Honors Algebra 2 Summer Homework

Name: __________________________

Show all steps in each problem for full credit. This packet is due at the start of class on the 1st school day of the year. Arithmetic Sequences: sequence in which each term is equal to the previous term plus a constant (or common difference d). Recursive formula: Explicit Formula: 1. Write the explicit formula from the recursive form and find the first 4 terms of each sequence a. b.

2. Write an arithmetic formula, recursive and explicit, to generate each sequence, and then find how many blocks are in the 17th term ( ). a. b.

3. A 50-gallon bathtub contains 20 gallons of water and is filling at a rate of 2.4 gallons per minute. You check the tub every minute on the minute. Write a formula for the arithmetic sequence, in both a recursive and an explicit form, for each situation below before solving. a. Suppose the drain is closed. When will you discover the water is flowing over the top?

b. Now suppose the bathtub contains 20 gallons of water is filling at a rate of 2.4 gallons per minute, but is draining water at a rate of 3.1 gallons per minute. When will you discover the tub is empty?

4. Write the equations in slope intercept form (if possible). Then graph and label each line on the coordinate plane. a. d.

b.

e.

c.

f.

Are lines a, b, or c parallel or perpendicular to each other? Explain your reasoning.

5. a. Graph the following inequalities using the correct types of lines (solid or dashed) and shade only the common region. Line A:

Line B:

Line C: Consider the edges of the graph to be -10 to 10 in both the x and y direction creating a boundary for each shading. i.e. Domain: [-10,10] or Range: [-10,10] or b. Find the perimeter of the pentagon shaped shaded region.

b. Find the area of the pentagon shaped shaded region.

6. The rise-to-run ratio of the roof of a house determines the steepness of the roof. The house is 32 feet wide. a. Determine a scale for the x axis to fit the width of the house and use the same scale on the y axis. Label each axis. b. Find 2 points the left side of the roof passes through.

C

B

D A

A: ( ______ , ______ )

B: ( ______ , ______ )

c. Write the equation of ⃡ the house.

for the left side of

E

d. Find the measure of

.

e. Write the equation of ⃡ .

f.

How much narrower would the house be if ⃡ was perpendicular to ⃡ at the point (16,15)?

7. The relationship between the length of an adult’s femur (thigh bone) and the height of the adult can be approximated by the linear equations where y is the length of the femur in inches and x is the height of the adult in inches. Female: Male: a. An anthropologist discovers a femur belonging to an adult human. The bone is 15 inches long. Provide a range estimating the height of the adult this bone belongs to.

b. From the foot bones of an adult human male, an anthropologist estimates the male was 65 inches tall. A few feet away from the site where the foot bones were discovered, the anthropologist discovers an adult male femur that is 17 inches long. Is it possible the left and foot bones came from the same person? Explain.

c. At what height would a male and female have the same size femur length, and how long would that femur be?

8. Your family wants to buy either a wood pellet stove or an electric furnace. The pellet stove costs $3650 and produces heat at a cost of $19.15 per 1 million Btu (British thermal units). The electric furnace costs $2780 and produces heat at a cost of $33.25 per 1 million Btu. a. Write an equation for the total cost y of buying each heating unit and producing x million Btu of heat.

b. Find the amount of heat produced for the same amount of money, and interpret the results in the context of the situation. (Use substitution or elimination to solve the system.)

9. A total of $12,000 is invested in two funds paying 5% and 3% simple interest. The yearly interest is $500. How much is invested at each rate?

10. Solve the equation for the indicated variable. a. Perimeter of a rectangle b. Volume of a right Circular Cylinder Solve for L Solve for h

c. Kinetic Energy Solve for v

d. Area of a trapezoid ( Solve for b

f. Investment at simple interest Solve for r

e. Area of a sector )

Solve for θ

11. Label all sides of the triangles below. Simplify all radicals and rationalize denominators if possible. No Decimals!

8

7

12

7

9

12. Factor the expressions. a.

b.

c.

d.

e.

f.

g.

h.

13. Write the equation of a circle in standard form ( center and radius. a. b.

Center: ( _____ , _____ ) Radius: ____

(

)

by completing the square. State the c.

Center: ( _____ , _____ ) Radius: ____

14. Solve the equations by using the quadratic formula ( a.

)

b.

7

Center: ( _____ , _____ ) Radius: ____

). Write solutions in a simplified form. c.