More Resources for SAT Preparation

More Lessons for SAT Math

Math Worksheets

The following are worked solutions for the questions in the math sections of the SAT Practice Tests found in the Official SAT Study Guide.

It would be best that you go through the SAT practice test questions in the Study Guide first and then look at the worked solutions for the questions that you might need assistance in. Due to copyright issues, we are not able to reproduce the questions, but we hope that the worked solutions will be helpful.

**6. Correct answer: (E)**

**Given:**

A small square inside a larger square

**To find: **

Area of shaded region in terms of *x*

**Solution: **

*Topic(s): Area of square *

Area of large square: 5 × 5 = 25

Area of small square: *x* × *x* = *x*^{2}

Shaded area is Area of large square – Area of small square = 25 – *x*^{2}

** Answer: (E) 25 – x^{2} **

**7. Correct answer: (D)**

**Given:**

*rstv* = 1

*stuv* = 0

**To find: **

Which one of the given answers is correct.

**Solution:**

Any value multiply by 0 will result in 0.

If *rstv* = 1, then we know *r* ≠ 0, *s* ≠ 0, *t* ≠ 0 and *v* ≠ 0.

So, if *stuv* = 0 then *u* must be 0.

** Answer: (D) u = 0 **

**8. Correct answer: (C) **

**Given: **

A team scored:

one-sixth of the points in the1st quarter

one-fourth of the points in the 2nd quarter

one-third of the points in the 3rd quarter

the remaining points in the 4th quarter

The total score is 36

**To find: **

The number of points scored in the 4 th quarter

**Solution**:

*Topic(s): Translating words to equations *

Let *x* be the score in the 4 th quarter.

**Answer: (C) 9**

**9. Correct answer: (B) **

**Given:**

**To find:**

The value of *x*

**Solution: **

*Topic(s): Exponents*

We can change 8 to 2^{3} and rewrite the equation as

When we have a **power of a power**, we multiply the exponents

With the bases the same, we can equate the exponents

**Answer: (B) 3**

**10. Correct answer: (E) **

**Given:**

4 less than 3 times a certain number is 2 more than the number

**To find: **

The number

**Solution: **

*Topic(s): Translating words to equations *

Let *x* be the number.

Translate from the question:

“4 less than 3 times a certain number” → “3*x* – 4”

“2 more than the number” → “2 + *x*”

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.