ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning
Study concepts, example questions & explanations for ISEE Middle Level Quantitative
All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #162 : How To Find The Area Of A Parallelogram
David wants to put a fence around his backyard. How much fencing will he need if his backyard is 
The fence is going around the backyard, so this is a perimeter problem.
Example Question #209 : Quadrilaterals
David wants to put a fence around his backyard. How much fencing will he need if his backyard is 
The fence is going around the backyard, so this is a perimeter problem.
Example Question #132 : How To Find The Perimeter Of A Rectangle
David wants to put a fence around his backyard. How much fencing will he need if his backyard is 
The fence is going around the backyard, so this is a perimeter problem.
Example Question #511 : Rectangles
David wants to put a fence around his backyard. How much fencing will he need if his backyard is 
The fence is going around the backyard, so this is a perimeter problem.
Example Question #1211 : Isee Lower Level (Grades 5 6) Quantitative Reasoning
What is the length of a rectangular room with a perimeter of 
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract 
Divide 
Example Question #1 : How To Find The Area Of A Rectangle
If the length of a rectangle is twice the width, and the width is three inches, what is the area of the rectangle?
In order to find the area of a rectangle we use the formula 
In this problem, we know the width is 
Now that we know that our length is 
The area of the rectangle is 
Example Question #1 : How To Find The Area Of A Rectangle
Using the information given in each question, compare the quantity in Column A to the quantity in Column B.
A certain rectangle is seven times as long as it is wide.
Column A Column B
the rectangle's the rectangle's
perimeter area
(in units) (in square units)
The two quantities are equal.
The quantity in Column B is greater.
The relationship cannot be determined from the information given.
The quantity in Column A is greater.
The relationship cannot be determined from the information given.
This type of problem reminds us to be wary of simply plugging in numbers (which works with certain problems). If you were to choose 1 and 7 here, the perimeter would be larger; if you chose 10 and 70, the area would be much larger.
To solve this problem with variables:
From here we can see that smaller values of 
The answer cannot be determined.
Example Question #2 : How To Find The Area Of A Rectangle
Which is the greater quantity?
(a) The surface area of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The surface area of a cube with sidelength 300 millimeters
(a) is greater
(b) is greater
It is impossible to tell from the information given
(a) and (b) are equal
(a) is greater
(a) The surface of a rectangular prism comprises six rectangles, so we can take the sum of their areas.
Two rectangles have area: 
Two rectangles have area: 
Two rectangles have area: 
Add the areas:
(b) The surface of a cube comprises six squares, so we can square the sidelength - which we rewrite as 30 centimeters - and multiply the result by 6:
The first figure has the greater surface area.
Example Question #1 : Rectangles
Column A Column B
The area of a The area of a square
rectangle with sides with sides 7cm.
11 cm and 5 cm.
The quantity in Column A is greater.
There is no way to determine the relationship between the columns.
The quantity in Column B is greater.
The quantities in both columns are equal.
The quantity in Column A is greater.
First, you must calculate Column A. The formula for the area of a rectangle is 
Example Question #118 : Geometry
Figure NOT drawn to scale
Refer to the above figure. The area of Rectangle 
The area of a rectangle is the product of its length and its width.
Since the area of Rectangle 
Substitute 40 for 
All ISEE Middle Level Quantitative Resources
