ISEE Lower Level Math : ISEE Lower Level (grades 5-6) Mathematics Achievement

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

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Example Questions

Example Question #11 : How To Find The Perimeter Of A Rectangle

If the width of a rectangle is 2 inches and the length is 6 inches, what is the perimeter in inches?

Possible Answers:

\(\displaystyle 15\ \text{in}\)

\(\displaystyle 24\ \text{in}\)

\(\displaystyle 16\ \text{in}\)

\(\displaystyle 12\ \text{in}\)

\(\displaystyle 20\ \text{in}\)

Correct answer:

\(\displaystyle 16\ \text{in}\)

Explanation:

The perimeter of a rectangle can be found by adding together all the sides. The formula is:

\(\displaystyle P=l+l+w+w=2l+2w\)

Use the given values for the length and the width to solve.

\(\displaystyle 2\text{in}+2\text{in}+6\text{in}+6\text{in}=16\text{in}\)

16 inches is the correct answer. 

Example Question #82 : Quadrilaterals

A rectangle has a width of 5 inches and an area of 35 inches. What is the length, in inches?

Possible Answers:

\(\displaystyle 8\ \text{in}\)

\(\displaystyle 9\ \text{in}\)

\(\displaystyle 5\ \text{in}\)

\(\displaystyle 7\ \text{in}\)

\(\displaystyle 6\ \text{in}\)

Correct answer:

\(\displaystyle 7\ \text{in}\)

Explanation:

The area of a rectangle is equal to the length times the width. 

\(\displaystyle A=l\times w\)

Here, we know that the area is 35, and the width is 5. We can fill in part of the equation with these values.

\(\displaystyle 35=l\times5\)

The only number that equals 35 when multiplied by 5 is 7.

\(\displaystyle 35\div5=7\)

\(\displaystyle 35=7\times5\)

7 is the correct answer. 

Example Question #83 : Quadrilaterals

If the width of a rectangle is 3 inches and the length is 5 inches, what is the perimeter?

Possible Answers:

\(\displaystyle 12\ \textup{inches}\)

\(\displaystyle 16\ \textup{inches}\)

\(\displaystyle 10\ \textup{inches}\)

\(\displaystyle 14\ \textup{inches}\)

Correct answer:

\(\displaystyle 16\ \textup{inches}\)

Explanation:

The perimeter of a rectangle can be found by adding together all the sides. This would give us:

\(\displaystyle 3+3+5+5=16\)

Therefore, 16 inches is the correct answer. 

Example Question #91 : Quadrilaterals

Marcell wants to put a new fence around the perimeter of his garden. Marcell's rectangular garden is 30 feet long and 15 feet wide. How many feet of fence does Marcell need?

Possible Answers:

\dpi{100} 90\ feet\(\displaystyle \dpi{100} 90\ feet\)

\dpi{100} 60\ feet\(\displaystyle \dpi{100} 60\ feet\)

\dpi{100} 50\ feet\(\displaystyle \dpi{100} 50\ feet\)

\dpi{100} 45\ feet\(\displaystyle \dpi{100} 45\ feet\)

Correct answer:

\dpi{100} 90\ feet\(\displaystyle \dpi{100} 90\ feet\)

Explanation:

\dpi{100} (30+30)+(15+15)\(\displaystyle \dpi{100} (30+30)+(15+15)\)

Example Question #76 : Rectangles

The length of a rectangle is \(\displaystyle 2y\), and the width of the rectangle is \(\displaystyle x+4\). What is the perimeter if \(\displaystyle y=7\) and \(\displaystyle x=6\)?

Possible Answers:

\(\displaystyle 48\)

\(\displaystyle 42\)

\(\displaystyle 36\)

\(\displaystyle 24\)

Correct answer:

\(\displaystyle 48\)

Explanation:

If the length of a rectangle is \(\displaystyle 2y\) and the width is \(\displaystyle x+4\), the perimeter is:

\(\displaystyle 2y+2y+x+4+x+4\)

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

Now plug in \(\displaystyle y=7\) and \(\displaystyle x=6\):

\(\displaystyle =4\cdot7+2\cdot6+8\)

\(\displaystyle =28+12+8\)

\(\displaystyle =48\)

Example Question #77 : Rectangles

If the perimeter of a rectangle is \(\displaystyle 120\) inches and its length is twice the value of its width, what is the value of the width of the rectangle in inches?

Possible Answers:

\(\displaystyle 40\) inches

\(\displaystyle 20\) inches

\(\displaystyle 60\) inches

\(\displaystyle 15\) inches

Correct answer:

\(\displaystyle 20\) inches

Explanation:

If the length of the rectangle is twice the value of its width, then if the width is equal to w, then the length is equal to 2w. 

Given that the perimeter of a rectangle is equal to the value of all the sides added together, the following equation would apply:

\(\displaystyle w+w+2w+2w=120\)

\(\displaystyle 6w=120\)

\(\displaystyle w=20\)

This means that the rectangle is \(\displaystyle 20\) inches wide.

Example Question #81 : Rectangles

The area of a rectangle is \(\displaystyle 600\). One of its sides is \(\displaystyle 15\). What is its perimeter?

Possible Answers:

\(\displaystyle 40\)

\(\displaystyle 55\)

\(\displaystyle 110\)

\(\displaystyle 78\)

\(\displaystyle 100\)

Correct answer:

\(\displaystyle 110\)

Explanation:

Remember that the area of a rectangle is equal to its base times its height. If its area is \(\displaystyle 600\) and one side has a length of \(\displaystyle 15\), we can find the other side by dividing these:

\(\displaystyle Other Side = \frac{600}{15}=40\)

So, our rectangle looks like this:

Untitled_7

The perimeter is easily calculated:

\(\displaystyle P = 40+40+15+15=110\)

Example Question #92 : Quadrilaterals

What is the perimeter of the following rectangle?

Untitled_8

 

Possible Answers:

\(\displaystyle 4563.2\)

\(\displaystyle 9126.4\)

199.3

631.1

\(\displaystyle 398.6\)

Correct answer:

\(\displaystyle 398.6\)

Explanation:

The perimeter of a rectangle is very easy to solve.  Merely add up all the sides:

\(\displaystyle P = 128+128+71.3+71.3=398.6\)

Example Question #83 : Rectangles

One of a rectangle's sides has a length of \(\displaystyle 40\). Another of its sides is half that length. What is its perimeter?

Possible Answers:

\(\displaystyle 100\)

\(\displaystyle 60\)

\(\displaystyle 120\)

\(\displaystyle 40\)

\(\displaystyle 80\)

Correct answer:

\(\displaystyle 120\)

Explanation:

If one side of the rectangle is \(\displaystyle 40\) and the other half of that, then the other side must be:

\(\displaystyle \frac{40}{2}=20\)

Our rectangle therefore looks like this:

Untitled_9

The perimeter is calculated very easily.  Just sum up all the sides!

\(\displaystyle P = 40+40+20+20=120\)

Example Question #81 : Rectangles

Lowerrectperim2

What is the perimeter of the above rectangle? 

Possible Answers:

\(\displaystyle 30\) ft

\(\displaystyle 16\) ft

\(\displaystyle 15\) ft

\(\displaystyle 26\) ft

\(\displaystyle 8\) ft

Correct answer:

\(\displaystyle 16\) ft

Explanation:

The perimeter of a rectangle is the length of all the sides added together. This rectangle has two short sides that are each \(\displaystyle 3\) feet long and two long sides that are each \(\displaystyle 5\) feet long. \(\displaystyle 3+3+5+5=16\), so the correct answer is \(\displaystyle 16\).

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