Instructions for the Week of June 8

Every day you should be watching the assigned video and taking notes. When completing notes please

do so in your notebook or in a space that can be transferred to your math binder as these will be

important when we return to school. When taking notes on specific sections you are not required to do

the investigations however if you have some free time it may be fun to give them a try!

You are not required to send me your notes however all exercises must be submitted by the end of the

day two days after they were assigned. For example, Monday’s lesson is due by the end of the day

Wednesday. Thursday and Friday’s lesson is due by the end of the day Monday. These can be

submitted through turnitin by taking a picture or scanning your work and saving it as a word document

or pdf (pictures/scans should be compiled into one document to submit. This can be done by inserting

your pictures into a word document).

**ALL LATE WORK MUST BE SUBMITTED VIA E-MAIL. IF YOU COMPLETE IXL LATE YOU MUST E-MAIL

TO RECEIVE CREDIT**

Collaboration is not allowed.

Collaboration: To work jointly with others or together especially in an intellectual endeavor. When

collaboration takes place, all students must demonstrate understanding of the new material.

If you have any questions throughout the week please feel free to e -mail and set up a time to discuss by

phone if necessary!

Monday- Warch Video on Inverse Normal Distribution

Complete IXL Y.14 for Classwork (20 minutes or until mastery)

Complete 14K for Homework

Tuesday- Watch Video on Inverse Normal Day 2 Video

Complete IXL Y.15 for Classwork (20 minutes or until mastery)

Complete 14L for Homework

*IA Topic Due Today*

Wednesday- Watch Video on Inverse Normal Find M and SD

Complete 14M for Homework

Thursday- Watch Video on Chapter 14 Review

Complete Exam Style Questions (#16-26 pg 623-625) for Homework

Friday- Complete Chapter 14 Quiz Posted to Microsoft Teams- due by 11:59pm Friday June 12th

LATE WORK- All Quarter 4 Work is due by Wednesday June 17th

FINAL EXAM- Study Guide is attached- Final Exam will be Tuesday June 23rd

**Extra help is available on Microsoft Teams Monday at 2PM and Wednesday at 9AM. Attending

Extra Help will give you class participation points for the week**

Ms. Reynolds – Math IBSL1 Final Exam Study Guide 2019-2020

The final exam will consist of material from chapters 8, 10, 11, 12, 13, and 15 of the textbook. The

review sections at the end of each chapter make for good practice problems, as well as any

questions from the tests and quizzes taken thus far this year. You will be allowed to use a graphing

calculator for the exam. You are allowed to have a clean copy of the IB information packet with you

during the exam, but it cannot have any additional notes whatsoever. The following is a list of topics

that you should be familiar with prior to taking the exam:

• Chapter 8 – Univariate Analysis (question #’s 14, 15, 17, 19, 20, 21)

Presentation of data (i.e. frequency charts, histograms)

Measures of central tendency (mean, median, mode)

Analysis of cumulative frequency graphs

• Chapter 10 – Bivariate Analysis (question # 16, 18)

Analyzing correlation coefficients of scatter plots

Analyzing the line of best fit through a scatter plot

Understanding the regression line and limitations of its use

• Chapter 11 – Trigonometry (#’s 2, 4, 6, 7, 10)

Solving right triangles using SohCahToa

Solving trigonometric word problems involving true bearings and directional coordinates

Trigonometry on the coordinate plane

Solving triangles using Law of Sines or Law of Cosines

Interpreting the ambiguous case of Law of Sines

Calculating arc lengths on a circle as well as area sector

• Chapter 13 – Circular Functions (#’s 9, 11, 12, 13) Using the unit circle and its properties to evaluate trigonometric functions at given angles without

the use of a calculator

Evaluating trigonometric functions for double angles

Proving trigonometric identities

Graphing trigonometric functions on a coordinate plane as well as their transformations (translating,

stretching/compressing, reflecting)

Modeling sine and cosine functions

Solving trigonometric equations

• Chapter 3 – Probability (question #’s 1, 3, 5, 8)

