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ISEE Lower Level Quantitative : Plane Geometry

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20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : How To Find Symmetry

Mr. Thomas' rectangular garden has a width of $\displaystyle 32$ feet. The length of his garden is exactly half the distance of the width of the garden. How long is the length of Mr. Thomas' garden?

Possible Answers:

$16 \text{ ft}$ $\displaystyle 16 \text{ ft}$

$8 \text{ in}$ $\displaystyle 8 \text{ in}$

$18 \text{ ft}$ $\displaystyle 18 \text{ ft}$

$8 \text{ ft}$ $\displaystyle 8 \text{ ft}$

Correct answer:

$16 \text{ ft}$ $\displaystyle 16 \text{ ft}$

Explanation:

The length of Mr. Thomas' garden is exactly half the distance of the width of the garden.

The width of the garden is $\displaystyle 32$ feet.

Thus, the length is equal to,

$\frac{32}{2}=16$ $\displaystyle \frac{32}{2}=16$

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Example Question #532 : Plane Geometry

Celeste is Debra's $\displaystyle 7$ year old daughter. Both Debra and Celeste measured their height on the wall. Celeste was surprised to find out that she is exactly half the height of her mother. If Debra is $5 \tfrac{1}{2}$ $\displaystyle 5 \tfrac{1}{2}$ feet tall, how tall is Celeste?

Possible Answers:

${}2\tfrac{1}{4} \text{ ft}$ $\displaystyle {}2\tfrac{1}{4} \text{ ft}$

$2\tfrac{2}{4} \text{ ft}$ $\displaystyle 2\tfrac{2}{4} \text{ ft}$

$2\tfrac{3}{4} \text{ ft}$ $\displaystyle 2\tfrac{3}{4} \text{ ft}$

${}\frac{11}{2} \text{ ft}$ $\displaystyle {}\frac{11}{2} \text{ ft}$

Correct answer:

$2\tfrac{3}{4} \text{ ft}$ $\displaystyle 2\tfrac{3}{4} \text{ ft}$

Explanation:

Debra is $5\tfrac{1}{2}$ $\displaystyle 5\tfrac{1}{2}$ feet tall. Celeste is half the height of her mother Debra.

Thus, to find Celeste's height, divide $5\tfrac{1}{2}$ $\displaystyle 5\tfrac{1}{2}$ in half.

The solution is:

Step one: convert $5\tfrac{1}{2}$ $\displaystyle 5\tfrac{1}{2}$ into an improper fraction.

$5\tfrac{1}{2}=\frac{11}{2}$ $\displaystyle 5\tfrac{1}{2}=\frac{11}{2}$

Step two: divide $\frac{11}{2}$ $\displaystyle \frac{11}{2}$ by $\displaystyle 2$.

$\frac{\frac{11}{2}}{2}=\frac{11}{2}\cdot\frac{1}{2}=\frac{11}{4}$ $\displaystyle \frac{\frac{11}{2}}{2}=\frac{11}{2}\cdot\frac{1}{2}=\frac{11}{4}$

Step three: express $\frac{11}{4}$ $\displaystyle \frac{11}{4}$ in feet as a mixed number.

$11\div4=2\tfrac{3}{4}$ $\displaystyle 11\div4=2\tfrac{3}{4}$

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Example Question #533 : Plane Geometry

Mr. Lam is planning on painting a rectangular wall in his living room. Before he starts painting, he decided to take a few measurements of the wall. He finds out that the width of the wall is twice the measurement of the height of the wall. If the width of the wall is $\displaystyle 25$ feet, what is the height of the wall?

Possible Answers:

$10\tfrac{1}{2} \text{ ft}$ $\displaystyle 10\tfrac{1}{2} \text{ ft}$

$12\tfrac{3}{4} \text{ ft}$ $\displaystyle 12\tfrac{3}{4} \text{ ft}$

$12\tfrac{1}{2} \text{ ft}$ $\displaystyle 12\tfrac{1}{2} \text{ ft}$

$11\tfrac{3}{4} \text{ ft}$ $\displaystyle 11\tfrac{3}{4} \text{ ft}$

Correct answer:

$12\tfrac{1}{2} \text{ ft}$ $\displaystyle 12\tfrac{1}{2} \text{ ft}$

Explanation:

Since the height of the rectangular wall is half the length of the width, divide $\displaystyle 25$ by $\displaystyle 2.$

The solution is:

$25 \div2=12\tfrac{1}{2}$ $\displaystyle 25 \div2=12\tfrac{1}{2}$

Check:

$12\times2=24$ $\displaystyle 12\times2=24$
$2\times \frac{1}{2}=1$ $\displaystyle 2\times \frac{1}{2}=1$
$\displaystyle 24 + 1= 25$

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Example Question #11 : How To Find Symmetry

The cable on Ryan's new cellphone charger is twice as long as his old cellphone charger cable. If Ryan's new cellphone charger has a $\displaystyle 3$ feet long cable, how long was his old charger cable?

