ISEE Lower Level Quantitative Reasoning Flashcards: Proportional Scaling

What this deck covers

This deck focuses on Proportional Scaling, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Lower Level Quantitative Reasoning.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the volume scale factor when the linear scale factor is $\frac{2}{3}$?

Answer: Volume factor $=\left(\frac{2}{3}\right)^3=\frac{8}{27}$. The volume scale factor is the cube of the linear scale factor for similar solids.

Flashcard 2: What is the time needed to travel $150$ miles if you travel $100$ miles in $2$ hours?

Answer: $3$ hours. Use constant speed to find time by dividing new distance by speed.

Flashcard 3: What is the new volume if the original volume is $27$ and the linear scale factor is $\frac{1}{3}$?

Answer: $1$. Volumes scale by the cube of the linear factor, reducing the original volume accordingly.

Flashcard 4: What is the new length if a $12$ cm segment is scaled by a factor of $\frac{3}{2}$?

Answer: $18$ cm. Multiply the original length by the given scale factor to determine the corresponding new length.

Flashcard 5: What is the area scale factor when the linear scale factor is $5$?

Answer: Area factor $=5^2=25$. The area scale factor is the square of the linear scale factor for similar figures.

Flashcard 6: What real distance corresponds to $3.5$ in on a map with scale $1$ in : $8$ mi?

Answer: $28$ miles. Multiply the map distance by the scale ratio to find the actual distance.

Flashcard 7: What map distance corresponds to $30$ mi on a map with scale $1$ in : $6$ mi?

Answer: $5$ in. Divide the actual distance by the scale ratio to find the map distance.

Flashcard 8: What is the missing value $x$ in the proportion $\frac{x}{9}=\frac{14}{21}$?

Answer: $6$. Cross-multiply in the proportion and solve for the missing variable.

Flashcard 9: What is the cost for $9$ pounds if $6$ pounds cost $15 and cost is proportional to weight?

Answer: $22.50. Use the proportional relationship by multiplying the unit cost by the new weight.

Flashcard 10: What is the scale factor from a model height of $9$ cm to an actual height of $1.8$ m?

Answer: Scale factor $=\frac{180}{9}=20$. Convert units and divide actual height by model height for the scale factor.

Flashcard 11: What is the new width if a $10$ by $6$ rectangle is scaled so the length becomes $25$?

Answer: New width $=15$. Determine the scale factor from lengths and apply it to the width for similarity.

Flashcard 12: What is the new area if a circle with area $36\pi$ is scaled by linear factor $\frac{1}{3}$?

Answer: $4\pi$. Circle areas scale by the square of the linear factor, reducing accordingly.

Flashcard 13: What is the linear scale factor if volume changes from $8$ to $64$ for similar solids?

Answer: Linear factor $=\sqrt[3]{\frac{64}{8}}=2$. The linear scale factor is the cube root of the ratio of new volume to original volume.

Flashcard 14: What is the original length if the new length is $24$ and the scale factor is $3$?

Answer: $8$. Divide the new length by the scale factor to find the corresponding original length.

Flashcard 15: What is the linear scale factor if area changes from $18$ to $72$ for similar figures?

Answer: Linear factor $=\sqrt{\frac{72}{18}}=2$. The linear scale factor is the square root of the ratio of new area to original area.

Flashcard 16: What is the scale factor from $9$ inches to $6$ inches?

Answer: Scale factor $=\frac{6}{9}=\frac{2}{3}$. The scale factor is the ratio of the new measurement to the original, simplified for a reduction.

Flashcard 17: What is the distance for $5$ hours if you travel $180$ miles in $3$ hours at constant speed?

Answer: $300$ miles. Determine constant speed and multiply by the new time to find the distance.

Flashcard 18: What is the new circumference if a circle with circumference $14\pi$ is scaled by factor $\frac{3}{2}$?

Answer: $21\pi$. Circumferences scale linearly, so multiply original by the scale factor.

Flashcard 19: What is the missing value $x$ in the proportion $\frac{4}{7}=\frac{x}{21}$?

Answer: $12$. Solve the proportion by cross-multiplying and dividing to find the missing value.

Flashcard 20: What is the scale factor from a $1$ in map distance to a $5$ mi real distance?

Answer: Scale $=1$ in : $5$ mi. The scale expresses the ratio of map distance to actual distance.

Flashcard 21: What is the new area if a figure with area $16$ is scaled by linear factor $\frac{1}{2}$?

Answer: $4$. Areas scale by the square of the linear factor, reducing the original area accordingly.

Flashcard 22: What is the new area if the original area is $50$ and the linear scale factor is $3$?

Answer: $450$. Multiply the original area by the square of the linear scale factor to find the new area.

Flashcard 23: What is the scale factor from an original length of $6$ to a new length of $15$?

Answer: Scale factor $=\frac{15}{6}=\frac{5}{2}$. The scale factor is calculated as the ratio of the new length to the original length, simplified to lowest terms.

Flashcard 24: What is the new perimeter if a figure with perimeter $30$ is scaled by factor $\frac{4}{3}$?

Answer: $40$. Perimeters scale linearly, so multiply the original perimeter by the linear scale factor.