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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2091 : Isee Middle Level (Grades 7 8) Mathematics Achievement

The perimeter of the following trapezoid is equal to 23 cm. Solve for $\displaystyle x$. (Figure not drawn to scale.)

Possible Answers:

x=4 $\displaystyle x=4$

x=2 $\displaystyle x=2$

x=12 $\displaystyle x=12$

x=8 $\displaystyle x=8$

Correct answer:

x=4 $\displaystyle x=4$

Explanation:

The perimeter is equal to the sum of all of the sides.

$P=23\: cm$ $\displaystyle P=23\: cm$

$P=23\: cm=5+6+x+2x$ $\displaystyle P=23\: cm=5+6+x+2x$

$\displaystyle 23=11+3x$

$\displaystyle 23-11=11+3x-11$

12=3x $\displaystyle 12=3x$

$\frac{12}{3}=\frac{3x}{3}$ $\displaystyle \frac{12}{3}=\frac{3x}{3}$

x=4 $\displaystyle x=4$

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

Find the perimeter of the trapezoid:
Question_12

Possible Answers:

$\small 23.5$ $\displaystyle \small 23.5$

$\small 21$ $\displaystyle \small 21$

$\small 26$ $\displaystyle \small 26$

$\small 40$ $\displaystyle \small 40$

Correct answer:

$\small 21$ $\displaystyle \small 21$

Explanation:

The perimeter of any shape is equal to the sum of the lengths of its sides:

$\small P=4+6+3+8=21$ $\displaystyle \small P=4+6+3+8=21$

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Example Question #2091 : Isee Middle Level (Grades 7 8) Mathematics Achievement

You recently bought a new bookshelf with a base in the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the arms are 1.5 feet, what is the perimeter of the base of your new bookshelf?

Possible Answers:

8ft $\displaystyle 8ft$

3.75ft $\displaystyle 3.75ft$

12ft $\displaystyle 12ft$

Cannot be determined from the information provided.

Correct answer:

8ft $\displaystyle 8ft$

Explanation:

To find the perimeter of a bookshelf, we need to add up the lengths of the sides.

We know the two bases, we just need to add the lengths of the arms.

$\displaystyle 2ft+1.5ft+1.5ft+3ft=8ft$

So, our answer is 8ft

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Example Question #1 : How To Find The Perimeter Of A Parallelogram

Find the perimeter of the parallelogram.

Possible Answers:

26 in

36 in

18 in

13 in

Correct answer:

26 in

Explanation:

To find the perimeter of a parallelogram, add the lengths of the sides. Opposite sides of a parallelogram are equivalent.

$P=9+4+9+4=26\: in$ $\displaystyle P=9+4+9+4=26\: in$

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Example Question #2 : How To Find The Perimeter Of A Parallelogram

If the perimter of a parallelogram is $\displaystyle 30$ and one of the sides is $\displaystyle 5$, what is the other side length?

Possible Answers:

$\displaystyle 20$

The answer cannot be found

$\displaystyle 25$

$\displaystyle 10$

$\displaystyle 5$

Correct answer:

$\displaystyle 10$

Explanation:

The perimeter of a parallelogram is found by adding up all four sides.

Since there are two pairs of side with equal lengths, two sides must have a length of $\displaystyle 5$.

So the perimeter would be

$\displaystyle 5+5+l+l=30$ or 2l=20 $\displaystyle 2l=20$.

To find the value of the other side length, you would divide the remaining perimeter not include in the other sides by $\displaystyle 2$.

So $20\div2=10$ $\displaystyle 20\div2=10$.

That means the other side length would be $\displaystyle 10$.

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Example Question #3 : How To Find The Perimeter Of A Parallelogram

If a parallelogram has side lengths of $\displaystyle 7$ and $\displaystyle 3$, what is the perimeter?

Possible Answers:

$\displaystyle 8$

$\displaystyle 10$

$\displaystyle 21$

$\displaystyle 20$

Correct answer:

$\displaystyle 20$

Explanation:

The perimeter of a parallelogram is two times the two side lengths and add them together.

