MATH 1 EOC REVIEW WORKSHEET WITH SOLUTION  

Problem 1 :

Which graph shows the solution for the system of inequalities below?

y ≤ 2x + 2

y > -3x - 1

a)  

b)

c)

Solution:

In general the overlapping region of the inequalities given can be considered as solution region.

From option A, choosing one of the points :

(5, 5)

So, option A is correct.

Problem 2 :

The amount of medicine in Elizabeth's blood is modeled by the function

M(t) = -t² + 10t

where t is the number of hours after she takes the medicine. How many hours after Elizabeth takes her medicine is the amount of medicine in her blood the highest?

A. 5 hours      B. 10 hours       C. 25 hours

Solution:

M(t) = -t² + 10t

x = -b/2a

Here a = -1 and b = 10

x = -10/2(-1)

= -10/-2

x = 5 hours

So, option (A) is correct.

Problem 3 :

What is the smallest positive integer for x, so that the value of f(x) = 200(2)^x is greater than the value of g(x) = 500x + 400?

Solution:

f(x) = 200(2)^x  ------(1)

g(x) = 500x + 400  ------(2)

(1) = (2)

200(2)^x = 500x + 400

Dividing by 100

2(2)^x = 5x + 4

2^x+1 = 5x + 4

Let us apply x = 5

2⁵⁺¹ = 5(5) + 4

2⁶ = 25 + 4

64 > 29 (true)

Let us apply x = 4

2⁴⁺¹ = 5(4) + 4

2⁵ = 20 + 4

32 > 24 (Ture)

Let us apply x = 3

2³⁺¹ = 5(3) + 4

2⁴ = 15 + 4

16 > 19 (false)

So, the smallest integer is 4.

Problem 4 :

What is the y-intercept of the function f(x) = 1/2(2x - 4)?

A. (0, -4)           B. (0, -2)        C. (0, 1)

Solution :

f(x) = 1/2(2x - 4)

f(x) = x - 2

y-intercept = (0, -2)

So, option (B) is correct.

Problem 5 :

A girl drops a ball from a height of 10 feet. Each time the ball hits the ground, it bounches to 2/3 its previous height. Which equation gives y, the height of the ball after x bounches?

Solution:

Given, initial height = 10 feet

Rate of decrease = 2/3

y = ab^x

y = 10(2/3)^x

So, option (B) is correct.

Problem 6 :

Which expression is equivalent to 3(x - 4)²?

A. 3x² + 48     B. 3x² - 24x + 48    C. 9x² - 72x + 144

Solution:

= 3(x - 4)²

= 3(x - 4)(x - 4)

= 3(x² - 8x + 16)

= 3x² - 24x + 48

So, option (B) is correct.

Problem 7 :

Jane owns x comic books. Derrek owns y comic books.

• The number of comic books Jane owns is 1 less than 2 times the number Derrek owns.
• Together they have a total of 11 comic books.

How many comic books does Derrek own?

Solution:

j = 2d - 1 ---> (1)

j + d = 11 ---> (2)

j = 11 - d

Substitute j = 11 - d in (1),

11 - d = 2d - 1

-3d = -12

d = 4

4 comic books does Derrek own.

Problem 8 :

James is at a gift sale where everything costs $4 (tax included).

• James has $50.
• James must have at least $28 remaining when he is finished buying gifts.

What is the greatest number of gifts James can buy?

Solution:

x = number of items

4x ≤ 50 - 28

4x ≤ 22

x ≤ 5.5

5 gifts James can buy.

Problem 9 :

The expression -5t² + 40t predicts the height, in meters, of an object t seconds after a person launches it into the air. Using this expression, how many seconds will it take the object to hit the ground?

Solution:

 -5t² + 40t = 0

 -5t(t - 8) = 0

-5t = 0 or t - 8 = 0

t = 0 or t = 8

t = 8

8 seconds will it take the object to hit the ground.

Problem 10 :

Solution: