MATH 1 EOC REVIEW PACKET WITH SOLUTION

Problem 11:

The function f(x) = 10,000 - 1,500x can be used to predict the number of termites in an area x days after the area has been treated. How many termites are predicted in the area after 5 days?

Solution:

f(x) = 10,000 - 1,500x

f(x) = 10,000 - 1500(5)

= 10000 - 7500

f(x) = 2500 

2500 termites are predicted in the area after 5 days.

Problem 12 :

Avis used a quadratic function to solve a problem. The factored form of the function is show below.

(4x + 3)(6x - 3) = 0

What is the positive solution to the problem?

Solution:

4x + 3 = 0

4x = -3

x = -3/4

6x - 3 = 0

6x = 3

x = 3/6

x = 1/2

So, the positive solution is x = 1/2.

Problem 13 :

The cost to rent a construction crane is $750 per day plus $250 per hour of use. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed $2500 per day?

Solution:

x be the number of hours.

250x + 750 ≤ 2500

250x ≤ 1750

x ≤ 7 hours

Problem 14 :

The average daily high temperature for the month of May in Ocala. Florida is approximated by the function

f(n) = 0.2n+ 80

where n is the day of the month. May has 31 days. The maximum daily high temperature occurred on May 31st. What was the maximum temperature?

Solution:

f(n) = 0.2n+ 80

n = day of  the month

n = 31

f(n) = 0.2(31)+ 80

= 6.2 + 80

f(n) = 86.2

So, the maximum temperature is 86.2°.

Problem 15 :

Jorge graphed the line shown below.

math-eoc-q15.png

Solution:

math-eoc-q15-answer

Slope = Rise/Run

Slope = 2/3

Problem 16 :

Shirley graphed the line shown on the coordinate plane below.

math-eoc-q16.png

Solution:

According to the graph. This line y = mx + b passes through points (1.00, 5.00) (3.00, 2.00).

m+b=5 (1)Slope m=-323m+b=2(2)3-32+b=2-92+b=2b=132y=-32x+132When y=0-32x+132=0x=-1322-3x=133

Problem 17 :

The table below shows the amount of money Bernard earned selling newspapers during a 6-week time period.

math-eoc-q17.png

Which describes the relationship between the week, x, and the money Bernard earned, y?

A. a week, positive relationship

B. a strong, negative relationship

C. a strong, positive relationship

Solution:

math1-eoc-q17

So, option (C) is correct.

Problem 18 :

A system of equations is shown below.

y = -2x + 4

y = (2)x + 1

What is the approximate value of x in the solution of the system?

A. 0.69          B. 0.75            C. 3.24

Solution:

y = -2x + 4

y = (2)x + 1

-2x + 4 = 2x + 1

-2x - 2x + 3 = 0

2x + 2x - 3 = 0

x = 0.69

So, option (A) is correct.

Problem 19 :

The volume of a cone can be found using the formula

V = 1/3Bh

where B is the area of the base of the cone and h is the height. A cone has a volume of 262 cubic inches and a height of 10 inches. What is the approximate length of the radius of the cone?

A. 2.5 inches         B. 5 inches          C. 25 inches

Solution:

Given, volume of a cone = 262 cubic inches

height = 10 inches

Volume of a cone=13BhB=𝜋r2V=13𝜋r2h262=12×3.14×r2×10786=31.4 ×r2r2=25.03r=5 inches

So, option (B) is correct.

Problem 20 :

M is the midpoint of KL. M is at (5, -2) and L is at (3, 6). What are the coordinates of K?

A. (2, -8)        B. (4, 2)          C. (7, -10)

Solution:

Given, M(5, -2) = (x, y)

L(3, 6) = (x1, y1) and k = (x2, y2)

By using midpoint formula.

(x,y)=x1+x22,y1+y22(5,-2)=3+x22,6+y22
3+x22=53+x2=10x2=7
6+y22=-26+y2=-4y2=-10

Therefore, the coordinates of K is (7, -10).

So, the option (C) is correct.

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