This complete lessons contains Desmos and GeoGebra interactives to demonstrate how to create voronoi diagrams, as well as examples. The lesson starts off with a review on finding equations of perpendicular bisectors then moves into a explorative task about voronoi diagrams. The lessons covers the following topics: equation of a perpendicular bisector how to construct a perpendicular bisector key terminology used when constructing voronoi diagrams how to construct a voronoi diagram with multiple sites finidng centre of a circle using perpendicular bisectors of cords finding locations of missing sites nearest neighbour adding new sites to a voronoi diagram toxic waste dump problems (largest circle) At the end this is a multiple choice quiz. There are also embedded link to Desmos Classroom activities. As well, throughout the PowerPoint there are worked examples and exercises and past paper exam questions for students to complete.
This PowerPoint follows the Oxford textbook. The following content is covered throughout the PowerPoint. I have also added a few extra concepts which can be used in students Internal Assessments (IA). For example, I spend a little time looking at the skewness formula, different ways of calculating outliers, 1.5 x IQR or 2 X SD, skewness in box plots, etc. Univariate data * qualitative vs quantitative * continuous vs discrete * which representations are used for specific types of data * primary and secondary data * choosing a good sample * sampling bias * reliability vs validity * skewness Questionnaires * biased questions Measures of central tendency * mean, meadian, mode * outliers * un-grouped and grouped * how to use the GDC * combined mean Measures of dispersion * range, quartiles, IQR, standard deviation * normal distribution curve * skewness * different formulas for sample and population for SD * how to use the GDC * effects on mean and SD Sampling techniques Presentation of data Bivariate data * scatter graphs * correlation * introduction into the line of best fit (leading into chapter 6) Throughout the PowerPoint there are worked examples and student exercises. There are also multiple links to various classroom and interactive activities using GeoGebra and Desmos Classrooms. As well, I have included links to certain Youtube videos to help with using the GDC.
This PowerPoint follows the entire content for Chapter 1 of the Oxford textbook. Certain topics included are not in chapter 1 but builds on the skills students are currently learning in the chapter and will be useful later on. For example, for the simplifying indices topic I go a little further into writing indices in non-fractional form which is useful for when you teach derivatives. Conent covered through the PowerPoint include: Measurements and Estimates Rounding and Significant Figures Upper and Lower Bounds Measurement Error Percentage Error Basic Exponent Rules * changing bases * writing in non-fractional form Standard form (scientific notation) Right angle trigonometry * Pythagoras * proving right angle triangles * algebraic problems * SOH-CAH-TOA * elevation and depression * problems involving circles * 3D problems * problems involving special quadrilaterals * angles between lines and planes Arc Length Throughout the PowerPoint you will find GeoGebra links (click the icon) as well as Past Paper questions. There are also worked examples and exercises for students to complete throughout the lesson.
Th bundle contains 32 days worth of starters. Each stater comprises of 2 questions. One being of level 4 or 5 and the other of level 7 to 9. The idea is that students will practice both questions from the beginning and ending of the exam. I find higher level students tend to make mistakes early of in the exam and this allows them to practice these types of questions in class. Thus helping to improve results.
Complete PowerPoints for Chapter 10 - Modelling Rates of Change: Exponential and Logarithmic Functions, for the Oxford textbook. The PowerPowers can be used with other textbooks. PowerPoints are built around students learning the the following topics online, but can also be used to deliver in-class. PowerPoints have embedded links to video examples, Desmos activities, GeoGebra, and Casio GDC videos. The following is the topics that the 8 PowerPoints cover. Geometric Sequences Geometric Series Compound Interest Annuities Amortization Exponential Functions Exponential Models Exponential & Logarithmic Equations There are also Past Paper questions in each section of the unit.
The following PowerPoint will take at least 2 days to complete. The lesson starts with Geometric Sequences and links it to Exponential Functions. The lesson also looks at the connection between geometric sequences, exponential functions and compound interest. By the end of the lesson students should be able to find the nth term of a geometric sequence and the equation of an exponential function.
Lesson introduces students to drawing and writing equations of circles with centers around the origin and (p,q). The lesson walks through how the equation of a circle is from by linking it with Pythagoras theorem. After the understanding of a circle with center (0,0), the lesson then moves to connect circles with the concept of translations, thus creating equations with centers at (p.q). The package includes lesson presentation, introductory activity to understand circle and its transformations, along with class work and homework exercises.
The following starter questions are for students targeting grades 7-9. Questions are taken from various exam boards and include solutions. Encourages students to think and apply their skills in different contexts. Entire PowerPoint includes over 50 questions in the following categories: Coordinate Geometry - Circles Geometric Problems and Proof Algebraic Proof Trigonometry Inequalities Functions Coordinate Geometry – Lines & Curves Sequences Algebraic Problems – including ratio Indices and Surds Statistics Extra
The Following presentation was created for the Applications and Interpretations SL course but can be used for any course such as A-levels that teach this topic. I have included exam question from both A-Level and the IB in the Presentation. The PowerPoint goes through the following: -linear sequences from GCSE -the nth term formula -embedded simultaneous equation problems -inequality problems -introduction to series and proof -both forms of writing the sum formula -sum problems involving inequalities -sigma notation -basic summation properties Throughout the PowerPoint there are worked examples along with exercises for students. I have also included a few video exam solutions with videos going through addition examples for students. There is also a video explain how the Arithmetic Sum formula evolved. At the end of each section I have included IB exam questions so students get get practice to the types and style of questioning they should expect to see when they write their exams.
