# SAT Math Test Collection
**Digital SAT Format 2024**
# Test 1: Standard SAT Math Practice
**(General SAT Math - All Majors)**
## Section 1: Heart of Algebra (11 questions)
### Question 1
If 3x + 5 = 17, what is the value of x?
A) 3
B) 4
C) 5
D) 6
### Question 2
Which of the following is equivalent to 2(x + 3) - 4?
A) 2x + 2
B) 2x + 6
C) 2x - 1
D) 2x + 10
### Question 3
If y = 2x - 1 and x = 3, what is the value of y?
A) 4
B) 5
C) 6
D) 7
### Question 4
The solution to 4x - 7 = 2x + 9 is:
A) x = 6
B) x = 7
C) x = 8
D) x = 9
### Question 5
If f(x) = x² + 2x - 3, what is f(2)?
A) 3
B) 5
C) 7
D) 9
### Question 6
The system of equations:
x + y = 10
2x - y = 5
has the solution:
A) x = 5, y = 5
B) x = 6, y = 4
C) x = 7, y = 3
D) x = 8, y = 2
### Question 7
If |x - 3| = 5, what are the possible values of x?
A) x = -2 or x = 8
B) x = 2 or x = -8
C) x = -5 or x = 3
D) x = 5 or x = -3
### Question 8
Which inequality represents “twice a number decreased by 5 is at least 7”?
A) 2x - 5 ≥ 7
B) 2x - 5 ≤ 7
C) 2(x - 5) ≥ 7
D) 2(x - 5) ≤ 7
### Question 9
If 3^x = 27, what is the value of x?
A) 2
B) 3
C) 4
D) 9
### Question 10
The graph of y = -x² + 4 has its vertex at:
A) (0, 4)
B) (0, -4)
C) (4, 0)
D) (-4, 0)
### Question 11
If h(x) = 3x - 2 and h(a) = 10, what is the value of a?
A) 3
B) 4
C) 5
D) 6
## Section 2: Problem Solving and Data Analysis (8 questions)
### Question 12
A store offers a 20% discount on all items. If an item originally costs $50, what is the sale price?
A) $30
B) $35
C) $40
D) $45
### Question 13
The average of 5 numbers is 18. If four of the numbers are 12, 15, 20, and 23, what is the fifth
number?
A) 18
B) 20
C) 22
D) 25
### Question 14
In a survey of 100 students, 60 like pizza, 40 like burgers, and 25 like both. How many students
like neither?
A) 15
B) 20
C) 25
D) 30
### Question 15
If the probability of rain is 0.3, what is the probability it will NOT rain?
A) 0.3
B) 0.7
C) 1.3
D) 3.0
### Question 16
A recipe calls for 2 cups of flour for 12 cookies. How many cups of flour are needed for 18
cookies?
A) 2.5
B) 3
C) 3.5
D) 4
### Question 17
The median of the data set {3, 7, 9, 12, 15, 18, 20} is:
A) 9
B) 12
C) 15
D) 18
### Question 18
If x varies inversely with y, and x = 8 when y = 3, what is x when y = 6?
A) 2
B) 4
C) 6
D) 16
### Question 19
A car travels 240 miles in 4 hours. What is its average speed in miles per hour?
A) 50 mph
B) 55 mph
C) 60 mph
D) 65 mph
## Section 3: Passport to Advanced Math (8 questions)
### Question 20
If x² - 5x + 6 = 0, what are the solutions?
A) x = 2 or x = 3
B) x = 1 or x = 6
C) x = -2 or x = -3
D) x = -1 or x = -6
### Question 21
What is the simplified form of (2x³)(3x²)?
A) 5x⁵
B) 6x⁵
C) 5x⁶
D) 6x⁶
### Question 22
If f(x) = x² + 1, what is f(x + 2)?
A) x² + 3
B) x² + 4x + 5
C) x² + 2x + 3
D) x² + 4x + 1
### Question 23
The expression √(18) can be simplified to:
A) 3√2
B) 2√3
C) 6√3
D) 9√2
### Question 24
If log₃(x) = 2, what is the value of x?
A) 6
B) 8
C) 9
D) 12
### Question 25
What is the sum of the roots of x² - 7x + 10 = 0?
A) -7
B) 7
C) -10
D) 10
### Question 26
If i = √(-1), what is the value of i³?
