### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : Coordinate Geometry

Choose the best answer from the four choices given.

The point (15, 6) is on which of the following lines?

**Possible Answers:**

**Correct answer:**

For this problem, simply plug in the values for the point (15,6) into the different equations (15 for the -value and 6 for the -value) to see which one fits.

(NO)

(YES!)

(NO)

(NO)

### Example Question #1 : How To Find The Points On A Coordinate Plane

Choose the best answer from the four choices given.

What is the point of intersection for the following two lines?

**Possible Answers:**

**Correct answer:**

At the intersection point of the two lines the - and - values for each equation will be the same. Thus, we can set the two equations as equal to each other:

point of intersection

### Example Question #1 : Coordinate Geometry

Choose the best answer from the four choices given.

What is the -intercept of the line represented by the equation

**Possible Answers:**

**Correct answer:**

In the formula , the y-intercept is represented by (because if you set to zero, you are left with ).

Thus, to find the -intercept, set the value to zero and solve for .

### Example Question #1 : Coordinate Geometry

The ordered pair is in which quadrant?

**Possible Answers:**

Quadrant II

Quadrant III

Quadrant IV

Quadrant V

Quadrant I

**Correct answer:**

Quadrant II

There are four quadrants in the coordinate plane. Quadrant I is the top right, and they are numbered counter-clockwise. Since the x-coordinate is , you go to the left one unit (starting from the origin). Since the y-coordinate is , you go upwards four units. Therefore, you are in Quadrant II.

### Example Question #2 : Coordinate Geometry

If angles s and r add up to 180 degrees, which of the following best describes them?

**Possible Answers:**

Acute

Obtuse

Supplementary.

Complementary

**Correct answer:**

Supplementary.

Two angles that are supplementary add up to 180 degrees. They cannot both be acute, nor can they both be obtuse. Therefore, "Supplementary" is the correct answer.

### Example Question #1 : How To Find The Points On A Coordinate Plane

The lines of the equations

and

intersect at a point .

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

It is impossible to determine which is greater from the information given

**Correct answer:**

(b) is the greater quantity

If and , we can substitute in the second equation as follows:

Substitute:

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