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Passport to Advanced Math Practice Questions

SAT · SAT Math · 99 free MCQs with instant results and detailed explanations.

99
Total
34
Easy
47
Medium
18
Hard

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Sample Questions from Passport to Advanced Math

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Q1
Easy
If f(x) = 2x + 3, what is f(4)?
A. 11
B. 10
C. 8
D. 7
Show Answer & Explanation
Correct Answer: A
To find f(4), substitute 4 for x in the function f(x) = 2x + 3. So, f(4) = 2(4) + 3 = 8 + 3 = 11.
Q2
Easy
What is the value of x if 3x - 7 = 11?
A. 6
B. 5
C. 4
D. 8
Show Answer & Explanation
Correct Answer: A
To solve for x, add 7 to both sides to get 3x = 18, then divide both sides by 3 to find x = 6.
Q3
Easy
A rectangle has a length of 10 units and a width of 5 units. What is its area?
A. 50 square units
B. 60 square units
C. 45 square units
D. 40 square units
Show Answer & Explanation
Correct Answer: A
The area of a rectangle is calculated by multiplying its length by its width. So, Area = length × width = 10 × 5 = 50 square units.
Q4
Medium
If the equation of a line is y = 3x + 2, what is the slope of the line?
A. 3
B. 2
C. 1/3
D. -3
Show Answer & Explanation
Correct Answer: A
The slope-intercept form is y = mx + b where m is the slope. Here, m = 3.
Q5
Medium
A rectangle has a length that is twice its width. If the perimeter is 48 units, what is the width of the rectangle?
A. 8
B. 12
C. 16
D. 10
Show Answer & Explanation
Correct Answer: A
Let the width be w. Then length = 2w. Using perimeter formula: 2(l + w) = 48 gives w = 8.
Q6
Medium
Which of the following represents the solution set for the inequality 3x - 7 < 2?
A. x < 3
B. x > 3
C. x < 2
D. x > 2
Show Answer & Explanation
Correct Answer: A
To solve 3x - 7 < 2, add 7 to both sides and divide by 3: 3x < 9 gives x < 3.
Q7
Medium
What is the equation of a circle with center at (2, -3) and radius 5?
A. (x - 2)^2 + (y + 3)^2 = 25
B. (x + 2)^2 + (y - 3)^2 = 5
C. (x - 2)^2 + (y - 3)^2 = 25
D. (x + 2)^2 + (y + 3)^2 = 5
Show Answer & Explanation
Correct Answer: A
The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center.
Q8
Hard
If the function f(x) = 2x^2 - 4x + 1 is transformed by shifting it 3 units to the right and then 2 units up, what is the new function g(x)?
A. g(x) = 2(x - 3)^2 - 4 + 2
B. g(x) = 2(x - 3)^2 - 1
C. g(x) = 2(x - 3)^2 + 1
D. g(x) = 2(x - 3)^2 + 3
Show Answer & Explanation
Correct Answer: C
To shift the function 3 units to the right, we replace x with (x - 3). Thus, f(x) becomes 2(x - 3)^2 - 4(x - 3) + 1. After shifting it up by 2, we add 2 to the function, yielding g(x) = 2(x - 3)^2 + 1.
Q9
Hard
If the function f(x) = 2x^2 - 3x + 5 represents a parabola, what is the minimum value of f(x)?
A. 4.5
B. 5
C. 3
D. 2
Show Answer & Explanation
Correct Answer: B
The minimum value of a quadratic function in the form f(x) = ax^2 + bx + c occurs at x = -b/(2a). Here, a = 2 and b = -3, so x = -(-3)/(2*2) = 3/4. Substituting x = 3/4 into f(x) gives f(3/4) = 2(3/4)^2 - 3(3/4) + 5 = 5, which is the minimum value.
Q10
Hard
If the function f(x) = 2x^2 + 3x - 5 is transformed by the equation g(x) = f(x - 4), what is the value of g(0)?
A. -21
B. -17
C. 3
D. 7
Show Answer & Explanation
Correct Answer: A
To find g(0), we substitute x = 0 into g(x) = f(x - 4). This means we need to compute f(-4). f(-4) = 2(-4)^2 + 3(-4) - 5 = 32 - 12 - 5 = 15. Therefore, g(0) = 15 - 36 = -21.

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Passport to Advanced Math — SAT SAT Math Practice Questions Online

This page contains 99 practice MCQs for the chapter Passport to Advanced Math in SAT SAT Math. The questions are organized by difficulty — 34 easy, 47 medium, 18 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.