ISEE Upper Level Math : ISEE Upper Level (grades 9-12) Mathematics Achievement

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

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Isee Upper Level (Grades 9 12) Mathematics Achievement

What is the sidelength, in feet and inches, of a regular hexagon with perimeter 16 feet?

Possible Answers:

\(\displaystyle 3 \textrm{ ft }2 \frac{2}{5} \textrm{ in}\)

\(\displaystyle 2 \textrm{ ft }\)

\(\displaystyle 1 \textrm{ ft }7 \frac{1}{5} \textrm{ in}\)

\(\displaystyle 1 \textrm{ ft }4 \textrm{ in}\)

\(\displaystyle 2 \textrm{ ft }8 \textrm{ in}\)

Correct answer:

\(\displaystyle 2 \textrm{ ft }8 \textrm{ in}\)

Explanation:

Divide the perimeter 16 feet by 6 to get the sidelength of the hexagon in feet:

\(\displaystyle 16 \div 6 = 2\frac{2}{3} \textrm{ ft }\)

Two-thirds of a foot is equal to eight inches, so this sidelength is 2 feet 8 inches.

Example Question #2 : Isee Upper Level (Grades 9 12) Mathematics Achievement

The perimeter of a regular hexagon is one mile. Give the sidelength in feet.

Possible Answers:

\(\displaystyle 990 \textrm{ ft}\)

\(\displaystyle 330 \textrm{ ft}\)

\(\displaystyle 660 \textrm{ ft}\)

\(\displaystyle 1,320 \textrm{ ft}\)

\(\displaystyle 880 \textrm{ ft}\)

Correct answer:

\(\displaystyle 880 \textrm{ ft}\)

Explanation:

One mile is equal to 5,280 feet, so divide this by 6:

\(\displaystyle 5,280 \div 6 = 880\) feet

Example Question #2 : Hexagons

A hexagon has a perimeter of 114in. Find the length of one side.

Possible Answers:

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

\(\displaystyle 22\text{in}\)

\(\displaystyle 17\text{in}\)

\(\displaystyle 19\text{in}\)

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

Correct answer:

\(\displaystyle 19\text{in}\)

Explanation:

A hexagon has 6 equal sides.  The formula to find perimeter of a hexagon is:

\(\displaystyle P = 6a\)

where a is the length of any side.  Now, to find the length of one side, we will solve for a

 

We know the perimeter of the hexagon is 114in.  So, we will substitute and solve for a.  We get

\(\displaystyle 114\text{in} = 6a\)

 

\(\displaystyle \frac{114\text{in}}{6} = \frac{6a}{6}\)

 

\(\displaystyle 19\text{in} = a\)

 

\(\displaystyle a = 19\text{in}\)

Therefore, the length of one side of the hexagon is 19in.

Example Question #2 : Geometry

The perimeter of a hexagon is 96cm. Find the length of one side.

Possible Answers:

\(\displaystyle 14\text{cm}\)

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

\(\displaystyle 19\text{cm}\)

\(\displaystyle 18\text{cm}\)

\(\displaystyle 13\text{cm}\)

Correct answer:

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

Explanation:

A hexagon has 6 equal sides. To find the length of one side of a hexagon, we will use the formula to find the perimeter.  

\(\displaystyle P = 6a\)

where a is the length of one side. So, we will solve for a.

Now, we know the perimeter of the hexagon is 96cm. So, we get

\(\displaystyle 96\text{cm} = 6a\) 

\(\displaystyle \frac{96\text{cm}}{6} = \frac{6a}{6}\)

\(\displaystyle 16\text{cm} = a\)

\(\displaystyle a = 16\text{cm}\)

Therefore, the length of one side of the hexagon is 16cm.

Example Question #1 : Plane Geometry

If the sum of \(\displaystyle 5\) angles in a hexagon is equal to \(\displaystyle 650^\circ\), what is the value of the remaining sixth angle?

Possible Answers:

\(\displaystyle 80^\circ\)

\(\displaystyle 100^\circ\)

\(\displaystyle 60^\circ\)

\(\displaystyle 70^\circ\)

Correct answer:

\(\displaystyle 70^\circ\)

Explanation:

The sum of the angles in a polygon can be found using the equation below, in which t is equal to the total sum of the angles, and n is equal to the number of sides. 

