Table of Contents

Common Math Tips for the SAT

  1. Multiple choice math questions increase in difficulty from the beginning of a section to end. The difficulty restarts for the student-response questions.
  2. Always put an answer (even for student-response questions). If you don’t know the answer, put a reasonable answer or 1.
  3. All figures are drawn to scale, unless otherwise noted. This means angles and lengths are drawn to scale.
  4. You can’t bubble in a negative answer in student-response questions.
  5. Don’t round your answer unless you are asked to.
  6. Don’t start with a zero when writing your answer.

Common Math Tricks

Adding & Subtracting Equations

Sometimes to find the answer to a system of equations question, we may be asked to find the value of x+y or x-y. In this situation, we likely don’t have to solve for x or y individually. It is possible to find the value of the expression without solving for x or y.


If  3x+2y=30 and 2x+3y=5, what is the value of x+y?

Explanation & Solution

In this case, we can solve for x and y using elimination. However, we don’t have to.

If we add the equations together, we get 5x+5y=35.

The question asks us to solve for x+y, so we can simply divide both sides of the equation by 5 to get x+y=7.

The answer is 7.

Use Factors

Similar to the previous tip, we can sometimes find the answer by factoring. If we have to find the value of an expression, the expression may be a factor of a polynomial in the equation.

This type of question commonly include perfect squares. For example, we would factor x^2 -y^2 to (x+y)(x-y).


What is the average of x and y, if x^2-y^2=54 and x-y=9?

Explanation & Solution

The question is asking for the average of x and y. To find the average of x and y, we would have to add the two together and then divide by two, so we need to know what x+y equals.

We can use factors to solve for this.

We are given the equation


and we can factor the left side of the equation to get


We are looking for the value of x+y, and we are given that x-y=9, so we can substitute 9 in to get


Divide both sides by 9 to get


The average of xand y is 6\div2 =3.

Use the Answer Choices

If numerical answers are given, it may be possible to try the answer choices and work backwards. Make sure to pay attention to what the question is asking for, so we know what to test each answer as. For exmplae. if the question asks to find the average cost of sneakers, then when we test the asnwers, we should test them as the average cost of sneakers and work backwards.


The length of a rectangle is 5 more than its width. If the area of the rectangle is 66 sq in, what is the length, in inches, of the rectangle?

  1. 5
  2. 6
  3. 8
  4. 11

Explanation & Solution

Lets try choice A. 

5 would equal the length. The question states that the length is 5 more than the width, which would make the width 0. That’s not possible, so A is wrong.

Let’s try choice C.

8 would equal the length. The questions states that the length is 5 more than the width, so the width would be 3.

These dimension would give an area of 24. (Area of a rectangle is length times width). However, the question states that the area is 66, so these dimensions don’t work. C is not the answer.

Try choice D.

11 would be the length, and that would make the width 6. The area of this rectangle would be 66 (6 times 11 is 66). This matches what the question states, so D is the answer.

Pick Numbers

When the answer choices are algebraic expressions, we can pick numbers for the values of the variables. We have to substitute those values in the question to find the numeric answer. After, we substitute the values into the variables in the answer choices to see which answer choice gives us the right numerical value.


Which of the following is equivalent to \dfrac{3t}{4x-1}-\dfrac{t+1}{2}, if x!=-\dfrac{1}/{4}?

A. \dfrac{5xt-1}{8x-2}

B. \dfrac{-4xt+7t-4x+1}{2(4x-1)}

C. \dfrac{2(2xt+1)}{4x-1}

D. \dfrac{-4xt+5t}{2}

Explanation and Solution

Let’s pick 4 for x and 3 for t.

Substitute 4 and 3 into the expression and evaluate. \dfrac{3(3)}{4(4)-1}-\dfrac{(3)+1}{2} gives us \dfrac{9}{15}-\dfrac{4}{2}, then reduce \dfrac{3}{5}-2 becomes -\dfrac{7}{5}.