$\\P=s_1+s_2+s_3+s_4 \\s_1=s_3 \\s_2=s_4 \\P=s_a+s_a+s_b+s_b \\P=2s_a+2s_b$ $\displaystyle \\P=s_1+s_2+s_3+s_4 \\s_1=s_3 \\s_2=s_4 \\P=s_a+s_a+s_b+s_b \\P=2s_a+2s_b$

Therefore, this particular problem becomes as follows.

2*7=14 $\displaystyle 2*7=14$

and

2*3=6 $\displaystyle 2*3=6$

14+6=20 $\displaystyle 14+6=20$.

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Example Question #2092 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Parallelogram

Note: Figure NOT drawn to scale.

$a = 18\; \textrm{in} ,b=26\; \textrm{in},h=12\; \textrm{in}$ $\displaystyle a = 18\; \textrm{in} ,b=26\; \textrm{in},h=12\; \textrm{in}$, where $\displaystyle a$ and $\displaystyle b$ represent side lengths of the parallelogram and $\displaystyle h$ represents the height.

Find the perimeter of the parallelogram in the diagram.

Possible Answers:

$88 \;\textup{in}$ $\displaystyle 88 \;\textup{in}$

$46 \;\textup{in}$ $\displaystyle 46 \;\textup{in}$

$44 \;\textup{in}$ $\displaystyle 44 \;\textup{in}$

$76 \;\textup{in}$ $\displaystyle 76 \;\textup{in}$

$60 \;\textup{in}$ $\displaystyle 60 \;\textup{in}$

Correct answer:

$88 \;\textup{in}$ $\displaystyle 88 \;\textup{in}$

Explanation:

The perimeter of the parallelogram is the sum of the four side lengths - here, that formula becomes

$\displaystyle P = a + b + a + b = 18 + 26 + 18 + 26 = 88$.

Note that the height $\displaystyle h$ is irrelevant to the answer.

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Example Question #2091 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Find the area of the following parallelogram:

Note: The formula for the area of a parallelogram is $A=b\times h$ $\displaystyle A=b\times h$.

Possible Answers:

$60\: in^2$ $\displaystyle 60\: in^2$

$30\: in^2$ $\displaystyle 30\: in^2$

$32\: in^2$ $\displaystyle 32\: in^2$

$50\: in^2$ $\displaystyle 50\: in^2$

Correct answer:

$50\: in^2$ $\displaystyle 50\: in^2$

Explanation:

The base of the parallelogram is 10, while the height is 5.

$A=b\times h$ $\displaystyle A=b\times h$

$A=10\times5=50\: in^2$ $\displaystyle A=10\times5=50\: in^2$

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Example Question #1 : Parallelograms

Find the area:

Question_5

Possible Answers:

$\small 32$ $\displaystyle \small 32$

$\displaystyle 15$

$\small 24$ $\displaystyle \small 24$

$\small 12$ $\displaystyle \small 12$

$\small 16$ $\displaystyle \small 16$

Correct answer:

$\small 24$ $\displaystyle \small 24$

Explanation:

The area of a parallelogram can be determined using the following equation:

$\small A=bh$ $\displaystyle \small A=bh$

Therefore,

$\small A=8\times3=24$ $\displaystyle \small A=8\times3=24$

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Example Question #1 : Parallelograms

You can solve the area of a parallelogram when you know the lengths of each of the sides. True or False?

Possible Answers:

TRUE $\displaystyle TRUE$

FALSE $\displaystyle FALSE$

Correct answer:

FALSE $\displaystyle FALSE$

Explanation:

The area of a parallelogram is found by computing $\displaystyle base * height$. In this situation, you would have the base which is the bottom side but you would not have the height measurement. Since you would not be able to solve for the area with just the side lengths, the statement is FALSE $\displaystyle FALSE$.

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #2091 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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

Example Question #2091 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Example Question #2 : How To Find The Perimeter Of A Parallelogram

Example Question #3 : How To Find The Perimeter Of A Parallelogram

Example Question #2092 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #2091 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #1 : Parallelograms

Example Question #1 : Parallelograms

All ISEE Middle Level Math Resources

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