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Test Citadel features an authentic Bluebook-calibrated countdown timer with visibility toggle, question navigation grid, choice eliminator cross-out tool, embedded Desmos graphing calculator, and official College Board formula sheets.

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SAT Math Difficulty: Hard (800) • Calibrated to 2026 Testing Standard

Digital SAT Math Practice Question #740

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

The function $ f(x) = a \sin(bx + c) + d $ has a maximum value of $ 12 $ and a minimum value of $ 2 $ in the $ xy $-plane. The period of the function is $ \frac{4\pi}{3} $. If $ f(0) = 7 $ and the function is increasing at $ x = 0 $, what is the value of $ f\left(\frac{\pi}{3}\right) $? (Assume $ a > 0 $ and $ b > 0 $).

Select Your Answer:

Socratic AI Engine Step-by-Step Derivation

0ms Precomputed

Tactical Insight (Hint 1)

Recall the standard circle equation: $ (x - h)^2 + (y - k)^2 = r^2 $. Complete the square if the equation is expanded.

Elimination Framework (Hint 2)

Desmos Tactical Shortcut: Type the function directly into Desmos. Tap the peak or trough of the curve to instantly reveal the extrema coordinates $ (h, k) $.

Masterclass Solution & Distractor Trap Analysis

This is a brilliantly constructed trigonometric modeling question that will filter out anyone who doesn't deeply understand the anatomy of a sine wave. Step 1: Find amplitude ($ a $) and vertical shift ($ d $). The maximum value is 12 a...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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