ACT Review

ACT Review

By Christina Early

What we are doing

We are going to look at ACT questions similar to topics we have covered this year.

Some text here about the topic of discussion

• Linear equation

  • Slope

  • Standard Form​

• Function notation

• Exponent Properties

Linear Equations

​Some text here about the topic of discussion.

How to find slope From a graph:

​Formulas that involve Slope

y=mx+b where m=slope, b=y-int​

Multiple Choice

What is the slope of line HM?

• $$-\frac{3}{2}$$

• -1

• $$-\frac{2}{3}$$

• $$\frac{2}{3}$$

• $$\frac{3}{2}$$

Multiple Choice

Find the slope of the line.

• -2
• 2
• -1
• 1

Multiple Choice

Find the slope of the line.

• -5/4
• 5/4
• -4/5
• 4/5

Multiple Choice

Find the slope of the line.

• 5/2

• -5/2

• 2/5

• -2/5

How to find slope from a table:

​Formulas that involve Slope

y=mx+b where m=slope, b=y-int​

Multiple Choice

Find the slope of the line that passes through:
(-4, 7) and (-6, -4)

• 2/11
• 13/2
• 3/10
• 11/2

Multiple Choice

Find the slope of the line that passes through:
(-3, -4) and (7, 6)

• 0
• Undefined
• -1
• 1

Multiple Choice

Determine the slope from the table. 

• -2
• 2
• -1/2
• 1/2

Multiple Choice

Determine the slope.

• -3
• 3
• -1/3
• 1/3

Multiple Choice

Which equation best represents the relationship between x and y in the table shown?

• y=5x + 10
• y=1/5x+5
• y= 5x+5 
• y=10x+5

Multiple Choice

What is the equation for the table?

• y =1/4x -3
• y =4x - 3
• y = -3x -3 
• y =-2x -3 

Multiple Choice

What is the algebraic equation for the following table?

• y = x + 3

• y = 3x

• y = x ÷ 3

• y = x - 3

The questions to follow will practice this conversion and using it.

​Convert to y=mx+b

​Sometime the ACT will give you linear equations in standard form(ax+by=c) and ask you do stuff with it. Knowing how to convert it to y=mx+b will help you answer those questions.

​

You do that by solving for y.​

​

Multiple Choice

Write the slope intercept form of the equation 3x - 2y = -16

• y = -3x - 8

• y = -3x + 8

• y = -3/2x - 8

• y = 3/2 x + 8

Multiple Choice

Write the slope intercept form of the equation 13x - 11y = -12

• y = 13/11x + 12/11

• y = 13x - 11

• y = -13/11x -12/11

• y = x + 1

Multiple Choice

Write the slope intercept form of the equation 9x - 7y = -7

• y = -9/7x + 1

• y = 9/7x + 1

• y = -9/7x - 7/9

• y = 9/7x + 7/9

Function Notation

We are only focusing on f(x) and plugging numbers in

Function Notation

"F of x" or f(x) means the function labeled "f" has an input of "x". It does NOT mean "f times x."

Multiple Choice

If a question asks you to find f(2), what does that mean?

• Let x = 2

• Let y = 2

Multiple Choice

If f(x) = 2x + 1, find f(1).

• f(1) = 1

• f(1) = 4

• f(1) = 0

• f(1) = 3

Multiple Choice

• 16

• 48

• -28

• 4

Multiple Choice

• -20

• 20

• -24

• 24

Multiple Choice

A company is selling bubble gum.  The function g(x)=3x+4 tells the company how much to charge if someone buys x packages of bubble gum.  Find g(8) and tell what it means within the context of the problem.

• g(8)=8.  This means that after 8 packages of gum, the company makes $8.
• g(8)=42.  This means that 8 packages of gum costs $42.
• g(8)=28.  This means that 8 packages of gum costs $28.
• g(8)=24.  This means that 8 packages of gum costs $24.

Exponent Properties

I will give you one practice for each property except fractional exponent bc we have not learned it yet.

​

These are the Exponent Rules

Multiple Choice

Simplify:  (5p⁹q³)(2pq⁷)

• 7p¹⁰q¹⁰
• 10p⁹q²¹
• 10p¹⁰q¹⁰
• 10p⁸q^-4

Multiple Choice

• $$\frac{27x^{15}z^3}{y^6}$$

• $$\frac{9x^{15}z^3}{y^6}$$

• $$27x^8yz^4$$

• $$\frac{27x^8z^4}{y}$$

Multiple Choice

Simplify the following expression:

(xyz)⁰ =

• 0

• 1

• xyz

• -1

Multiple Choice

Simplify so there are no negative exponents in the answer.

$$\frac{3x^3\cdot4x^4}{x^2}$$  

• $$12x^5$$  

• $$12x^9$$  

• $$7x^5$$  

• $$7x^4$$  

Multiple Choice

Simplify so there are no negative exponents in the answer.

$$\left(3n^3\right)^{-3}$$  

• $$\frac{1}{27n^9}$$  

• $$\frac{-27}{n^9}$$  

• $$\frac{-27}{n^6}$$  

• $$\frac{-9}{n^6}$$  

Multiple Choice

• 2x²z⁴

• 3x²y⁵z⁴