# Digital SAT Math Practice Questions – Advanced : Units

## SAT MAth Practice questions – all topics

• Problem-solving and Data Analysis Weightage: 15%  Questions: 5-7
• Ratios, rates, proportional relationships, and units
• Percentages
• One-variable data: distributions and measures of centre and spread
• Two-variable data: models and scatterplots
• Probability and conditional probability
• Inference from sample statistics and margin of error
• Evaluating statistical claims: observational studies and Experiments

## SAT MAth and English  – full syllabus practice tests

[Calc]  Question  Hard

There are 640 acres in 1 square mile. The area of a forest is increasing at a rate of 1 acre per decade. Which of the following is closest to the rate at which the area of the forest is increasing, in square kilometers per decade? (Use 1 kilometer $$=0.62$$ mile.)
A) 0.0006
B) 0.0010
C) 0.0025
D) 0.0041

D

To find the rate at which the area of the forest is increasing in square kilometers per decade, we first need to convert the rate from acres to square kilometers.

1. Convert acres to square miles:

There are 640 acres in 1 square mile. Therefore:
$1 \text{ acre} = \frac{1}{640} \text{ square miles}$

The forest is increasing at a rate of 1 acre per decade. Thus, the rate in square miles per decade is:
$\frac{1}{640} \text{ square miles per decade}$

2. Convert square miles to square kilometers:

We know that $$1 \text{ mile} = 1.60934 \text{ kilometers}$$, so:
$1 \text{ square mile} = (1.60934)^2 \text{ square kilometers} = 2.58999 \text{ square kilometers}$

Using the approximation given in the problem, $$1 \text{ mile} \approx 0.62 \text{ kilometers}$$, thus:
$1 \text{ square mile} \approx (0.62)^2 \text{ square kilometers} \approx 0.3844 \text{ square kilometers}$

3. Calculate the rate in square kilometers per decade:

Now, convert the rate from square miles per decade to square kilometers per decade:
$\frac{1}{640} \text{ square miles per decade} \times 2.58999 \text{ square kilometers per square mile} \approx \frac{2.58999}{640} \text{ square kilometers per decade}$

Calculate the above expression:
$\frac{2.58999}{640} \approx 0.0040469 \text{ square kilometers per decade}$

Rounding to four decimal places, we get:
$0.0041 \text{ square kilometers per decade}$

Question

A scale drawing of a room uses the scale 2 centimeters $=1$ foot. In the drawing, one wall has a length of 22 centimeters. What is the actual length, in feet, of this wall?

Ans: 11

Questions

How many cups, each with a capacity of 8 fluid ounces, can be filled with water from a cooler that contains 10 gallons of water? ( 1 gallon=128 fluid ounces)

An instrument shows the number of revolutions per minute made by each tire of a car. In each revolution, the car travels a distance equal to the circumference of one of its tires. The circumference of each tire is equal to $2 \pi r$, where $r$ is the radius of the tire.
If the radius of each tire on Maria’s car is 0.30 meter, what is the approximate speed of Maria’s car, to the nearest kilometer per hour, when the instrument is showing 779 revolutions per minute? ( 1 kilometer $=1000$ meters)