SSAT Upper Level Quantitative Flashcards: Scale And Rate Problems

What this deck covers

This deck focuses on Scale And Rate Problems, giving you a quick way to review the definitions, rules, and examples that matter most for SSAT Upper Level Quantitative.

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: How long does it take to travel $150\text{ km}$ at $75\text{ km/h}$?

Answer: $2\text{ h}$. Divide the distance by the speed to determine the time required.

Flashcard 2: What is the speed if a car travels $120\text{ miles}$ in $3\text{ hours}$?

Answer: $40\text{ mph}$. Divide the total distance by the total time to find the constant speed.

Flashcard 3: State the scale factor formula when map distance is $d_m$ and actual distance is $d_a$.

Answer: $k=\frac{d_a}{d_m}$. The scale factor is the ratio of actual distance to map distance.

Flashcard 4: What is the actual distance if the scale is $1:50\,000$ and the map shows $3\text{ cm}$?

Answer: $150\,000\text{ cm}$. Multiply the map distance by the scale ratio to convert to actual distance.

Flashcard 5: What is the volume scale factor if the linear scale factor is $k$?

Answer: $k^3$. Volumes of similar figures scale by the cube of the linear scale factor.

Flashcard 6: What is the map distance if the scale is $1:20$ and the actual length is $60\text{ m}$?

Answer: $3\text{ m}$. Divide the actual distance by the scale ratio to find the map distance.

Flashcard 7: What is the density if a substance has mass $30\text{ g}$ and volume $10\text{ cm}^3$?

Answer: $3\text{ g/cm}^3$. Divide the mass by the volume to compute the density.

Flashcard 8: Find the average speed for $60\text{ mi}$ at $30\text{ mph}$ then $60\text{ mi}$ at $60\text{ mph}$.

Answer: $40\text{ mph}$. Compute total distance over total time for varying speeds to find average speed.

Flashcard 9: State the unit rate formula for speed using distance $d$ and time $t$.

Answer: $v=\frac{d}{t}$. Speed is calculated as the distance traveled divided by the time taken.

Flashcard 10: What is the area scale factor if the linear scale factor is $k$?

Answer: $k^2$. Areas of similar figures scale by the square of the linear scale factor.

Flashcard 11: If a model uses linear scale $1:5$, what is the ratio of model volume to actual volume?

Answer: $1:125$. Cube the linear scale ratio to obtain the volume ratio of model to actual.

Flashcard 12: State the average speed formula for total distance $D$ and total time $T$.

Answer: $\text{avg speed}=\frac{D}{T}$. Average speed equals total distance divided by total time elapsed.

Flashcard 13: State the formula for density using mass $m$ and volume $V$.

Answer: $\rho=\frac{m}{V}$. Density is mass divided by the volume it occupies.

Flashcard 14: What is the combined rate if worker A does $\frac{1}{4}$ job/h and worker B does $\frac{1}{6}$ job/h?

Answer: $\frac{5}{12}\text{ job/h}$. Sum the individual work rates to obtain the combined rate.

Flashcard 15: What is the scale factor from figure A to figure B if a side changes from $8$ to $12$?

Answer: $\frac{3}{2}$. Divide the new side length by the original to find the scale factor.

Flashcard 16: If a model uses linear scale $1:10$, what is the ratio of model area to actual area?

Answer: $1:100$. Square the linear scale ratio to obtain the area ratio of model to actual.

Flashcard 17: State the proportion to convert map distance $d_m$ using scale $1:n$ to actual distance $d_a$.

Answer: $\frac{d_m}{d_a}=\frac{1}{n}$. The ratio of map distance to actual distance equals the reciprocal of the scale denominator.

Flashcard 18: If the linear scale factor from A to B is $\frac{2}{3}$, what is the area scale factor from A to B?

Answer: $\frac{4}{9}$. Square the linear scale factor to determine the area scale factor.

Flashcard 19: What is the unit price if $12$ items cost $18?

Answer: \1.50\text{ per item}$. Divide the total cost by the number of items to find the price per item.

Flashcard 20: Identify the scale $1:n$ if $2\text{ cm}$ on a map represents $10\text{ km}$.

Answer: $1:500\,000$. Convert actual distance to cm and divide by map distance to determine $n$.

Flashcard 21: How far do you travel in $0.5\text{ h}$ at $60\text{ mph}$?

Answer: $30\text{ miles}$. Multiply the speed by the time to calculate the distance traveled.

Flashcard 22: How long to finish a job if one person takes $6\text{ h}$ and another takes $3\text{ h}$ working together?

Answer: $2\text{ h}$. Add individual rates and take the reciprocal to find combined time for one job.

Flashcard 23: State the formula for price per unit if total cost is $C$ for $q$ units.

Answer: $\text{unit price}=\frac{C}{q}$. Unit price is the total cost divided by the quantity of units.

Flashcard 24: State the work rate formula if one job takes $t$ hours at constant rate.

Answer: $\text{rate}=\frac{1}{t}$. Work rate is the reciprocal of the time to complete one full job.