The following PowerPoint covers Chapter 6 from the Oxford textbook. Modelling Relationships: Linear Correlation and Bivariate Data. The Lesson contains various interactive activities such as Desmos Classroom for review exercises, Geogebra and Phet Simulations for showing line of best fit, least-squares, etc. There are also video links on how to used the GDC to find correlation and linear regression. The PowerPoint covers the following content below. correlation review (from chapter 3) finding correlation coefficient (PMCC) discussion about covariance interpreting PMCC correlation and causation coefficient of determination line of best fit interpolation and extrapolation reliability linear regression residuals piecewise functions * step functions All my PowerPoints have worked examples and exercises for students to complete. I have also added past paper questions in each section to get students accustom to the type and style of questions they will see on their exam. This PowerPower in particular comes with a Microsoft Teams quiz on Correlation and Linear Regression.
The PowerPoint covers the complete content of Chapter 2 of the Oxford textbook. I have also added a few extension topics which build upon what students are learning and will be useful further in the course. Topics cover in the PowerPoint include: The sine law * the ambiguous case The cosine law Area of non-right angle triangles Algebraic triangle problems 3D Problems involving non-right angle triangles Area of sectors Area of Segments 3D shapes * surface area * volume * writing expressions * algebraic problems * capacity There are also Past Paper questions embedded into the lesson along with various GeoGebra and Desmos interactive activities.
The following PowerPoint covers the following topics following the Oxford textbook. Topics covered include: Functions * reation * domain and range * mapping diagrams * number system * set notation * interval notation * what is a function * vertical line test * function notation (numerical, graphical, and algebraic) * finding equation of functions from a mapping diagram Linear Models * recap equation of a line * rates of change * simultaneous equations * direct proportion * inverse functions * domain and range * horizontal line test (one-to-one) * finding inverse functions Arithmetic Sequences Arithmetic Series * sigma notation Simple interest Modelling Through the PowerPoint there are links to youtube videos, GeoGebra and Desmos interactives, and Desmos Classroom activities. The PowerPoint has worked examples, and student exercises. I have also put in past paper exam questions for each topic.
Those teaching Application and Interpretation SL, I have created 8 quizzes on Microsoft Teams for Chapter 10 (Modelling Rates of Change: Exponential and Logarithmic Functions) following the Oxford textbook. Quizzes can be used with other textbooks. Each quiz are written in the following form; true/false, multiple choice, short answer, and problem. The number of questions for each quiz ranges from 12 to 20 marks. The quizzes are as follow: Geometric Sequences Geometric Series Compound Interest Annuities Amortization Exponential Functions Exponential Functions - Modelling Exponential & Logarithmic Equations I have also attached worked solutions to all the quizzes for students.
The following four presentation was created for the Applications and Interpretations SL course following the order of teaching for the Kognity textbook but can also be used with the Pearson or Oxford textbook. The following PowerPoints go through the following: Introduction to Statistics -types of data - qualitative and quantitative -types of data - discrete and continuous -collecting data - primary and secondary -population, sample, census -choosing a good sample - sampling frame, sampling unit, etc. -sampling bias -reliability vs validity -questionnaires -what makes a good survey - eg. biased questions, vague questions, leading questions, etc. Sampling Techniques -types of sampling - simple random, stratified, systematic, voluntary, convenience, and quota -pros and cons for each Measures of Central Tendency ** -mean, median and mode -skewed data -difference between population mean and sample mean -grouped and un-grouped data -how to use GDC -outliers -effect of outliers on mean and median -combined mean Measures of Spread -Range, IQR, variance, and standard deviation -lower quartile and upper quartile -how to use GDC -difference between population and sample standard deviation -effects of SD on normal distribution curve -normal distribution curve -transformation of data -outliers using mean and SD Throughout the PowerPoint there are worked examples along with exercises for students. I have also included a few Desmos and Geogebra interactive links to help students get a better understanding of the concepts through visuals. At the end of each section I have included IB exam questions so students get get practice to the types and style of questioning they should expect to see when they write their exams. I also have included a few thinking questions, a few taken from A Level maths exams. There are also links to YouTube videos to help students understanding with certain content.
This stater is for students who have learnt basic algebraic manipulation already.
Lesson 1: Quadratic Sequences Lesson 2: Completing the Square Lesson 3: Iteration Lesson 4: Composite Functions Each lesson includes worked examples and practice questions. Alternative methods are shown for completing the square. Iteration lesson includes a video and graphical representation of how iteration works to deepen student understanding.
Full completing the square lesson. Includes completing the square for both simple and complex trinomials and solving using completing the square. Lesson includes full process of how completing the square works with all steps in between.
The following problem incorporates linear simultaneous equations within an index problem (prime factorization). This question is for those students looking to get 8+ and have the ability to transfer various skills to different contexts. Though this is only one question it will take a lot of time for students to attempt and then walk through the solution. The solution is attached to the slides.