Shading Venn diagrams Unions, intersections, and complements of simple events Calculation of independent and / or mutually exclusive events

Creating sample spaces Conditional probability of events Using tree diagrams to help in the aid of probability calculations

• Chapter 15 – Probability Distributions (#’s 22, 23, 24)

Finding probability distributions of discrete random variables

Finding expected values of a random variable

Probability, expected value, and variance in binomial distributions

Finding probability and parameters in a normal distribution

IBSL1 2018-2019 Final Exam Study Guide Sample Questions

1. The events B and C are dependent, where C is the event “a student takes Chemistry”, and B is the event “a student takes Biology”. It is known that

P(C) = 0.4, P(B | C) = 0.6, P(B | C) = 0.5.

(a)Complete the following tree diagram.

(b)Calculate the probability that a student takes Biology.

(c)Given that a student takes Biology, what is the probability that the student takes Chemistry?

2. In the following diagram, O is the center of the circle and (AT) is the tangent to the circle at T

Diagram not to scale

If OA = 12 cm, and the circle has a radius of 6 cm, find the area of the shaded region.

3. Events E and F are independent, with P(E) = and P(E F) = . Calculate

P(E∪F)′

O

T

A

4. (a) Express 2 cos2 x + sin x only terms of sin x

(b) Solve the equation 2 cos2 x + sin x = 2 for x in the interval 0 x , giving your

answers exactly

5. The events A and B are independent such that P(B) = 3P(A) and P(AB) = 0.68. Find P(B)

6. Solve the equation 2cos x = sin 2x, for 0 ≤ x ≤ 3π.

7. A ship leaves port A on a bearing of 30°. It sails a distance of 25 km to point B. At B, the ship changes direction to a bearing of 100°. It sails a distance of 40 km to reach point C.

A second ship leaves port A and sails directly to C.

(a) Find the distance the second ship will travel.

(b) Find the bearing of the course taken by the second ship.

8. Consider the events A and B, where P(A) = , P(B′) = and P(A B) = .

(a)Write down P(B).

(a) Find P(A B).

(b) Find P(A B).

9. The graph of y = p cos qx + r, for –5 ≤ x ≤ 14, is shown below.

There is a minimum point at (0, –3) and a maximum point at (4, 7).

Find the value of

(i) p;

(ii) q;

(iii) r.

10. The following diagram shows a circle with centre O and radius 4 cm.

diagram not to scale

The points A, B and C lie on the circle. The point D is outside the circle, on (OC). Angle ADC = 0.3 radians and angle AOC = 0.8 radians.

(a) Find AD

(b) Find OD

(c) Find the area of sector OABC

(d) Find the area of region ABCD

11. A formula for the depth d metres of water in a harbour at a time t hours after midnight is

where P and Q are positive constants. In the following graph the point (6, 8.2) is a minimum point and the point (12, 14.6) is a maximum point.

(a) Find the value of

(i) Q

(ii) P

(b) Find the first time in the 24-hour period when the depth of the water is 10 meters.

(c) (i) Use the symmetry of the graph to find the next time when the depth of the water is 10 meters

(ii) Hence find the time intervals in the 24-hour period during which the water is less than 10 meters deep.

,240,6

cos

+= ttQPd

0 6 12 18 24

15

10.

5

d

t

(6, 8.2)

(12, 14.6)

12. Let f(t) = a cos b (t – c) + d, t ≥ 0. Part of the graph of y = f(t) is given below.

When t = 3, there is a maximum value of 29, at M. When t = 9 , there is a minimum value of 15.

(i) Find the value of a

(ii) Show that b =

(iii) Find the value of d

(iv) Write down a value for c

6

π

13. At an amusement park, a Ferris wheel with diameter 111 metres rotates at a constant speed.

The bottom of the wheel is k metres above the ground. A seat starts at the bottom of the wheel.

