PROBLEM SET IN MATHEMATICS 8

Name: ___________________________________________________________________ Score: ________

GENERAL INSTRUCTION. Show your detailed solution for all the items and always box your final answer. Write your answers on a separate sheet of paper and attached it to this questionnaire when you submit this problem set.

I. Operations on Functions. Given the functions below, perform the indicated operation in each number. Show your detailed solution. Box your final answer. (20 points)

f(x) = x2 - 6x + 9g(x) = 3x + 1h(x) = 2x3

1) f(-4)2) g(3)3) h(x + 1)4) (f + g)(3)5) (h - f)(-2)

6) (g ● h)(1/2)7) (h/g)(-1)8) (f o g)(1)9) (g o h)(0)10) (h o g o f)(1)

II. Systems of Linear Equations. For each system of linear equation, do the following: (15 points)

a. Express each equation in the form of y = mx + bb. Classify the system as consistent and dependent, consistent and independent, or

inconsistent.c. State if the graph of the system is intersecting, parallel or coinciding.d. State the number of solutions of each system

1) 2x + y = 25x + 2y = 5

2) x + y = 63x + 3y = 12

3) 9x - 3y = 183x - y = 6

III. Solutions to Systems of Linear Equations in Two Variables. Find the ordered pair that satisfy each system of linear equation by using elimination or substitution method. (15 points)

1) 2x - 5y = 303x - 4y = 52

2) x - 16y = 329x + 3y = 6

3) 2x + 3y = 124x + 5y = 2

IV. Word Problems on Systems of Linear Equations in Two Variables. Analyze the following problems and solve using systems of linear equations. (30 points)

1. The sum of twice a larger integer and 3 times a smaller is 10. When the 4 times the smaller integer is added to the larger, the result is 0. Find the integers.

2. The width of a rectangle is 2 centimeters less than one-half its length. If the perimeter measures 62 centimeters, then find the dimensions of the rectangle.

3. The sum of 3 times a larger integer and 2 times a smaller is 15. When 3 times the smaller integer is subtracted from twice the larger, the result is 23. Find the integers.

4. Harry’s Php 22,000 savings is in two accounts. One account earns 2% annual interest and the other earns 4%. His total interest for the year is Php 690. How much does he have in each account?

5. A customer ordered 4 pounds of a mixed peanut product containing 12% cashews. The inventory consists of only two mixes containing 10% and 26% cashews. How much of each type must be mixed to fill the order?

6. Jerry took two buses on the 265-mile trip from Los Angeles to Las Vegas. The first bus averaged 55 miles per hour and the second bus was able to average 50 miles per hour. If the total trip took 5 hours, then how long was spent in each bus?

V. Linear Inequalities. On a graphing paper, graph the following system of inequalities. (20 points)

1) 3x - 2y > 6x + 6y < 6

2) x - y ≤ 103x + y ≤ 6

3) 4x + 3y < 12-3x - 4y < 12

4) -10x + 3y ≥ 303x - 10y ≥ 30