3AT Looking at probability and Circles

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

What would be the advantages of owning the same outfit 7 times?

How many combinations can you make with your clothes?

Today

Maths A or C : Start with §12A.1 and continue with §12A.2 on p. 212 and onwards. Make sure you finish §12A.1 before the end of the first lesson. 

Maths B : Take notes and start with §12B.1, p. 242 and onwards. 

Everyone : Check, adjust and update your planner before the end of the lesson. 

Hand in your work on exercise R4a on p. 240

Solve the equation 4(2x-1) + x = 14

§12B.1

• Pythagoras' theorem
• Exact answers
• Radius
• Coordinates
• Equation
• Show, explain, give, make or calculate
• You may skip ex. 1 and 3

Start with ex. 2, 4, 5, 6 and 7. 

Continue with §12B.2 

§12A.1 and §12A.2

Any questions? 

Samples

Most important: 

- Is it reliable? 

-- Equal chance of being chosen

-- Is the sample large enough

Are you able to explain if a survey is carried out correctly?

Simulations

Important

- Can you find the button on your calculator? See 'pushpin' for pictures

- Exercise 11 <-- do you understand the difference? 

- Calculations and explanations

Calculator steps

Upload your work on ex. 5

§12B.2, p. 246-248

Goal

- rearrange formula

- completing the square

rearranging

Write a formula in a different form by for instance adding, subtracting and dividing on both sides. In this chapter you do this by using 'completing the square' and adding/subtracting. 

completing the square

§12B.2 | Do at least 9, 11 and 12

Continue working on C12 and/or skills

• Set a goal for yourself (notation, number of exercises, asking questions, checking your work, focus, ......)

§12AB.3

Maths A or C: Start by checking your work and continue with §12A.3, p. 

Maths B: Take notes and continue with §12B.3, p. 250-252

Maths B: at least 15, 16, 17 and 20 

Maths A or C: 15, 16 and 17

How can you find a point of intersection?

What help do you need?

Goal

- rearrange

- substitute

- solve equations

- calculate point(s) of intersection of a circle and a line

Example finding the points

§12A.3, p. 220

• How to predict a probability
• Expectations <-> chance
•  Calculations and explanations

Calculations

part/whole*100 = percentage 

or 

(number of specific results)/(number of total results)*100= percentage

Skills 4, 5 and 6 book B, p. 40-45 ; p. 122-127 ; p. 268-273.
Look at the contents on p. 4-5,
and write down one skill you need to practice.

Ratio, Calculations, Equations, Geometry, Functions and Graphs,
Statistics, Rearranging, Decimal numbers, Inequalities,
Square roots and powers.

§12.4AB 

• Maths B: Check your work and continue with §12B.4, p.  254
• Maths A: Take notes and continue with §12A.4, p. 224

Everyone : Check, adjust and update your planner before the end of the lesson.  

Calculating probabilities

Take a screenshot of slide 2 to see if they can answer the question

You have three trousers, five shiShirtsrts and two pairs of shoes. You randomly pick an outfit. What is the probability of picking your favorite outfit?

§12B.4 

Intersect, touch or no points

Intersect --> 2 points --> D > 0

Touch --> 1 point --> D = 0

No points --> 0 points --> D < 0

Difficult?

See theory on p. 256. Do you need extra help? Make sure you ask a question and check your work after every exercise you made. 

Quadratic formula

a, b and/or c can be more than one term. What is the formula for instance when a = 4, b = 3k and c = k^2 - 7?