The wheel completes one revolution in 16 minutes.

a. After 8 minutes, the seat is 117 m above the ground. Find k.

b. After 𝑡 minutes, the height of the seat above ground is given by ℎ(𝑡) = acos (𝜋

8𝑡) for

the interval 0 ≤ 𝑡 ≤ 32. Find 𝑎

c. Find when the seat is 30m above the ground for the third time

14. Let a, b, c and d be integers such that a < b, b < c and c = d.

The mode of these four numbers is 11. The range of these four numbers is 8. The mean of these four numbers is 8.

Calculate the value of each of the integers a, b, c, d.

15. A fisherman catches 200 fish to sell. He measures the lengths, l cm of these fish, and the results are shown in the frequency table below.

Length l cm 0 ≤ l < 10 10 ≤ l < 20 20 ≤ l < 30 30 ≤ l < 40 40 ≤ l < 60 60 ≤ l < 75 75 ≤ l < 100

Frequency 30 40 50 30 33 11 6

A cumulative frequency diagram is given below for the lengths of the fish.

Use the graph to answer the following.

i. Estimate the interquartile range. ii. Given that 40 % of the fish have a length more than k cm, find the value of

k.

16. Several candy bars were purchased and the following table shows the weight and the cost of each bar.

Yummy Chox Marz Twin Chunx Lite BigC Bite

Weight (g) 60 85 80 65 95 50 100 45

Cost (Euros) 1.10 1.50 1.40 1.20 1.80 1.00 1.70 0.90

a. Given that sx = 19.2, sy = 0.307 and sxy = 5.81, find the correlation coefficient, r,

giving your answer correct to 3 decimal places.

b. Describe the correlation between the weight of a candy bar and its cost.

c. Calculate the equation of the regression line for y on x.

d. Use your equation to estimate the cost of a candy bar weighing 109 g.

17. A supermarket records the amount of money d spent by customers in their store during a busy period. The results are as follows:

Money in $ (d) 0–20 20–40 40–60 60–80 80–100 100–120 120–140

Number of customers (n) 24 16 22 40 18 10 4

Find an estimate for the mean amount of money spent by the customers, giving your answer to the nearest dollar ($).

18. The heat output in thermal units from burning 1 kg of wood changes according to the wood’s percentage moisture content. The moisture content and heat output of 10 blocks of the same type of wood each weighing 1 kg were measured. These are shown in the table.

Moisture content % (x) 8 15 22 30 34 45 50 60 74 82

Heat output ( y) 80 77 74 69 68 61 61 55 50 45

a. Write down the product-moment correlation coefficient, r.

b. The equation of the regression line y on x is y = –0.470x + 83.7.

c. Estimate the heat output in thermal units of a 1 kg block of wood that has 25 % moisture content.

19. Given the following frequency distribution

Number (x) 1 2 3 4 5 6

Frequency (f ) 5 9 16 18 20 7

a. the median b. the mean.

20. Three positive integers a, b, and c, where a < b < c, are such that their median is 11, their mean is 9 and their range is 10. Find the value of a.

21. A student measured the diameters of 80 snail shells. His results are shown in the following

cumulative frequency graph. The lower quartile (LQ) is 14 mm and is marked clearly on the

graph.

On the graph, mark clearly in the same way and write down the value of

a. the median

b. the upper quartile

c. Write down the interquartile range

90

80

70

60

50

40

30

20

10

0

Cu

mu

lati

ve

freq

uen

cy

0 5 10 15LQ = 14

20 25 30 35 40 45

Diameter (mm)

22. A random variable X is distributed normally with mean 450. It is known that

.

a. Represent all this information on the following diagram.

b. Given that the standard deviation is 20, find a . Give your answer correct to the

nearest whole number

23. The heights of a group of seven-year-old children are normally distributed with mean

and standard deviation . A child is chosen at random from the group.

a. Find the probability that this child is taller than .

b. The heights of a group of seven-year-old children are normally distributed with mean

and standard deviation . A child is chosen at random from the group.

The probability that this child is shorter than is . Find the value of k .

24. The random variable is normally distributed with mean and standard deviation .

a. Find .

b. Given that , find the value of .