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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

 

SAT Math: Algebra

If 7 less than 4 times a number is 2 more than 3 times that number, what is the number?

Knowsys Method

Read the problem carefully.  This is a grid in question.  Instead of bubbling in a letter, you will bubble in your answer.  You should always guess on grid in questions because, unlike multiple choice questions, grid in questions do not have a wrong answer penalty.

Identify the bottom line.   the value of the number = ? 

Assess your options.  You could start guessing and trying, but the more effective method will be to use a method.  In this type of problem, it is most straightforward to translate the statement from English to math and then solve. 

Attack the problem.  

The statement translates to:  4x – 7 = 3x + 2

The bottom line is:  what is x?

When we solve for x we get x = 9. 

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

The correct answer is 9.  Grid it in.

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

SAT Math: Algebra

Functions

Let the function be defined by f(x) = 5x - 10.  If 2f(m) = 20, then what is the value of f(3m)? 

Knowsys Method

Read the problem carefully.  This is a grid in question.  Instead of bubbling in a letter, you will bubble in your answer.  You should always guess on grid in questions because, unlike multiple choice questions, grid in questions do not have a wrong answer penalty. 

Identify the bottom line.  f(3m) = ?

Assess your options.  This function problem is very straightforward.  All you have to do is plug in the information given to you and solve. 

Attack the problem. 

2f(m) = 20, so f(m) = 10

If f(x) = 5x - 10, then f(m) = 5m - 10.  Set that equal to the value you already know for f(m) and solve for m.

10 = 5m - 10
20 = 5m
4 = m

Now plug in the value of m to find f(3m).

f(3m) = f(12) = 5(12) - 10 = 50

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

The correct answer is 50.

This is a medium level problem.  

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email

 

SAT Math: Algebra

Symbol Problems

Screen Shot 2014-01-15 at 4.02.34 PM.jpg

A. -16
B. -4
C. -2
D. -1
E. -3/4

Knowsys Method

Read the problem carefully.  If you have never seen this problem type before, it might look strange to you.  Don't worry, though.  We will show you just how simple these problems are!

Identify the bottom line. c = ?

Assess your options.  At Knowsys, we call these problems "symbol problems" because they use fnon-mathematical symbols like stars, hearts, smiley faces, etc.  To solve a symbol problem, all you have to do is plug in the information given to you.  Use the following steps to ace these problems on the SAT. 

1. Write out the symbol problem defined in the question.  For instance,

&a = a + 2

2. Directly below that, write out the new version of the symbol problem, aligning the symbol in the original with the symbol in the new version.

&a = a + 2

&b =

&7 =

3. Substitute the variable(s) or number(s) in the new version for the variables in the original. 

&a = a + 2

&b = b + 2

&7 = 7 + 2 = 9

Attack the problem.  Let's apply those steps to the symbol problem above.  First, write out the original symbol problem defined in the question.

Screen Shot 2014-01-15 at 4.02.38 PM.jpg

You will have to deal with the right and left sides of the new version of the symbol problem separately.  Start with the left side.  Write that part out below the original, and substitute the variables into the original. 

Screen Shot 2014-01-15 at 4.02.44 PM.jpg

Now, repeat the same step with the right side. 

Screen Shot 2014-01-15 at 4.02.50 PM.jpg

Use FOIL, distribute the -2, and combine like terms.

Screen Shot 2014-01-15 at 4.02.59 PM.jpg

Now, set the solutions you have found for each side equal to each other and solve for c.

Screen Shot 2014-01-15 at 4.03.07 PM.jpg

Loop back.  Check to make sure that you have solved for the bottom line.

The correct answer is D.

This is a hard level problem.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email

SAT Math: Algebra

Simultaneous Equations

Emmanuel owns a printing business.  He ordered boxes of copy paper for $10 each and boxes of photo paper for $12 each.  If Emmanuel ordered 10 boxes of paper and spent $112 (before tax), how many boxes of photo paper did he order?

A.  2
B.  3
C.  4
D.  6
E.  7

Knowsys Method

Read the problem carefully.  Be careful to identify the correct bottom line- which type of paper is the problem asking about?

Identify the bottom line.  boxes of photo paper = ?

Assess your options.  At Knowsys we call these problems “How Many? How Much?” problems.  To solve these problems, you can test out each of the answer choices, or you can create two simultaneous equations.  Unless the first answer choice you test out is correct, the latter strategy will save you time.  

Attack the problem.  Create two equations.   One should tell you “how many,” as in “how many boxes of paper are there total?”  The other equation should tell you “how much,” as in “how much do the boxes of paper cost?”  We will use c to represent copy paper and p to represent photo paper.

Screen Shot 2013-12-16 at 4.26.07 PM.jpg

The 10 and 12 in the second equation are the prices of each box.  The next step is to eliminate the variable that you are not focusing on, in this case, c.  To get rid of 10c in the second equation, you need to have -10c in the first equation, so multiply the entire first equation by -10 and then add the equations together to solve for p.  

Screen Shot 2013-12-16 at 4.26.16 PM.jpg

Loop back.  Did you solve for p (photo paper)? Yes.

The correct answer is D.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email

SAT Math: Algebra

Roots and Radicals

Screen Shot 2013-12-02 at 4.56.24 PM.jpg

A.  7
B.  13
C.  49
D.  91
E.  364

Knowsys Method

Read the problem carefully.  Note that an integer is a whole number, not a fraction.

Identify the bottom line.  Least potential value of x = ?

Assess your options.  You could plug in each of the answer choices and find the smallest choice that results in an integer, but there is a much quicker way to solve this type of problem.

Attack the problem.

Screen Shot 2013-12-02 at 4.58.26 PM.jpg

Loop back.  Did you solve for the bottom line? Yes.  

The correct answer is D.
This is a medium-level problem.

 

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email

SAT Math: Algebra

Exponents

Screen Shot 2013-11-06 at 3.15.39 PM.jpg

Read the question carefully.  This question requires you to know exponent rules.  It is important for you to note that a and b are positive integers and that you are asked for a in terms of b.

Identify the bottom line.  a = ?

Assess your options.  Unfortunately, this problem is going to be difficult for you to solve if you have not memorized exponent rules.  If the rules you need to solve this problem do not immediately pop into your head, go back and review the exponent rules.  

Attack the problem.  There are two rules that apply to this problem:

Screen Shot 2013-11-20 at 10.16.43 AM.jpg

The first thing you have to do is get all the bases to look the same.  Look back at the original equation:

Screen Shot 2013-11-06 at 3.28.13 PM.jpg

The number 9 is three squared, so you can rewrite the equation like this:

Screen Shot 2013-11-06 at 3.29.07 PM.jpg

Now apply the first exponent rule to the left side of the equation:

Screen Shot 2013-11-06 at 3.29.26 PM.jpg

Now you can apply the second rule.  If the base is 3 on both sides, then the exponents must be the same number.  Set them equal to one another and solve for the variable.

Screen Shot 2013-11-06 at 3.29.45 PM.jpg

Loop back.  You found a in terms of b, so now you just need to select the correct answer choice, which is (B).

Correct answer: (B)

This is a medium level question.

 

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

Subscribe to Knowsys SAT & ACT Blog by Email