip: Be calm and confident during the Q and A session after presenting your points.

We hope you have gained a new understanding towards the overall syllabus and examination format for your STPM Maths T subject through this article.

All the best!

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heap: A priority queue implemented as a heap. More...

#include <heap.h>

Detailed Description

Template<class t, class compare = std::less<t>> class heap< t, compare >.

heap: A priority queue implemented as a heap.

Constructor & Destructor Documentation

◆  heap() [1/2].

Constructs an empty heap.

◆  heap() [2/2]

Constructs a heap from a vector of elements by copying the elements into the heap's storage and then running the buildHeap algorithm.

Member Function Documentation

◆  empty().

Determines if the given heap is empty.

◆  hasAChild()

Helper function that determines whether a given node has a child.

◆  heapifyDown()

Helper function that restores the heap property by sinking a node down the tree as necessary.

◆  heapifyUp()

Helper function that restores the heap property by bubbling a node up the tree as necessary.

◆  leftChild()

Helper function that returns the index of the left child of a node in the heap.

Required for grading purposes! (And it should be useful to you as well).

◆  maxPriorityChild()

Helper function that returns the index of the child with the highest priority as defined by the higherPriority() functor.

For example, if T == int and the left child of the current node has data 5 and the right child of the current node has data 9, this function should return the index of the left child (because the default higherPriority() behaves like operator<).

This function assumes that the current node has children.

◆  parent()

Helper function that returns the index of the parent of a node in the heap.

◆  peek()

Returns, but does not remove, the element with highest priority.

◆  pop()

Removes the element with highest priority according to the higherPriority() functor.

◆  push()

Inserts the given element into the heap, restoring the heap property after the insert as appropriate.

◆  rightChild()

Helper function that returns the index of the right child of a node in the heap.

◆  root()

Helper function that returns the root index of this heap.

Required for grading purposes! (This function should be ridiculously easy: either return 0 if you plan to store the root at index 0, or 1 if you plan on storing it at index 1).

◆  updateElem()

Updates the element at the provided index of the heap array.

The update is done in such a way that the array will be corrected, so it will remain as a valid heap.

Friends And Related Function Documentation

◆  operator<<.

Prints the heap to an std::ostream.

Given for you. Uses the helper functions below to do its work, so please implement them!

Member Data Documentation

◆  _elems.

The internal storage for this heap.

You may choose whether your heap is 0-based or 1-based (i.e., you are free to store the root at either index 0 or index 1). You should pick one , and write the helper functions according to that choice.

◆  higherPriority

Comparison functor.

This functor takes two parameters and returns true if the first parameter has a higher priority than the second.

Compare is a template parameter and defaults to std::less, which creates a min-heap. So, if T = int and a = 3 and b = 5 , higherPriority(a, b) = true ( a < b , so a has higher priority) and higherPriority(b, a) = false ( b > a , so b has lower priority)

• src/ heap.h