Possible Answers:

${}\small 1\tfrac{1}{2}$ $\displaystyle {}\small 1\tfrac{1}{2}$

$\displaystyle 2$

$1\tfrac{3}{4}$ $\displaystyle 1\tfrac{3}{4}$

$1\tfrac{1}{4}$ $\displaystyle 1\tfrac{1}{4}$

Correct answer:

${}\small 1\tfrac{1}{2}$ $\displaystyle {}\small 1\tfrac{1}{2}$

Explanation:

To find the length of Ryan's old cellphone cable, divide the length of his new cellphone charger in half.

The solution is:

$\small 3\div2=1\tfrac{1}{2}$ $\displaystyle \small 3\div2=1\tfrac{1}{2}$

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Example Question #763 : Geometry

Line segment $\small \bar{AE}$ $\displaystyle \small \bar{AE}$ is twice as long as line segment $\small \bar{AC}$ $\displaystyle \small \bar{AC}$. If line segment $\small \bar{AE}$ $\displaystyle \small \bar{AE}$ is $\displaystyle 56$ inches, how many inches is $\small \bar{AC}$ $\displaystyle \small \bar{AC}$?

Possible Answers:

$\small 28 \text{ in}$ $\displaystyle \small 28 \text{ in}$

$\small 36 \text{ in}$ $\displaystyle \small 36 \text{ in}$

$\small 34 \text{ in}$ $\displaystyle \small 34 \text{ in}$

$\small 26 \text{ in}$ $\displaystyle \small 26 \text{ in}$

Correct answer:

$\small 28 \text{ in}$ $\displaystyle \small 28 \text{ in}$

Explanation:

The length of line segment $\small \bar{AC}$ $\displaystyle \small \bar{AC}$ is half the length of line segment $\small \bar{AE}$ $\displaystyle \small \bar{AE}$.

Therefore, divide $\small 56$ $\displaystyle \small 56$ by $\small 2$ $\displaystyle \small 2$.

$\small 56 \div2=28$ $\displaystyle \small 56 \div2=28$

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Example Question #12 : How To Find Symmetry

Line segment $\small \bar{JK}$ $\displaystyle \small \bar{JK}$ is twice as long as line segment $\small \bar{LP}$ $\displaystyle \small \bar{LP}$. If line segment $\small \bar{JK}$ $\displaystyle \small \bar{JK}$ is $\small 148$ $\displaystyle \small 148$ centimeters, how many centimeters is line segment $\small \bar{LP}$ $\displaystyle \small \bar{LP}$?

Possible Answers:

$\small 72 \text{ in}$ $\displaystyle \small 72 \text{ in}$

$\small 72 \text{ cm}$ $\displaystyle \small 72 \text{ cm}$

$\small 74 \text{ cm}$ $\displaystyle \small 74 \text{ cm}$

$\small 86 \text{ cm}$ $\displaystyle \small 86 \text{ cm}$

Correct answer:

$\small 74 \text{ cm}$ $\displaystyle \small 74 \text{ cm}$

Explanation:

To find the length of line segment $\small \bar{LP}$ $\displaystyle \small \bar{LP}$, divide the length of line segment $\small \bar{JK}$ $\displaystyle \small \bar{JK}$.
Therefore, the length of line segment $\small \bar{LP}$ $\displaystyle \small \bar{LP}$ is:

$\small 148 \div 2=74$ $\displaystyle \small 148 \div 2=74$

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Example Question #762 : Geometry

Find the midpoint between coordinate points $\small (-2,4)$ $\displaystyle \small (-2,4)$ and $\small \small (4,4)$ $\displaystyle \small \small (4,4)$.

Possible Answers:

$\small (1,4)$ $\displaystyle \small (1,4)$

$\small (1,0)$ $\displaystyle \small (1,0)$

$\small (0,4)$ $\displaystyle \small (0,4)$

$\small (0,0)$ $\displaystyle \small (0,0)$

Correct answer:

$\small (1,4)$ $\displaystyle \small (1,4)$

Explanation:

To find the midpoint between these two coordinate points, use the formula,

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right )$ $\displaystyle \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right )$

Since our $\displaystyle (x_1,y_1)=(-2,4)$ and our $\displaystyle (x_2,y_2)=(4,4)$ the midpoint formula becomes,

$\left(\frac{-2+4}{2},\frac{4+4}{2}\right )=\left(\frac{2}{2}, \frac{8}{2} \right )=(1,4)$ $\displaystyle \left(\frac{-2+4}{2},\frac{4+4}{2}\right )=\left(\frac{2}{2}, \frac{8}{2} \right )=(1,4)$.

