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ACT Math: Algebra

What is the slope-intercept form of 3x - y - 6 = 0? 

A.  y = -3x - 6

B.  y = -3x + 6

C.  y = 3x - 6

D.  y = 3x + 6

E.  y = 6x - 3 

 

Knowsys Method

Read the problem carefully.  

Identify the bottom line.   What is the slope-intercept form (the y = form)?

Assess your options.  If you momentarily forgot what the “slope-intercept” form is, glance at the answer choices.  You’ll see that all of them start with y =.  So, we need to rearrange the question into y = format.  The trick will be to not mess up the signs since the y is negative in the original. 

Attack the problem.  

3x – y = 6

3x – 6 = y

So:  y = 3x – 6

Loop back.  Verify that you solved for the bottom line.

The correct answer is C.

Level = Easy  

Want some help reviewing the math concepts you need to master?  Try these Knowsys resources:

  1. Knowsys Pre-Algebra Flashcards
  2. Knowsys Algebra I Flashcards
  3. Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email

ACT Arithmetic: Counting Methods

Frank has 8 hats, 5 scarves, and 4 pairs of gloves.  How many distinct outfits, each consisting of a hat, scarf, and pair of gloves, can Frank create?  

A.  17

B.  80

C.  160

D.  458

E.  480

 

Knowsys Method

Read the problem carefully.  

Identify the bottom line.   The number of distinct combinations = ? 

Assess your options.  You could start creating “outfits,” but we are looking at a large number so this will not be effective.  Let’s use what we know about counting methods.    

Attack the problem.  

Since an “outfit” consists of 1 of each item, the number of permutations will be:  8 x 5 x 4 = 160 (good thing we didn’t try to count them!)

The most common mistake here is adding (for answer A) rather than multiplying the options. 

Loop back.  Verify that you solved for the bottom line.

The correct answer is 160.  Pick C.

Level = Medium  

Want some help reviewing the math concepts you need to master?  Try these Knowsys resources:

  1. Knowsys Pre-Algebra Flashcards
  2. Knowsys Algebra I Flashcards
  3. Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email

 

ACT Math: Data Analysis

Directions:  Solve each problem and choose the correct answer.

On the first 5 of 6 semester tests, each of which is worth 100 points, a student has earned the following grades:  75, 87, 83, 89, and 94.  What score must the student earn on the sixth 100-point exam to earn an average test grade of 89 for all 6 tests?

     A.  86
     B.  89
     C.  94
     D.  99
     E.  The student cannot earn an average of 89.

Knowsys Method

Read the problem carefully.  Be sure to keep the numbers in this problem straight so that you do not make any careless mistakes in your work. 

Identify the bottom line.   last score needed so that average of 6 is 89?

Assess your options.  You could sub in the different answers for the 6th test score or you could leave the missing number as a variable.  Either way, you need to use the "average formula," which you should definitely memorize.  Every time you see the word "average" on the exam, you should immediately think:  "average = the sum divided by the number."  Let's use that formula to solve this problem quickly and easily. 

The Average Formula

average formula.gif

Attack the problem.  

We are looking for the 6th test, which is part of the sum.  Here's what we are given:  

20140210 ACT average question.gif

All we have to do now is solve for x.  

89 * 6 = 428 + x

    534 = 428 + x

     106 = x 

Hmmm.  Since the test is only worth 100 points, can the student earn a 106?  Nope.  So, our answer is E.

Loop back.  Verify that you solved for the bottom line.

 

The correct answer is E.

Level = Medium  

Want some help reviewing the math concepts you need to master?  Try these Knowsys resources:

  1. Knowsys Pre-Algebra Flashcards
  2. Knowsys Algebra I Flashcards
  3. Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email