### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : Geometry

Give the equation of the line through point that has slope .

**Possible Answers:**

**Correct answer:**

Use the point-slope formula with

### Example Question #2 : Coordinate Geometry

Which is the greater quantity?

(A) The slope of the line

(B) The slope of the line

**Possible Answers:**

(A) is greater

(A) and (B) are equal

(B) is greater

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

**Correct answer:**

(A) is greater

Rewrite each in the slope-intercept form, ; will be the slope.

The slope of this line is .

The slope of this line is .

Since , (A) is greater.

### Example Question #3 : Coordinate Geometry

Which is the greater quantity?

(A) The slope of the line

(B) The slope of the line

**Possible Answers:**

(A) and (B) are equal

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

(B) is greater

(A) is greater

**Correct answer:**

(A) and (B) are equal

Rewrite each in the slope-intercept form, ; will be the slope.

The slope of the line of is

The slope of the line of is also

The slopes are equal.

### Example Question #4 : Coordinate Geometry

and are positive integers, and . Which is the greater quantity?

(a) The slope of the line on the coordinate plane through the points and .

(b) The slope of the line on the coordinate plane through the points and .

**Possible Answers:**

(a) and (b) are equal

(a) is the greater quantity

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

(b) is the greater quantity

**Correct answer:**

(a) and (b) are equal

The slope of a line through the points and can be found by setting

in the slope formula:

The slope of a line through the points and can be found similarly:

The lines have the same slope.

### Example Question #5 : Coordinate Geometry

A line passes through the points with coordinates and , where . Which expression is equal to the slope of the line?

**Possible Answers:**

Undefined

**Correct answer:**

The slope of a line through the points and , can be found by setting

:

in the slope formula:

### Example Question #6 : 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 #7 : Coordinate Geometry

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 #8 : 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 #9 : Coordinate Geometry

The ordered pair is in which quadrant?

**Possible Answers:**

Quadrant II

Quadrant V

Quadrant IV

Quadrant III

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 #10 : Coordinate Geometry

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

**Possible Answers:**

Complementary

Obtuse

Acute

Supplementary.

**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.