Term 3 Content for Grade 10 - 12 Maths and Technical Maths - Sponsored by Sharp and SMD Technologies
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Term 3 Content for Grade 10 – 12 Maths and Technical Maths Sponsored by Sharp and SMD Technologies
Agenda • Sharpies • Basics • Topics • Trigonometry (2D problems) • Statistics • Probability • Finance and Growth • Analytical Geometry • Measurement • Circles, Angles and Angular Movement*
Sharpies • A reward program just for teachers • Earn points for attending this webinar. • Exchange your points for gifts. • Sign up – link • Tell all your friends - link
Free Downloads and Resources • Download the simulator • Link • Download Geogebra • Link • Worksheets • www.mathsatsharp.co.za • www.e-classroom.co.za • www.math-drills.com • https://www.mathx.net/ • https://www.worksheetworks.com/ (one of my favourites for younger grades and fully customisable) • https://www.mathwarehouse.com/sheets/ (FET mostly) • ATP documents (link) • My maths blog – www.themathsjourney.com
Calculator Basics • Turn the calculator on • 2nd Function – used to activate orange functions • Turn the calculator off by pressing 2nd F and ON • ALPHA – used to activate teal functions • Mode – change to different modes • BS – backspace – to delete something. • Change – change between mixed, improper and decimal answers. • Equals – to find an answer or used as enter.
Modes • Press • 0: Normal • Fractions, integers, probability, trigonometry and much more • 1: Stat • Single data, linear regression and more • 2: Table • Functions but can also be used for teaching finance • 3: Drill • Mental maths fun!
Trigonometry (2D problems) Grade 10 and 11
2D Problems • Trig ratios: • Worksheets • sin = = • Grade 10 ℎ • Basics • cos = = • 2D problems ℎ • tan = = • Tech maths • Grade 11 • Angle of elevation: • Area, Sine and Cos rule • Looking up at • Grade 12 • Angle of depression • 2D and 3D problems • Looking down on • Study guide • Think of a flirty lady ;)
Shortcut ☺ • Given a right-angled triangle with x and y (or breadth and height) we can find the hypotenuse and angle. • E.g. P (3; 4) • Press
Area Rule • Area rule: 1 • = መ 2 1 • = sin 2 1 • = sin መ 2
Sine Rule • Sine Rule • = = መ • = =
Cosine Rule • Cosine Rule • 2 = 2 + 2 − 2 cos መ • 2 = 2 + 2 − 2 cos • 2 = 2 + 2 − 2 cos መ
Statistics Grade 10, 11, and 12
Theory • Percentiles • Grade 12 Study Guide • Dividing a frequency polygon • Worksheets into groups of 100. %( +1) • = 100 • Quartiles • Dividing the data into groups of 4 +1 • 1 = 4 3( +1) • 3 = 4 • Interquartile range = Q3 – Q1
• Histograms • A bar graph with no gaps • Frequency polygons • Joining the midpoint of each frequency bar to get a line graph. • Ogives • Cumulative frequency curves • Each point is the frequency added to the previous frequencies
• Symmetric data • Data that gives a mirror image around the middle of the graph. • Skewed data • Data that tails off to the left or the right • Positively skewed • A long tail on the right, most of the values are on the left • Negatively skewed • A long tail on the left, with most of the values on the right
Let’s have some fun • Example: A coffee shop counts the number of cappuccinos that they sell on any one day for two weeks. These are their results: • 34 44 99 39 10 56 71 71 41 93 89 11 77 68 • First go to basic statistics: • Press • And choose SD, so press
34 44 99 39 10 56 71 71 41 93 89 11 77 68 • Type in the data by typing in each value and pressing afterwards. • E.g. • And so on…
• Once you have finished entering your data press the button • To find the mean press • And choose • Scroll to see the other screens and information.
Linear Regression • Shows the relationship between 2 variables • Remember – correlation does not imply causation • Correlation measures the strength and direction of the relationship • Draw a scatterplot and look at the graph carefully.
