Power Base:
4.1  Problem Solving
4.2  Communication
4.3  Connections
4.4  Reasoning
4.5  Tools & Tech.
4.8  Numerical Oper.
4.9  Measurement
4.10 Estimation
4.16 Excel. & Equity

Question Types:
Multiple Choice (MC)
Short Constructed
    Response (SC)
Open Ended (OE)

Technology:
Calculator

Manipulatives:

KNOWLEDGE:
The student should have a conceptual understanding of:

1. Real numbers
   1. Rational numbers
   2. Irrational numbers
2. Powers, roots, and exponents
3. Absolute value
4. Scientific notation
5. Properties of equivalence relations  (e.g., reflexive, symmetric, transitive)
6. Properties of arithmetic operations (e.g., associative, commutative)
7. Primes, factors, and multiples

The student should be able to:

8. Extend understanding of the real number system to include rational and irrational numbers
9. Represent equivalent forms of the same number
10. Evaluate expressions containing powers, roots, and factorials

PROBLEM-SOLVING SKILLS:
In problem settings, using abilities that comprise the power base, the student should be able to:

11. Use primes, factors and multiples in real-world situations
12. Determine whether or not properties of equivalence relations and arithmetic operations apply to different relations and operations
13. Use absolute values, exponents, and approximations for roots of numbers in real-life situations
14. Distinguish between rational and irrational numbers from their decimal representations
15. Distinguish between terminating and repeating decimal forms of rational numbers
16. Apply approximation techniques to situations involving initial portions of infinite decimal

(5.382 x 10⁵ ) x ( 2. x 10² )

If three digits are unreadable, give the range of possible values for the product.

Answer: (10.764 x 10⁷  <  p <  16.141 x 10⁷)

Sample SC Item

What kind of number am I?

(Answer:  Irrational)

Sample OE Item
Every Tuesday, at the Dog Deli, the manager gives away free hot dogs and soda. Every sixth customer gets a free soda, and every eighth customer gets a free hot dog. The Dog Deli served 73 customers last Tuesday.

• How many free sodas did the Dog Deli give away last Tuesday? How many hot dogs were given away?
• Did any customers receive both a free hot dog and a free soda? If so, how many customers?
• If a soda sells for 99¢ and a hot dog sells for $1.99, how much did the Dog Deli lose in income by giving away these items?

Justify your answers.

Sample OE Item
[This item illustrates connections with II C and inclusion of the Building Blocks of Calculus]

• Find the length, width, and area of each of the 5 shaded rectangles.
• What is the total area represented by the 5 rectangles?
• How do you think the area of the 5 rectangles compares to the area of the region under the curve? Explain your reasoning.

Sample SC Item
Two cars are driving around a two-mile track. One car makes a lap every 80 seconds, and the other every 60 seconds. At these rates, how long will it take the faster car to gain exactly one lap on the slower car?
(Answer: 4 min.)

Sample MC Item
Which of the following types of numbers would solve the equation x² = 15?

Sample SC Item
Use the clues to determine the number.

(Answer: 28)

Sample MC Item
Which of the following is an irrational number?

Sample SC Item
In the compound interest formula A = P(1 + r/n)^nt, A represents the value of the investment in the future, P is the amount of the original investment,  r is the annual interest rate, t is the number of years of the investment, and n is the number of times the interest is compounded each year. Find the total amount after $2500 is invested for 18 years at a rate of 6%, compounded quarterly.
(Answer: $7302.89)