**This is for SAT in Jan 2016 or before.**

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

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.

**11. Correct answer: (A)**

**Given:**

*g*(*x*) = *ax*^{2}
+ *bx + c *

*a* and *c* are negative constants

**To find: **

The graph of *g *

**Solution:**

*g*(*x*) = *ax*^{2} + *bx + c*, where *a* and *c* are negative constants.

*c* is the intercept at the *y*-axis and it is negative.

This means the graph must cross the *y*-axis at a negative value.

From the given graphs, only (A) satisfies that condition.

**Answer: (A)**

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

**Given:**

*ABCD* is a retangle

*BC* = 4

*AB* = 6

*P, Q* and *R* are points on a line that is parallel to

Points *P* and *Q* are symmetric about the line *AB
*Points

T**o find: **

Length of

** Solution: **

Let the line

Let the length of *SQ* be *x*, then the length of *QT* would be 4 – *x*.

* PQ* is symmetric about the line *AB*. So, the length of *PS* = *SQ* = *x*

* QR * is symmetric about the line *CD*. So the length of *TR* = *QT* = 4 – *x*

Length of PR = PS + SQ + QT + TR = *x + x + *4 – *x* + 4 – *x* = 8

**Given: **

Price was first increased by 10%

New price was decreased by 25%

**To find: **

The final price was what percent of the initial price

**Solution: **

Topic(s): Percent

Increased by 10% means to multiply by 100% + 10% = 110%

Decreased by 25% means to multiply by 100% – 25% = 75%

Change percent to decimal.

110% × 75% = 1.1 × 0.75 = 0.825 = 82.5%

**Given:**

The number *w* is multiplied by 4 and the result is the same as when 4 is added to *w*

**To find: **

The value for 3*w *

**Solution: **

Topic(s): Translating words to equations

*w* × 4 = 4 + *w* ⇒ 4*w* = 4 + *w* ⇒ 3*w* = 4

**Given: **

Lengths of sides of right triangle are consecutive even integers

Length of shortest side is *x*

**To find:**

The equation that can be used to find *x*

**Solution:**

Topic(s): Consecutive even numbers, Pythagorean theorem

Being consecutive even numbers we need to add 2 to the previous number. The sides of the triangle would then be

Using the Pythagorean formula, we get the equation.

*x*^{2} + (*x* + 2)^{2} = (*x* + 4)^{2}

**Answer: (C) x^{2} + (x + 2)^{2} = (x + 4)^{2}**

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

**Given:**

*y* > 1

**To find: **

The statement that is true

** Solution:**

**Answer: (D) I and III only**

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