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Example Question #12 : How To Find Symmetry

In a football contest, Jeff threw the football twice as far as Robby. If Jeff threw the ball $\small 38$ $\displaystyle \small 38$ yards, how many yards did Robby throw the ball?

Possible Answers:

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

$\small 18 \text{ yds}$ $\displaystyle \small 18 \text{ yds}$

$\small 24 \text{ yds}$ $\displaystyle \small 24 \text{ yds}$

$\small 19 \text{ yds}$ $\displaystyle \small 19 \text{ yds}$

Correct answer:

$\small 19 \text{ yds}$ $\displaystyle \small 19 \text{ yds}$

Explanation:

Since Jeff threw the football twice as far as Robby, divide $\small 38$ $\displaystyle \small 38$ by $\small 2$ $\displaystyle \small 2$.

$\small 38\div2=19$ $\displaystyle \small 38\div2=19$

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Example Question #535 : Plane Geometry

Line segment $\small \bar{xy}$ $\displaystyle \small \bar{xy}$ goes exactly halfway across a sheet of paper. If the sheet of paper has a width of $\small 12\tfrac{1}{2}$ $\displaystyle \small 12\tfrac{1}{2}$ inches, how long is line segment $\small \bar{xy}$ $\displaystyle \small \bar{xy}$?

Possible Answers:

$\small 6\tfrac{3}{4} \text{ in}$ $\displaystyle \small 6\tfrac{3}{4} \text{ in}$

$\small 6\tfrac{1}{2} \text{ in}$ $\displaystyle \small 6\tfrac{1}{2} \text{ in}$

$\small 6\tfrac{1}{4} \text{ in}$ $\displaystyle \small 6\tfrac{1}{4} \text{ in}$

$\small 6 \text{ in}$ $\displaystyle \small 6 \text{ in}$

Correct answer:

$\small 6\tfrac{1}{4} \text{ in}$ $\displaystyle \small 6\tfrac{1}{4} \text{ in}$

Explanation:

Since the length of line segment $\small \bar{xy}$ $\displaystyle \small \bar{xy}$ is half of $\small 12\tfrac{1}{2}$ $\displaystyle \small 12\tfrac{1}{2}$, convert $\small 12\tfrac{1}{2}$ $\displaystyle \small 12\tfrac{1}{2}$ to a mixed number.

$\small 12\tfrac{1}{2}= \frac{12 \cdot 2 +1}{2}= \frac{25}{2}$ $\displaystyle \small 12\tfrac{1}{2}= \frac{12 \cdot 2 +1}{2}= \frac{25}{2}$

Then divide $\small \frac{25}{2}$ $\displaystyle \small \frac{25}{2}$ by $\displaystyle 2$.

$\small \frac{25}{2}\div2=\frac{25}{2}\times \frac{1}{2}=\frac{25}{4}$ $\displaystyle \small \frac{25}{2}\div2=\frac{25}{2}\times \frac{1}{2}=\frac{25}{4}$

Then convert $\small \frac{25}{4}$ $\displaystyle \small \frac{25}{4}$ to a mixed number.

$\small \frac{25}{4}=6\tfrac{1}{4}$ $\displaystyle \small \frac{25}{4}=6\tfrac{1}{4}$

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Example Question #1522 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

The Johnson family had an extension put onto their driveway that doubled the width of the driveway. If their driveway was originally $\small 13$ $\displaystyle \small 13$ feet wide, how wide is their new driveway?

Possible Answers:

$\small 29 \text{ ft}$ $\displaystyle \small 29 \text{ ft}$

$\small 26 \text{ ft}$ $\displaystyle \small 26 \text{ ft}$

$\small 24\text{ ft}$ $\displaystyle \small 24\text{ ft}$

$\small 32 \text{ ft}$ $\displaystyle \small 32 \text{ ft}$

Correct answer:

$\small 26 \text{ ft}$ $\displaystyle \small 26 \text{ ft}$

Explanation:

Since the original driveway was half the width of the new driveway, multiply $\small 13$ $\displaystyle \small 13$ by $\small 2$ $\displaystyle \small 2$.

$\small 13\times2=26$ $\displaystyle \small 13\times2=26$

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : Plane Geometry

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #3 : How To Find Symmetry

Example Question #532 : Plane Geometry

Example Question #533 : Plane Geometry

Example Question #11 : How To Find Symmetry

Example Question #763 : Geometry

Example Question #12 : How To Find Symmetry

Example Question #762 : Geometry

Example Question #12 : How To Find Symmetry

Example Question #535 : Plane Geometry

Example Question #1522 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

All ISEE Lower Level Quantitative Resources

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