IB SL Mathematics – Summer Packet
Please do not do this packet the week after school gets out. Wait until mid-summer. I want these techniques to be relatively fresh in your mind in the fall. At the same time, do not wait until the night before school starts in August! These will take time!
To receive full credit, all work and thinking will be shown and recorded (if you need more room feel free to use a separate piece of paper). Do as much as you can without a calculator. Half of the AP test is taken without a calculator! This packet is due the first day back to school. It will be graded. You need to get off to a good start, so spend some quality time on this packet during the summer.
Have a wonderful summer! I cannot wait to meet you!
TOPICS:
- Negative and Fractional Exponents
- Special Factorization
- Domain and Functions
- Solving Inequalities
- Solving Quadratic Equations
- Asymptotes
- Complex Fractions
- Composition of Functions
- Solving Rational equations
- Basic Right angle trig
- Solving Trig Equations
- Log and exponent rules and equations
Topic 1: Fractional and Negative Exponents
Simplify using only positive exponents
1. 2. 3.
4. 5. 6.
7. 8. 9.
Topic 2: Special Factorization
Factor completely
1. 2. 3.
4. 5. 6.
7. 8.
9.
Topic 3: Domain andFunctions
If describe in words what the following would do to the graph of :
1. 2. 3.
4. 5. 6.
Find the domain of the following functions:
7. 8. 9.
10. 11. 12.
13. Identify each graph by its family of function and write the general equation.
Topic 4: Solving Inequalities
Solve the following by factoring and making appropriate sign charts.
1. 2. 3.
4. 5. 6.
Write the following absolute value expressions as piecewise expressions
7. 8.
Graph the following piecewise functions
9. 10.
Topic 5: Solving Quadratic Equations
Solve each equation
1. 2. 3.
4. 5. 6.
7. 8. 9.
Topic 6: Asymptotes
For each function, find the equation of both vertical asymptotes(s) and horizontal asymptotes (if they exist).
1. 2. 3.
4. 5. 6.
7. 8. 9.
Topic 7: Complex Fractions
Simplify the following
1. 2.3.
4. 5. 6.
7. 8. 9.
Topic 8: Composition of Functions
If , find the following
1. 2. 3.
4. 5. 6.
7. 8. 9.
Topic 9:Solving Rational Equations
Solve each equation for x
1. 2. 3.
4. 5. 6.
7. 8. 9.
Topic 10: Right Triangle Trig and Unit Circle
Solve the following problems
If point P is on the terminal side of , find all 6 trig functions of . Draw a picture.
1. 2.
3. If and find 4. If and find
Recreate the unit circle with degrees, radians, and values, then find the exact values without a calculator.
______5. ______6.
______7. ______8.
______9. ______10.
______11. ______12
13. 14.
15.
Topic 11: Solving Trig Equations
Solve each equation on the interval
1. 2. 3.
4. 5. 6.
7. 8. 9.
Topic 12: Logarithm and Exponential Rules and Equations
Simplifyor expand using logrules:
1. 2. 3. 4.
Solve:
5. 6. 7.
8. 8. 9.