# SAT Practice Test 1, Section 3: Questions 6 - 10

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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.

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 = x2
Shaded area is Area of large square – Area of small square = 25 – x2

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.

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.

Given:

To find:
The value of x

Solution:
Topic(s): Exponents

We can change 8 to 23 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

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” → “3x – 4”
“2 more than the number” → “2 + x