A) -1
B) -i
C) 1
D) i
### Question 27
The function f(x) = 2ˣ passes through which point?
A) (0, 0)
B) (0, 1)
C) (1, 0)
D) (1, 1)
## Section 4: Additional Topics in Math (5 questions)
### Question 28
A circle has a radius of 6. What is its circumference?
A) 6π
B) 12π
C) 18π
D) 36π
### Question 29
In a right triangle, if one angle is 30°, what is the other acute angle?
A) 30°
B) 45°
C) 60°
D) 90°
### Question 30
What is the volume of a rectangular prism with dimensions 3 × 4 × 5?
A) 12
B) 47
C) 60
D) 120
### Question 31
If sin θ = 0.5, what is θ in degrees (0° ≤ θ ≤ 90°)?
A) 30°
B) 45°
C) 60°
D) 90°
### Question 32
The distance between points (1, 2) and (4, 6) is:
A) 3
B) 4
C) 5
D) 7
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# Test 2: SAT Math for Architecture Focus
**(Specialized for Architecture Students)**
## Section 1: Geometry and Spatial Reasoning (12 questions)
### Question 1
An architect designs a triangular roof with a base of 24 feet and a height of 8 feet. What is the
area of the triangle?
A) 32 ft²
B) 96 ft²
C) 128 ft²
D) 192 ft²
### Question 2
A cylindrical column has a diameter of 2 feet and a height of 12 feet. What is its volume? (Use π
= 3.14)
A) 37.68 ft³
B) 75.36 ft³
C) 150.72 ft³
D) 301.44 ft³
### Question 3
The Golden Ratio (φ) is approximately equal to:
A) 1.414
B) 1.618
C) 1.732
D) 2.236
### Question 4
A building casts a shadow of 150 feet when the angle of elevation of the sun is 35°.
What is the height of the building? (tan 35° ≈ 0.7)
A) 100 ft
B) 105 ft
C) 115 ft
D) 120 ft
### Question 5
A regular hexagonal floor tile has a side length of 6 inches. What is its area? (Area =
(3√3/2)s²)
A) 54√3 in²
B) 108√3 in²
C) 162√3 in²
D) 216√3 in²
### Question 6
An arched doorway is in the shape of a semicircle with a diameter of 8 feet. What is the area of
the semicircle? (Use π = 3.14)
A) 25.12 ft²
B) 50.24 ft²
C) 100.48 ft²
D) 200.96 ft²
### Question 7
A spiral staircase makes a complete 360° turn while rising 10 feet. If the radius is 4 feet, what is
the length of the helical path?
A) 2π√116 ft
B) 4π√29 ft
C) 8π√5 ft
D) 16π ft
### Question 8
The cross-section of a roof beam is an I-beam. If the top flange is 8 inches wide, 1 inch thick,
the web is 10 inches tall, 0.5 inches thick, and the bottom flange matches the top, what is the
total cross-sectional area?
A) 21 in²
B) 21.5 in²
C) 22 in²
D) 22.5 in²
### Question 9
A dome has a hemisphere shape with a radius of 20 feet. What is its surface area? (Surface
area of sphere = 4πr²)
A) 800π ft²
B) 1600π ft²
C) 2400π ft²
D) 3200π ft²
### Question 10
In architectural drafting, if a scale is 1:100, and a room measures 5 cm on the drawing, what is
the actual length?
A) 5 m
B) 50 m
C) 500 m
D) 5000 m
### Question 11
A truss is designed as an equilateral triangle with side length 20 feet. What is the height of this
truss?
A) 10 ft
B) 10√2 ft
C) 10√3 ft
D) 20√3 ft
### Question 12
The load-bearing capacity of a beam varies with the square of its depth. If a beam 6 inches
deep can support 1000 pounds, how much can a beam 9 inches deep support?
A) 1500 lbs
B) 2000 lbs
C) 2250 lbs
D) 2500 lbs
## Section 2: Structural Analysis and Forces (8 questions)
### Question 13
A simply supported beam of length 20 feet has a uniformly distributed load of 100 pounds per
foot. What is the maximum bending moment? (M = wL²/8)
A) 2500 ft-lbs
B) 5000 ft-lbs
C) 7500 ft-lbs
D) 10000 ft-lbs
### Question 14
In a right triangle representing forces, if the horizontal component is 300 N and the vertical
component is 400 N, what is the resultant force?
