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Section 2, Module 2: Math (Upper Adaptive Track)1540 Elo Track

28:14

Desmos Calculator

Built-In Desmos Calculator·The Great KD Regression Shortcut

DEG

Type the function from the question:

f(x) = (x + a)(x - 15)

Let Desmos solve for a and b automatically:

[-75/7, 0] \sim [f(0) - 12, (1 + a)(1 - 15) - (1^2 + b(1) + f(0))]

PARAMETERSR² = 1

a = -0.0857143(-3/35)

b = -15.085714(-528/35)

Click fraction icon for exact answer:

ab = 45.7142857

= 320 / 7

Intercept: (0, 9/7)ab = 320/7 ✓

Difficulty: Hard (750+ Level)

The polynomial

f(x) = (x + a)(x - 15)

can be written in the form

f(x) = x^2 + bx + c

, where

a

b

, and

c

are constants. Given that

f(0) - 12 = -\frac{75}{7}

, what is the value of

ab

Click ABC buttons to test option strikeoutOpen Full Practice Test

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THE GREAT KD SOLVERBuilt-In Desmos Shortcuts

Solve 3-Minute Algebra Problems in 10 Seconds

Skip scratch-paper algebra mistakes. Learn how to use Desmos factor tables and tilde ( $\sim$ ) regressions to solve complex systems like $(hx + 4)(qx + 5) = ax^2 + bx + 20$ instantly.

DESMOS FACTOR PAIR TABLESolved in 8s

hqb = 5h + 4q

11253

2634 (Match ✓)

3431

REGRESSION SHORTCUT

x_1 = [1, 2, 3, 4, 5]

[(hx_1+4)(qx_1+5), 12] \sim [ax_1^2+bx_1+20, hq]

Verified Output:b = 34 ✓

TRAP DECODER14 SAT Trap Types

Spot How the SAT Tricks You

Wrong answers on the SAT aren't random—they're engineered traps. Our Trap Decoder labels the exact trick behind every wrong choice so you never fall for it twice.

A) -320 / 7Trap: Sign Flip

B) -75 / 7Trap: Solved for c, not ab

D) 320 / 7 ✓Verified Answer

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ELO RATING PROGRESSIONCurrent: 1570 Elo

SKILL HEATMAP

Nonlinear Systems96%

Quadratic Vertex Form92%

Cross-Text Evidence94%

Punctuation Boundaries88%

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STEP-BY-STEP PROOFVerified Answer Key ✓

\Delta = b^2 - 4ac = (-12)^2 - 4(3)(k) = 0 \implies k = 12

Condition: Exactly One Real Solutionk = 12 ✓

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PASSAGE EVIDENCE HIGHLIGHTInformation & Ideas

“While early paleoclimatologists attributed the Younger Dryas cooling exclusively to Laurentide meltwater pulses, isotopic ratios in Greenland ice cores indicate a concurrent shift in North Atlantic thermohaline circulation that amplified regional temperature anomalies.”

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