SAT MAth Practice questions – all topics
- Geometry and Trigonometry Weightage: 15% Questions: 5-7
- Area and volume
- Lines, angles, and triangles
- Right triangles and trigonometry
- Circles
SAT MAth and English – full syllabus practice tests
Question Easy
On average, one square inch of human skin contains 650 sweat glands. A certain area of skin contains 1,170 sweat glands. Based on this information, which of the following is closest to the size of this area, in square inches?
A. 0.44
B. 0.56
C. 0.80
D. 1.80
▶️Answer/Explanation
Ans:D
If one square inch of human skin contains \(650\) sweat glands and a certain area of skin contains \(1,170\) sweat glands, we can find the size of this area by dividing the total number of sweat glands by the number of sweat glands per square inch.
So, the size of the area in square inches is:
\[\frac{1,170 \text{ sweat glands}}{650 \text{ sweat glands/square inch}}\]
\[\approx 1.8 \text{ square inches}\]
Therefore, the closest option is option D: \(1.80\) square inches.
Question Easy
\(0.79 x+1.0 y=100\)
The mass of a solution of isopropanol and water is 100 grams. The given equation represents this situation, where \(x\) is the volume of isopropanol, in cubic centimeters, and \(y\) is the volume of water, in cubic centimeters. If the volume of isopropanol is 70 cubic centimeters, what is the approximate volume of water, in cubic centimeters?
A. 45
B. 55
C. 70
D. 79
▶️Answer/Explanation
Ans:A
To solve the equation \(0.79x + 1.0y = 100\), where \(x\) is the volume of isopropanol and \(y\) is the volume of water, and we’re given that \(x = 70\) cubic centimeters, we can find the volume of water (\(y\)).
\[0.79(70) + 1.0y = 100\]
\[55.3 + 1.0y = 100\]
Subtracting \(55.3\) from both sides:
\[1.0y = 100 – 55.3\]
\[1.0y = 44.7\]
Dividing both sides by \(1.0\):
\[y = 44.7\]
So, the approximate volume of water is \(45\) cubic centimeters.
Question Easy
If each side of a larger square is three times as long as each side of a smaller square, how does the perimeter of the larger square compare to that of the smaller square?
A) It is 3 times as long.
B) It is 6 times as long.
C) It is 9 times as long.
D) It is 12 times as long.
▶️Answer/Explanation
A) It is 3 times as long.
If each side of a larger square is three times as long as each side of a smaller square, we need to compare the perimeter of the larger square to that of the smaller square.
1. Let the side length of the smaller square be \(s\):
Perimeter of the smaller square \(P_{\text{small}} = 4s\)
2. The side length of the larger square is \(3s\):
Perimeter of the larger square \(P_{\text{large}} = 4 \times 3s = 12s\)
3. Compare the perimeters:
The perimeter of the larger square is \(12s\), which is 3 times the perimeter of the smaller square (since \(12s = 3 \times 4s\)).
Thus, the perimeter of the larger square is 3 times as long as that of the smaller square:
\[ \boxed{\text{A}} \]A) It is 3 times as long.
Question Easy
Leonardo da Vinci’s rectangular painting Mona Lisa measures 21 inches wide and 30 inches long. An artist is creating a larger-scale replica of Mona Lisa, where the equation \(A=(21 x)(30 x)\) gives the area of the replica, in square inches. Which of the following is the best interpretation of \(x\) in this context?
A) The width of the replica is \(x\) inches greater than the width of the original Mona Lisa.
B) The length of the replica is \(x\) inches greater than the length of the original Mona Lisa.
C) The measure of each side of the replica is \(x\) times as great as the measure of the corresponding side of the original Mona Lisa.
D) The area of the replica is \(x\) times as great as the area of the original Mona Lisa.
▶️Answer/Explanation
C
The equation \(A = (21x)(30x)\) gives the area of the replica of Mona Lisa, where \(x\) is a scaling factor.
To interpret \(x\), let’s consider its effect on the dimensions and area of the replica compared to the original Mona Lisa:
Option A) The width of the replica is \(x\) inches greater than the width of the original Mona Lisa.
Option B) The length of the replica is \(x\) inches greater than the length of the original Mona Lisa.
Option C) The measure of each side of the replica is \(x\) times as great as the measure of the corresponding side of the original Mona Lisa.
Option D) The area of the replica is \(x\) times as great as the area of the original Mona Lisa.
Given the equation \(A = (21x)(30x)\), \(x\) appears as a scaling factor, multiplying both the width and the length. Therefore, the most appropriate interpretation is:
\[ \boxed{C) \, \text{The measure of each side of the replica is } x \text{ times as great as the measure of the corresponding side of the original Mona Lisa.}} \]
Question Easy
A certain soccer field has an area of 7,000 square meters. What is this area in square feet?
(Use 1 square meter = 10.76 square feet.)
A) 60
B) 651
C) 75,320
D) 810,443
▶️Answer/Explanation
C) 75,320
To convert the area from square meters to square feet, we’ll use the conversion factor provided: \(1\) square meter \(= 10.76\) square feet.
Given that the area of the soccer field is \(7,000\) square meters, we’ll multiply this by the conversion factor:
\[ 7,000 \, \text{square meters} \times 10.76 \, \text{square feet/square meter} = 75,320 \, \text{square feet} \]
So, the area of the soccer field in square feet is \(75,320\).
Question Easy
A field has a perimeter of 960 feet. Of the following, which is closest to the perimeter of the field, in meters? ( 1 foot $=0.3048$ meter $)$
A) 89
B) 290
C) 3,200
D) 10,000
▶️Answer/Explanation
B