### All SAT Mathematics Resources

## Example Questions

### Example Question #1 : Graphing Inequalities

For the following system of equations, what shape does the corresponding graph make:

**Possible Answers:**

Rectangle

It does not form a shape.

Square

Triangle

**Correct answer:**

Triangle

When we graph the three inequalities as equations, we get the below graph. Testing a point within the triangle does in fact fulfill all three conditions, so the shape formed by the inequalities is a triangle. If a tested point within the triangle did not fulfill one or more conditions, then we would have chosen “it does not form a shape.”

### Example Question #1 : Graphing Inequalities

Which of the following graphs correctly describes the system of inequalities:

**Possible Answers:**

**Correct answer:**

After plotting the lines, shade the regions corresponding to each individual inequality. The area of intersection (in purple) is the solution to the system of inequalities. Another way to check your answer is to pick a point in all four regions delineated by the two equations and test those four coordinate points in the system of inequalities.

### Example Question #1 : Graphing Inequalities

For the following system of equations, what shape does the corresponding graph make:

**Possible Answers:**

Square

It does not form a shape

Rectangle

Triangle

**Correct answer:**

Triangle

When we graph the three inequalities as equations, we get the below graph. Testing a point within the triangle does in fact fulfill all three conditions, so the shape formed by the inequalities is a triangle. If a tested point within the triangle did not fulfill one or more conditions, then we would have chosen “it does not form a shape.”

### Example Question #2 : Graphing Inequalities

Which of the following graphs correctly describes the system of inequalities:

**Possible Answers:**

**Correct answer:**

After plotting the lines, shade the regions corresponding to each individual inequality. The area of intersection (in purple) is the solution to the system of inequalities. Another way to check your answer is to pick a point in all four regions delineated by the two equations and test those four coordinate points in the system of inequalities.

### Example Question #1 : Graphing Inequalities

Which of the following ordered pairs (x,y) is a solution to the system of inequalities:

**Possible Answers:**

**Correct answer:**

This is the only coordinate point that fulfills the system of inequalities.

### Example Question #6 : Graphing Inequalities

If the system of inequalities and is graphed on the xy- plane above, which quadrant contains no solutions to the system?

**Possible Answers:**

III

II

I and II

I

**Correct answer:**

I and II

The graph of the system of inequalities is shown below. The solution (in purple) does not go into region I or II.

### Example Question #1 : Graphing Inequalities

If the system of inequalities and is graphed on the xy- plane above, which quadrant contains no solutions to the system?

**Possible Answers:**

There are solutions in all 4 quadrants.

III

II

IV

**Correct answer:**

There are solutions in all 4 quadrants.

The graph of the system of inequalities is shown below. The solution (in purple) is present in all four regions.

### Example Question #8 : Graphing Inequalities

If the system of inequalities and is graphed on the xy- plane above, which quadrant contains no solutions to the system?

**Possible Answers:**

IV

There are solutions in all 4 quadrants.

III

II

**Correct answer:**

There are solutions in all 4 quadrants.

The graph of the system of inequalities is shown below. The solution (in purple) is present in all four regions.

### Example Question #2 : Graphing Inequalities

The graph shown above is best represented by which inequality?

**Possible Answers:**

**Correct answer:**

The x-intercept is (4,0) so when equals 0, , and the y-intercept is (0,3) so when equals 0, . These points only work for a line corresponding to . To determine which direction the inequality points, you can plug in any point. If we use (0,0), , so this is the direction the inequality must face.

### Example Question #4 : Graphing Inequalities

Which of the following are solutions to the system of equations and ?

I)

II)

III)

**Possible Answers:**

II

I

I, II, and III

I and II

**Correct answer:**

I

With this question, it is important to recognize the system of inequalities utilizes the “greater than” sign, not the “greater than or equal to” sign. does not fulfill . appears to fulfill both conditions but . 18 is not greater than 8, leaving only as a possible solution.