ISEE Lower Level Quantitative : ISEE Lower Level (grades 5-6) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

varsity tutors app store varsity tutors android store

Example Questions

Example Question #152 : Geometry

Select the point that has the shortest distance to the \displaystyle \small y axis. 

Possible Answers:

\displaystyle \small (2,4)

\displaystyle \small (-5,0)

\displaystyle \small (2,7)

\displaystyle \small (-1,8)

Correct answer:

\displaystyle \small (-1,8)

Explanation:

Since the \displaystyle \small y-axis runs vertically, the point that has the \displaystyle \small x coordinate with the lowest absolute value will be closest to the \displaystyle \small y-axis. Therefore, coordinate point \displaystyle \small (-1,8) has the shortest distance to the \displaystyle \small y-axis, because the point is only a distance of \displaystyle \small 1 away from the \displaystyle \small y-axis. Every other coordinate point has an absolute distance of \displaystyle \small 2 or more. 

Example Question #161 : Coordinate Geometry

Which coordinate point is farthest from the \displaystyle \small x-axis? 

Possible Answers:

\displaystyle \small (1,-7)

\displaystyle \small (1,5)

\displaystyle \small (5,-5)

\displaystyle \small (-1,4)

\displaystyle \small (-5,5)

Correct answer:

\displaystyle \small (1,-7)

Explanation:

Compare the absolute value of each of the coordinate points \displaystyle \small y values. Since, the \displaystyle \small y value of point \displaystyle \small \small (1.-7) has the greatest absolute value, this point has the farthest distance to the horizontal \displaystyle \small x-axis.

Example Question #162 : Geometry

Find the equation of the line that passes through coordinate point \displaystyle \small (6,4).

Possible Answers:

\displaystyle \small y=\frac{2}{3}x+5

\displaystyle \small y=\frac{3}{2}+5

\displaystyle \small y=\frac{2}{3}x-5

\displaystyle \small y=\frac{3}{2}x-5

Correct answer:

\displaystyle \small y=\frac{3}{2}x-5

Explanation:

To find the equation of the line that passes through coordinate point \displaystyle \small (6,4), plug the \displaystyle \small x and \displaystyle \small y values into each equation. The correct equation will end with a true statement. 

The solution is:
\displaystyle \small x=6\displaystyle \small y=4


\displaystyle \small y=\frac{3}{2}x-5

\displaystyle \small 4=\frac{3}{2}(6)-5

\displaystyle \small 4=\frac{18}{2}-5

\displaystyle \small 4=9-5

\displaystyle \small 4=4

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

Select the coordinate point with the farthest distance from the \displaystyle \small y-axis. 

Possible Answers:

\displaystyle \small (-6,2)

\displaystyle \small (8,-5)

\displaystyle \small (4,9)

\displaystyle \small (5,8)

\displaystyle \small (5,-8)

Correct answer:

\displaystyle \small (8,-5)

Explanation:

Since the \displaystyle \small y-axis runs vertically, the point that has the \displaystyle \small x coordinate with the greatest absolute value will be farthest from the \displaystyle \small y-axis. Therefore, coordinate point \displaystyle \small \small (8,-5) has the longest distance to the \displaystyle \small y-axis, because the point is a distance of \displaystyle \small 8 away from the \displaystyle \small y-axis. Every other coordinate point has an absolute distance of \displaystyle \small \small 6 or less. 

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

The coordinate point \displaystyle \small (4,8)  is on the line represented by which of these linear expressions? 

Possible Answers:

\displaystyle \small y=-2x

\displaystyle \small y=2x+8

\displaystyle \small y=-2x+8

\displaystyle \small y=2x

Correct answer:

\displaystyle \small y=2x

Explanation:

To find the equation of the line that passes through coordinate point \displaystyle \small (4,8), plug the \displaystyle \small x and \displaystyle \small y values into each equation. The correct equation will end with a true statement. 

The solution is:
\displaystyle \small x=4,\displaystyle \small y=8

\displaystyle \small y=2x
\displaystyle \small 8=2(4)
\displaystyle \small 8=8

Example Question #3 : How To Find The Points On A Coordinate Plane

Which of the following points corresponds to \displaystyle (2, 2)?

1

Possible Answers:

\displaystyle D

\displaystyle C

\displaystyle A

\displaystyle B

Correct answer:

\displaystyle A

Explanation:

Recall that in a coordinate \displaystyle (x, y), the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point \displaystyle (2, 2), move \displaystyle 2 units to the right on the x-axis, then move \displaystyle 2 units up on the y-axis.

Example Question #161 : Geometry

Which of the following points corresponds to \displaystyle (-6, 2)?

2

Possible Answers:

\displaystyle B

\displaystyle D

\displaystyle A

\displaystyle C

Correct answer:

\displaystyle A

Explanation:

Recall that in a coordinate \displaystyle (x, y), the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point \displaystyle (-6, 2), move \displaystyle 6 units to the left on the x-axis, then move \displaystyle 2 units up on the y-axis.

Example Question #5 : How To Find The Points On A Coordinate Plane

Which of the following points corresponds to \displaystyle (-12, -5)?

3

Possible Answers:

\displaystyle A

\displaystyle D

\displaystyle B

\displaystyle C

Correct answer:

\displaystyle B

Explanation:

Recall that in a coordinate \displaystyle (x, y), the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point \displaystyle (-12, -5), move \displaystyle 12 units to the left on the x-axis, then move \displaystyle 5 units down on the y-axis.

Example Question #161 : Geometry

Which of the following points corresponds to \displaystyle (-6, -6)?

5

Possible Answers:

\displaystyle A

\displaystyle B

\displaystyle C

\displaystyle D

Correct answer:

\displaystyle D

Explanation:

Recall that in a coordinate \displaystyle (x, y), the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point \displaystyle (-6, -6), move \displaystyle 6 units to the left on the x-axis, then move \displaystyle 6 units down on the y-axis.

Example Question #161 : Geometry

Which of the following corresponds with the point \displaystyle (13, -7)?

6

Possible Answers:

\displaystyle C

\displaystyle B

\displaystyle D

\displaystyle A

Correct answer:

\displaystyle C

Explanation:

Recall that in a coordinate \displaystyle (x, y), the first number corresponds to how to move on the horizontal x-axis, and the second number corresponds to how to move on the veritcal y-axis.

Every time you see a positive number in the x-coordinate, you will move to the right. Every time you see a negative number in the x-coordinate, you will move to the left.

When you see a positive number in the y-coordinate, you will move up. When you see a negative number in the y-coordinate, you will move down.

To get to the point \displaystyle (13, -7), move \displaystyle 13 units to the right on the x-axis, then move \displaystyle 7 units down on the y-axis.

Learning Tools by Varsity Tutors