Substitute the value into the answer choices and see which one also gives us -\dfrac{7}{5}.

A. \dfrac{5(4)(3)-1}{8(4)-2}
which gives us \dfrac{59}{30}
B. \dfrac{-4(4)(3)+7(3)+4(4)-1}{2(4(4)+1)} which gives us \dfrac{-42}{30} and that reduces to -\dfrac{7}{5}. This matches the answer, so B is the answer.

You should double check to make sure C or D doesn’t also give you the right answer. If one of them does, you need to pick new numbers and do the process over again, but only check the two answers choices that worked .

Combining Like Terms

Like terms have the same combination of variables and exponents but may have different coefficients.

When combining like terms, simply add the coefficients together.


In the example above, the coefficients are 4 and 6. We simply add them together to get


More examples:


We only add coefficients together of like terms. In the example below, there are many terms and not all of them are like terms.

12x-4y+3x^2-20y+3xy-4x +2xy

We can combine 12x and -4x to get 8x.

Notice that I treated the minus sign in front of  as a negative sign. Make sure to take the signs in front of the numbers along with the terms when combining like terms.

We can combine -4y and -20y to get -24y

We can also combine 3xy and 2xy to get 5xy

That’s all of the like terms, so we end up with 8x+5xy+3x^2-24y

Adding and Subtracting Expressions

When questions ask us to add and subtract expressions, we are really being asked to combine like terms.

What is the sum of x^2-2x+7 and 2x^2-3x-4?

Explanation & Solution
To solve this let’s add them together.
Distribute the plus sign (+1) to each of the terms in the second expression. When you do that, all of the terms remain the same and we can drop the parentheses.
Now, just combine like terms to get

Simplify (4x^2-5x+2)-(2x^2+x-3)

Explanation & Solution
Distribute the minus sign (-1) to each of the terms in the second expression. When you do that, all of the terms get negated and we can drop the parentheses.
Now, just combine like terms to get

Solving Equations

Distribute or Divide

If there is a number outside a set of parentheses, you can choose to distribute it or divide it.

The equation 3(x-4)=15 can be solved two different ways.

We can either distribute the 3 into the expressions or divide it.

Example of Distributing


distribute the 3 into the parenthesis and the equation becomes


add 12 to both sides of the equation


divide both sides by 3 to get


Example of Dividing First


divide both side by 3 to get


add 5 to both sides of the equation to get


With both methods we are able to get x=9. However, on the SAT there may be questions in which one method works better than another.


9(2x+3)=36. What is the value of 2x+3?

Explanation & Solution

In this question, the expression we are solving for can be found directly.

If we divide both sides by 9, we will have the answer immediately. It would be a waste of time to distribute the 9.


divide both sides by 9 to get


The answer is 4.

Multiply by Least Common Denominator (LCD) to Eliminate Fractions in Equations

The following equation


can be intimidating for students.

Many students are not comfortable working with fractions. Plus, there is room to make mistakes with fractions.

We can multiply all of the terms in the equation by the LCD to cancel out the denominators, so we are left with integers.


What is the value of x in the following equation?

Explanation & Solution

The denominators in the equation above are 3, 5, and 6.
To find the least common denominator, we need the least common multiple of the denominators.

In this case, the LCD is 30.

We should multiple each term in the equation by 30 to get

Reduce each term to get


Simplifying further gives us


Now, we can solve like normal.

Add 24 to both sides to get


Divide both sides by 20 to get


Cross Multiply When a Fraction Equals a Fraction

If you have an equation in which one fraction equals another fraction, it is a proportion. To solve a proportion you should cross-multiply.

It is best to simplify each fraction as much as possible before cross-multiplying.


Solve for x in the equation below.


Explanation & Solution


Cross-multiply to get


Simplify both sides


Since there is an x-term on both sides of the equation, we should get them both on one side.

Subtract 8x from both sides. (You can subtract 24x from both sides instead. It is up to you)


Add 84 to both sides to get


Divide both sides by 16