A) 500 N
B) 600 N
C) 700 N
D) 800 N
### Question 15
The compressive strength of concrete is 3000 psi. A column has a cross-sectional area of 144
square inches. What is the maximum load it can support?
A) 432,000 lbs
B) 216,000 lbs
C) 108,000 lbs
D) 54,000 lbs
### Question 16
A cable supports a load at an angle of 30° from the horizontal. If the tension in the cable is 1000
N, what is the vertical component of the force?
A) 500 N
B) 866 N
C) 1000 N
D) 1732 N
### Question 17
The deflection of a cantilever beam is given by δ = (wL⁴)/(8EI). If all parameters remain constant
except the length doubles, how does the deflection change?
A) Doubles
B) Quadruples
C) Increases 8 times
D) Increases 16 times
### Question 18
A foundation must distribute a load of 50,000 pounds over soil with a bearing capacity of 2000
psf. What minimum area is required?
A) 20 ft²
B) 25 ft²
C) 30 ft²
D) 35 ft²
### Question 19
In a pin-jointed truss, if member AB has a tensile force of 5000 N and makes a 45° angle with
the horizontal, what is its horizontal component?
A) 2500 N
B) 3536 N
C) 5000 N
D) 7071 N
### Question 20
The moment of inertia of a rectangular cross-section is I = bh³/12. If both width and height are
doubled, how does the moment of inertia change?
A) Doubles
B) Quadruples
C) Increases 8 times
D) Increases 16 times
## Section 3: Environmental and Sustainable Design (6 questions)
### Question 21
A building’s energy consumption is 50 kWh per square foot per year. If the building has 10,000
square feet, what is the annual energy consumption?
A) 500 kWh
B) 5,000 kWh
C) 50,000 kWh
D) 500,000 kWh
### Question 22
Solar panels have an efficiency of 20%. If solar irradiance is 1000 W/m² and the panel area is
50 m², what is the power output?
A) 5 kW
B) 10 kW
C) 15 kW
D) 20 kW
### Question 23
A green roof reduces building temperature by 5°C. If the original temperature was 35°C, what is
the new temperature in Fahrenheit? (F = 9C/5 + 32)
A) 86°F
B) 90°F
C) 95°F
D) 104°F
### Question 24
LEED certification requires a 20% reduction in water usage. If a building typically uses 10,000
gallons per month, what is the target usage?
A) 7,000 gallons
B) 7,500 gallons
C) 8,000 gallons
D) 8,500 gallons
### Question 25
Daylighting reduces artificial lighting needs by 60%. If electricity for lighting costs $200 per
month, what are the monthly savings?
A) $80
B) $100
C) $120
D) $140
### Question 26
A rain collection system captures 0.623 gallons per square foot of roof area per inch of rainfall.
For a 2000 ft² roof with 3 inches of rain, how much water is collected?
A) 3,738 gallons
B) 4,000 gallons
C) 4,246 gallons
D) 4,500 gallons
## Section 4: Design Mathematics and Proportions (6 questions)
### Question 27
The Modulor system by Le Corbusier is based on the golden ratio. If a room height is 8 feet,
what should be the width according to golden ratio proportions?
A) 4.94 feet
B) 5.55 feet
C) 6.18 feet
D) 12.94 feet
### Question 28
A building facade uses a rhythm of 1:2:1 for window-wall-window proportions. If the total width is
24 feet, what is the width of each window?
A) 4 feet
B) 6 feet
C) 8 feet
D) 12 feet
### Question 29
In perspective drawing, if an object appears 6 inches tall at a distance of 10 feet, how tall will it
appear at 15 feet? (Assuming similar viewing conditions)
A) 3 inches
B) 4 inches
C) 9 inches
D) 12 inches
### Question 30
A circular plaza has a diameter of 100 feet. If benches are placed every 15° around the
perimeter, how many benches are there?
A) 20
B) 24
C) 30
D) 36
### Question 31
Using the rule of thirds in architectural composition, where should the main focal point be placed
in a 12-foot wide elevation?
A) 3 feet from either side
B) 4 feet from either side
C) 5 feet from either side
D) 6 feet from the center
### Question 32
A double-height space has a ceiling of 20 feet. For acoustical reasons, the reverberation time
should not exceed 2 seconds. If the current time is 3 seconds, by what percentage must the
absorption be increased?
A) 25%
B) 33%
C) 50%
D) 67%
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should be familiar with
