Algebra 2 Quarter 4 Review
Name: ________________________ Class: ____________ Date: _______________
Section 1: Logarithms and Exponential Relations
Definitions to Know: * Natural Logarithm * Common Logarithm * Mathematical * Exponential Growth * Exponential Decay
Question 1) Change the following from exponential form to logarithmic form (1 mark each):
a) b)
Question 2) Change the following from logarithmic form to exponential form (1 mark each):
a) b)
Question 3) Solve for WITHOUT using a calculator. Show all of your work. (Hint: Use the definition of a logarithm.) (2 marks each)
a) b)
c) d)
Question 4) Apply the Change of Base Formula to rewrite the logarithms with the common logarithm. (1 mark each)
a) b)
Question 5) Solve for the variable. Show all of your work and all of your steps. (Hint: Use the properties of logarithms.) (4 marks each)
a)
b)
c)
d)
Question 6) Solve for the variable. Show all of your work and all of your steps. Show the answer to 4 decimal places. (Hint: Use the common logarithm.) (4 marks each)
a)
b)
c)
Question 7) Solve for . Show all of your work and all of your steps. Show the answer to 4 decimal places. (Hint: Use the natural logarithm and the definition of a logarithm.) (4 marks each)
a)
b)
c)
Question 8) Ms. Mary bought a condo for $145 000. Assuming that the value of the condo will appreciate at most 5% a year, how much will the condo be worth in 5 years?
Section 2: Conic Sections
Standard forms to Know: * Parabola * Circle * Ellipse * And what does a hyperbola look like? (No formula necessary)
Question 1) Write an equation for the circle that satisfies each set of conditions. (2 marks each)
a) centre (12, -4), radius 81 units
_________________________________________
b) centre (0, 0), radius 3/5 units
_________________________________________
Question 2) Given the equation of the parabola answer the following questions. (10 marks)
a)
b)
c)
i. What is the vertex? ii. Does the parabola face up or down? iii. Is the parabola wide or narrow compared to the basic parabola? iv. What is the axis of symmetry? v. Make an x-y table to show at least 4 coordinate points on the parabola. vi. Graph the parabola showing the vertex and coordinate points.
Question 3) Change the equation of the parabola from general form to standard form then answer the questions. (14 marks)
a)
b)
i. What is the vertex? ii. Does the parabola face up or down? iii. Is the parabola wide or narrow compared to the basic parabola? iv. What is the axis of symmetry? v. Make an x-y table to show at least 4 coordinate points on the parabola. vi. Graph the parabola showing the vertex and coordinate points.
Question 4) Given the equation of the circle answer the following questions. (4 marks each)
a)
b)
i. What is the centre? ii. What is the radius? iii. Graph the circle showing the centre and 4 other coordinate points.
Question 5) Given the equation of the ellipse answer the following questions.
(5 marks)
a)
b)
i. What is the centre? ii. What is the radius on the x-axis? iii. What is the radius on the y-axis? iv. Graph the ellipse showing the centre and two other coordinate points.
Section 3: Real Life Applications
Scenario: You are a contestant on the popular TV show, Ms. Mary’s Mathematics. You will win the car of your choice, a vacation house and a really cute pet tiger if you can answer these questions: * Where do people use logarithms in real life? * Where do people use parabolas, circles and ellipses in real life?
Are you going to win the car, house and tiger? 