SAT - Scholastic Assessment Test Math 3 — Questions and Answers
Question 1: A car rental company charges x dollars per day for a vehicle. The total cost for a one-day rental includes a fuel surcharge that is a percentage of the daily rate, plus a flat $9 airport fee. The total cost is given by the expression 1.15x + 9. What is the fuel surcharge expressed as a percentage?
- 15% (Correct answer)
- 1.15%
- 9%
- 115%
Correct answer: 15%
The coefficient 1.15 means the customer pays the base rate x plus an additional 0.15x. That extra 0.15x represents 15% of the daily rate. The $9 is a separate flat fee, not part of the percentage.
Question 2: Which of the following equations has a vertex of (−2, 6)?
- y = (x − 2)² + 6
- y = (x + 2)² − 6
- y = (x + 2)² + 6 (Correct answer)
- y = (x − 2)² − 6
Correct answer: y = (x + 2)² + 6
In vertex form y = a(x − h)² + k, the vertex is (h, k). To get h = −2, we need (x − (−2))² = (x + 2)², and k = 6 gives the +6 outside. So y = (x + 2)² + 6 is correct.
Question 3: A freelance designer earns x dollars per month from clients. She pays 1/4 of her earnings in self-employment taxes and also pays a fixed $60/month software subscription. Which equation represents her monthly take-home pay T?
- T = x + (1/4)x − 60
- T = (3/4)x − 60 (Correct answer)
- T = (1/4)x − 60
- T = x − 60
Correct answer: T = (3/4)x − 60
After paying 1/4 in taxes, she retains 1 − 1/4 = 3/4 of her earnings. Then the fixed $60 subscription is subtracted, giving T = (3/4)x − 60.
Question 4: What is the equation of a line that passes through the point (−1, 5) and has a slope of 3?
- y = 3x + 8 (Correct answer)
- y = 3x + 2
- y = 3x − 8
- y = 3x + 6
Correct answer: y = 3x + 8
Using slope-intercept form y = mx + b with m = 3 and the point (−1, 5): 5 = 3(−1) + b → 5 = −3 + b → b = 8. The equation is y = 3x + 8.
Question 5: Given f(x) = 2x² − 8x + 3, what is the x-coordinate of the vertex?
- x = 2 (Correct answer)
- x = −2
- x = 4
- x = −4
Correct answer: x = 2
Using the vertex formula x = −b/(2a) with a = 2 and b = −8: x = −(−8)/(2 · 2) = 8/4 = 2. The vertex is at x = 2.
Question 6: A clothing store marks up its wholesale prices by 40% to set retail prices. During a weekend sale, an additional 10% discount is applied to the retail price. If the wholesale price is w, which expression represents the final sale price?
- 0.40w − 0.10
- 1.26w (Correct answer)
- 0.50w
- 1.30w
Correct answer: 1.26w
The retail price after a 40% markup is 1.40w. A 10% discount on the retail price means multiplying by 0.90: 0.90 × 1.40w = 1.26w. The discount applies to the marked-up price, not the original.
SAT - Scholastic Assessment Test Math 3
A car rental company charges x dollars per day for a vehicle.
The total cost for a one-day rental includes a fuel surcharge that is a percentage of the daily rate, plus a flat $9 airport fee.
The total cost is given by the expression 1.15x + 9.
What is the fuel surcharge expressed as a percentage?