Review Test on Tuesday

1. ReviewTeston Tuesday Feb 5th, Wayward Wednesday

2. A note on report cards Perseverant problem-solving paid off for many of you. A number of you managed to increase your course mark with your exam (a rare occurrence!)

3. Memory Activity • Bed • Rest • Chair • Tired • Dream • Wake • Snooze • Blanket • Water • Slumber • Snore • Nap • Peace • Yawn • Drowsy

4. Sing!

5. Memory (Recognition) Task • Write down all of the following ONLY that were also shown earlier: rest tired sleep table blanket carrot slumber bus pencil yawn door class

6. Memory (Recognition) Task • Write down all of the following ONLY that were also shown earlier: rest tired sleep table blanket carrot slumber bus pencil yawn door class

7. Memory (Recognition) Task • Write down all of the following ONLY that were also shown earlier: rest tired sleep table blanket carrot slumber bus pencil yawn door class

8. Memory (Recognition) Task • The correct answers: rest tired sleep table blanket carrot slumber bus pencil yawn door class

9. Memory task • This phenomenon is called “memory intrusion” where I use certain words to adjust a memory that never existed. • It was discovered via statistical analysis!

10. Review What is a tangent? A line that connects two points on a curve A line that just barely touches a curve An average rate of change An instantaneous rate of change

11. Review What is a tangent? A line that connects two points on a curve A line that just barely touches a curve An average rate of change An instantaneous rate of change

12. Review What is a secant? A line that connects two points on a curve A line that just barely touches a curve An average rate of change An instantaneous rate of change

13. Review What is a secant? A line that connects two points on a curve A line that just barely touches a curve An average rate of change An instantaneous rate of change

14. Review Tangent = instantaneous rate of change Secant = average rate of change

15. Solve in your teams On our snow day, Annie built a snowman. The snowball that she used for the base grew in radius from 5cm to 40cm. A) What is the average rate of change of the snowball’s area as a function of radius? B) What is the average rate of change of the snowball’s volume as a function of radius? Area of a sphere = 4πr2 Volume of a sphere = (4/3)πr3

16. Review f(a + h) – f(a) h • What does this equation represent in it’s current form? • The function at the value a + h • The function at the value a • Rise/Run of a secant • Rise/Run of a tangent

17. Review f(a + h) – f(a) h • What does this equation represent in it’s current form? • The function at the value a + h • The function at the value a • Rise/Run of a secant • Rise/Run of a tangent Subtle, but true!

18. Review f(a + h) – f(a) h lim h 0 • What does this equation represent in it’s current form? • The function at the value a + h • The function at the value a • Rise/Run of a secant • Rise/Run of a tangent Now we have a tangent

19. Review f(a + h) – f(a) h • What is this equation called? • The slope quotient • The difference quotient • The slope product • The difference product

20. Review f(a + h) – f(a) h • What is this equation called? • The slope quotient • The difference quotient • The slope product • The difference product

21. Solve in your teams On our snow day, Nick also built a snowman! Use the difference quotient to figure out an expression for the instantaneous rate of change of the area of the snowball as a function of radius Use the difference quotient to figure out an expression for the instantaneous rate of change of the volume of the snowball as a function of radius Area of a sphere = 4πr2 Volume of a sphere = (4/3)πr3

22. Review d(t) = 2t5 • The snowmen created by Nick and Annie turn out to be relatives of Frosty. They dance through Chatham traveling a distance (in metres) as a function of time (in minutes). • What is their velocity after 3 mins? • 810 • 648 • 486 • I have no idea

23. Review d(t) = 2t5 • The snowmen created by Nick and Annie turn out to be relatives of Frosty. They dance through Chatham traveling a distance (in metres) as a function of time (in minutes). • What is their velocity after 3 mins? • 810 • 648 • 486 • I have no idea

24. Review d(t) = 2t5 v(t) = 2(5t4) a(t) = 2(5(4t3))

25. Given the following information: f(x) = –8 f(x) = +8 f(3) = +8 lim x3- lim x3+ • The limit of f(3) exists • f(3) is continuous • The limit of f(3) is 1 • None of the above are true Which of the following is true?

26. Given the following information: f(x) = –8 f(x) = +8 f(3) = +8 lim x3- lim x3+ • The limit of f(3) exists • f(3) is continuous • The limit of f(3) is 1 • None of the above are true Which of the following is true?

27. Given the following information: f(x) = –8 f(x) = –8 f(3) = 1 lim x3- lim x3+ • The limit of f(3) exists • f(3) is continuous • The limit of f(3) is 1 • None of the above are true Which of the following is true?

28. Given the following information: f(x) = –8 f(x) = –8 f(3) = 1 lim x3- lim x3+ • The limit of f(3) exists • f(3) is continuous • The limit of f(3) is 1 • None of the above are true Which of the following is true?

29. Solve in your teams On our snow day, Jon made cool patterns in the snow. Graph Jon’s pattern. Where does the limit not exist? Where is the function not continuous? { One pattern that he made followed the piecewise function: (x2– 9)/(x – 3)if x > 2 f(x) = 5if x = 2 ½x + 4 if x < 2

30. Review The function that describes the volume of a snowball is: V(r) = 4πr3 Which limit rules are involved in solving this limit as r  5? A) B) C) D)

31. Review The function that describes the volume of a snowball is: V(r) = 4πr3 Which limit rules are involved in solving this limit as r  5? A) B) C) D)

32. Tips for solving limits Get rid of square roots by multiplying: (√(4 + x) + 2) (√(4 + x) – 2) x (√(4 + x) + 2)

33. Tips for solving limits Get rid of fractions by finding a common denominator: + 1 1 x 4 x + 4

34. Solve in your teams Evaluate the limit if the limit exists. lim x 1 x2 – 1 x3 – x2 – 3x + 3 x2 – 1 x3 – x2 – 3x + 3 lim x √3