\(\displaystyle t=(n-2)(180)\)

Given that a hexagon has 6 angles, the total number of angles will be:

\(\displaystyle t=(6-2)(180)\)

\(\displaystyle t=4\cdot 180\)

\(\displaystyle t=720\)

Given that 5 of the angles have a sum of 650 degrees, we would subtract 650 from 720, resulting in 70 degrees. 

Example Question #1 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Find the perimeter of a hexagon with one side having a length of 15cm.

Possible Answers:

\(\displaystyle 105\text{cm}\)

\(\displaystyle 90\text{cm}\)

\(\displaystyle 135\text{cm}\)

\(\displaystyle 75\text{cm}\)

\(\displaystyle 120\text{cm}\)

Correct answer:

\(\displaystyle 90\text{cm}\)

Explanation:

To find the perimeter of a hexagon, we will use the following formula:

\(\displaystyle P = 6 \cdot a\)

where a is the length of one side of the hexagon.

 

Now, we know the length of one side of the hexagon is 15cm.

Knowing this, we can substitute into the formula.  We get

\(\displaystyle P = 6 \cdot 15\text{cm}\)

\(\displaystyle P = 90\text{cm}\)

Example Question #3 : Plane Geometry

Find the perimeter of a hexagon with a side having a length of 13cm.

Possible Answers:

\(\displaystyle 78\text{cm}\)

\(\displaystyle 91\text{cm}\)

\(\displaystyle 76\text{cm}\)

\(\displaystyle 104\text{cm}\)

\(\displaystyle 65\text{cm}\)

Correct answer:

\(\displaystyle 78\text{cm}\)

Explanation:

A hexagon has 6 sides.  So, to find the perimeter, we will use the following formula:

\(\displaystyle P = 6a\)

where a is the length of one side.

 

Now, we know a side has a length of 13cm.  Knowing this, we can substitute into the formula. 

\(\displaystyle P = 6 \cdot 13\text{cm}\)

\(\displaystyle P = 78\text{cm}\)

Example Question #1 : Isee Upper Level (Grades 9 12) Mathematics Achievement

A hexagon has a side of length 13cm.  Find the perimeter.

Possible Answers:

\(\displaystyle 91\text{cm}\)

\(\displaystyle 65\text{cm}\)

\(\displaystyle 78\text{cm}\)

\(\displaystyle 52\text{cm}\)

\(\displaystyle 104\text{cm}\)

Correct answer:

\(\displaystyle 78\text{cm}\)

Explanation:

To find the perimeter of a hexagon, we will use the following formula:

\(\displaystyle P = 6a\)

where a is the length of one side of the hexagon.  We multiply it by 6 because a hexagon has 6 equal sides.

So, we know the length of one side is 13cm.  Knowing this, we can substitute into the formula.  We get

\(\displaystyle P = 6 \cdot 13\text{in}\)

\(\displaystyle P = 78\text{in}\)

Example Question #2 : Plane Geometry

Find the perimeter of a hexagon with a side having a length of 12in.

Possible Answers:

\(\displaystyle 60\text{in}\)

\(\displaystyle 84\text{in}\)

\(\displaystyle 108\text{in}\)

\(\displaystyle 96\text{in}\)

\(\displaystyle 72\text{in}\)

Correct answer:

\(\displaystyle 72\text{in}\)

Explanation:

To find the perimeter of a hexagon, we will use the following formula:

\(\displaystyle P = 6 \cdot a\)

where a is the length of one side of the hexagon.  Because a hexagon has 6 equal sides, we can use any side in the formula.

So, we know the length of one side is 12in.  So, we can substitute.  We get

\(\displaystyle P = 6 \cdot 12\text{in}\)

\(\displaystyle P = 72\text{in}\)

Example Question #1 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Find the perimeter of a hexagon if it contains a side having a length of 17cm.

Possible Answers:

\(\displaystyle 119\text{cm}\)

\(\displaystyle 102\text{cm}\)

\(\displaystyle 153\text{cm}\)

\(\displaystyle 85\text{cm}\)

\(\displaystyle 136\text{cm}\)

Correct answer:

\(\displaystyle 102\text{cm}\)

Explanation:

To find the perimeter of a hexagon, we will use the following formula:

\(\displaystyle P = 6 \cdot a\)

where a is the length of one side of the hexagon.

 

Now, we know the length of one side of the hexagon is 17cm.

Knowing this, we can substitute into the formula.  We get

\(\displaystyle P = 6 \cdot 17\text{cm}\)

\(\displaystyle P = 102\text{cm}\)

Learning Tools by Varsity Tutors