Correlation • Values lie between -1 and 1. • The closer to -1 and 1, the stronger the relationship • The closer to 0 the weaker the relationship • At 0 – no relationship • At -1 or 1, perfect relationship
Number of years 2 4 6 8 10 12 14 16 18 20 driving Example Number of accidents 17 15 12 7 10 4 5 3 1 1 in the last year • We need to go to our linear regression statistics mode. • Press • Draw a scatterplot to examine the type of relationship we have
Input the data • To type in the coordinate pairs, type in the independent variable ( ) first, then press type in the dependent variable (y) and press • E.g. • And so on…
Let’s find the linear regression line • Or line of best fit ;) • Press • Then press
Probability Grade 10, 11 and 12 Study guide grade 12 Worksheets
Basics • Relative frequency • How many times a specific result occurs in an experiment divided by the total number of experiments • Real life • Theoretical probability • The possible number of outcomes we expect based on the information we have about the experiment
Let’s Play • Press • Now press • Now we have 4 options: • Random • Random decimals between 0 and 1 to 3 decimal places • R.Dice • A dice with random values Ideas/ Suggestions: between 1 and 6 • Play the dice game • R.Coin • Play the lottery • A coin with either 0 or 1 • Create a class tally table • R.Int • Choose any two numbers to generate random numbers between
More Theory • Mutually exclusive events • Either one OR the other, cannot be both • E.g. boy or girl • Coffee or tea • Being still or moving • Brown eyes or blue eyes • P(A and B) = 0 • Complementary events • Occur if they are mutually exclusive
Dependent and Independent Events • Independent Events • The occurrence of one event has no effect on the occurrence of another event. • P(A and B) = P(A) x P(B) • Dependent Events • One event depends on the other to occur. • Drawing marbles from a bag: • Putting it back = independent • Keeping it = dependent
Venn Diagrams • A visual description of individual events • When the circles DO NOT overlap, the events are mutually exclusive • P(A or B) = P(A) + P(B) – P(A and B)
Two way Contingency Table • A way to represent 2 or more categorical variables • Mutually exclusive groups • Who did better – men or women?
Fundamental Counting Principle • If there are n slots to fill, and m different pieces, you can have n x m different combinations. • E.g. there are 3 flavours of ice cream, and 4 different toppings, that means that there are 3 x 4 = 12 different ways to eat your ice cream ☺
Permutations & Combinations Fundamental Counting Principle • If order doesn’t matter • Combination • We are throwing all the elements into a bag. • If order does matter • Permutation • The different elements are lined up in different ways.
Permutation: • To find a permutation: • 4 different options, 3 spaces: • Press
Combination • To find a combination: • 4 different options, 3 spaces: • Press
Finance and Growth Grade 10 and 12 Study guide grade 10 Study guide grade 12 Worksheets
Simple interest • Press • E.g. A = 1000 (1+ 5% x n) • Press
• Press
Compound interest • Lets add compound interest into function 2. • Press
• Press
Exchange Rates • Pay attention to the “direction” of the exchange. • E.g. $1 = R14.52 • Small to big • If we have $10, how many Rands do we have? • Small to big so we multiply • If we have R1000, how many Dollars can we buy? • Big to small so we divide
• Exchange rate = R1 = $0,069 • Big to small • If we have R10 how many Dollar do we have? • Big to small, so we multiply • If we have $100, how many Rands do we have? • Small to big so we divide. • Note: going in the same direction means multiply, going in the opposite direction means divide.
Analytical Geometry Grade 10 Worksheet
Theory • Distance •= 2 − 1 2 + 2 − 1 2 • Gradient 2 − 1 • = 2 − 1 • Parallel – gradients are equal • Perpendicular: 1 × 2 = −1 • Horizontal line: m = 0 • Vertical line: m = undefined • Mid-Point 1 + 2 1 + 2 • ; 2 2
Measurement Grade 11 Notes
Volume and Surface Area • Know your formulas • Extra notes • Includes exercises and a memo. • Revise grade 10 work
Investigating the effect of k • Let’s investigate Surface area of a cube • = 6 2 • Make = 1. •
• Then • We can also use this to investigate the effects of k on other shapes and on volume.
Circles, Angles and Angular Movement Grade 11 and 12 TM Worksheet
Theory • What is radian? • Segments • Area of a sector of a circle: • Between an arc and a chord • When is in degrees: • 4ℎ2 − 4 ℎ + 2 = 0 • = × 2 • h = height of segment 360° • d = diameter • When is in radians: 1 • = length of chord. • = × 2 2 • From math24.net • Or = 2 • Where s is the length of the arc. • Sector • Between 2 radii and the arc • Think slice of pie
Degrees, Radians and Gradians • We can change our angle units from degrees to radians to gradians and back again by using • E.g. convert 30˚ into radians. • Press • To convert back to degrees again press • Note: You can also use the Setup menu to change back to degrees or save it into a D-key. 52
DMS / Time Functions • Changing minutes to hours • E.g. How many hours are 470 minutes? • Press to clear any chain calculations • Press • Press to change it into fraction or decimal format (remember to use your button). 53
DMS / Time Functions • Adding / Subtracting Time • E.g. find the length of time spent on a bus if the bus left at 9.45 and arrived at 12.32. • Press • The answer is 2 hours and 47 minutes • To change back to a fraction notation press 54
DMS/ Time Functions • Finding time in a speed-distance- time calculation. • E.g. How long does it take to travel 450km at an average speed of 117km/h? • Press • Press • Press • The answer is 3 hours, 50 minutes and 46.154 seconds. 55
Time Conversions • Hours to seconds: • E.g. 96 hours • Type in 96 • Press MATH • 4 • You can also convert hours to minutes by choosing 5
Thank you for your valuable time! Free worksheets and simulator: www.mathsatsharp.co.za
You can also read
