Digital SAT: Comprehensive Practice (Math & Reading-Writing) · Öffentliche Lernkarten

Frage 1: How is the Digital SAT structured in terms of sections and timing?

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Two sections: Reading and Writing (64 min, 54 questions) and Math (70 min, 44 questions). Total duration is 2 hours 14 minutes.

Each section consists of two equal-length adaptive modules separated by a 10-minute break. Performance in Module 1 dictates the difficulty of Module 2.

Frage 2: What is the slope-intercept form of a linear equation, and what do $m$ and $b$ represent?

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$y = mx + b$ , where $m$ is the slope (rate of change) and $b$ is the y-intercept $(0, b)$ .

Slope is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$ . Parallel lines share identical slopes ( $m_1 = m_2$ ), while perpendicular lines have negative reciprocal slopes ( $m_1 \cdot m_2 = -1$ ).

Frage 3: For the quadratic equation $ax^2 + bx + c = 0$ , what does the discriminant $D = b^2 - 4ac$ determine?

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If $D > 0$ , 2 distinct real solutions; if $D = 0$ , exactly 1 real solution; if $D < 0$ , 2 complex/no real solutions.

The discriminant is derived under the radical in the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .

Frage 4: What is the vertex form of a parabola, and how are the coordinates of the vertex expressed?

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$y = a(x - h)^2 + k$ , where the vertex is located at $(h, k)$ and the axis of symmetry is $x = h$ .

If $a > 0$ , the parabola opens upward and $k$ is the minimum value; if $a < 0$ , it opens downward and $k$ is the maximum value.

Frage 5: In a circle with radius $r$ , what is the equation in standard form with center $(h, k)$ ?

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$(x - h)^2 + (y - k)^2 = r^2$ .

If an expanded equation $x^2 + y^2 + Dx + Ey + F = 0$ is given, complete the square on $x$ and $y$ terms to find the center $(h, k)$ and radius $r$ .

Frage 6: What is the relationship between the sine and cosine of complementary angles in right triangles?

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$\sin(x) = \cos(90^\circ - x)$ or in radians $\sin(x) = \cos\left(\frac{\pi}{2} - x\right)$ .

Since acute angles in a right triangle sum to $90^\circ$ , the side opposite angle $x$ is adjacent to $(90^\circ - x)$ , making the ratios identical.

Frage 7: In SAT Writing, how do semicolons (;) function compared to periods (.)?

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A semicolon connects two independent clauses without a coordinating conjunction (FANBOYS), functioning identically to a period.

Both sides of a semicolon must be complete sentences capable of standing alone. If one side is a dependent clause, a semicolon cannot be used.

Frage 8: What is a dangling modifier and how is it corrected in SAT conventions?

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A descriptive introductory phrase whose logical subject does not immediately follow the comma.

Example: 'Walking into the lab, the experiment was observed.' (Incorrect). 'Walking into the lab, the scientist observed the experiment.' (Correct).

Frage 9: How should transitions like 'however', 'therefore', and 'moreover' be selected in SAT Reading & Writing?

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By analyzing the logical relationship between sentences: contrast ('however'), cause-and-effect ('therefore'), or addition ('moreover').

Never choose a transition without identifying whether Sentence 2 confirms, contrasts, illustrates, or qualifies the claim in Sentence 1.

Frage 10: In SAT Math data analysis, how does an extreme outlier affect the mean versus the median?

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The mean is pulled significantly toward the outlier, while the median remains resistant and largely unchanged.

Mean incorporates all numerical values; a high outlier inflates the sum. The median depends only on middle rank order.

Frage 11: How do you solve systems of linear equations on the Digital SAT using the built-in Desmos calculator?

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Graph both equations directly and click the intersection point; the $(x, y)$ coordinates provide the exact solution.

Desmos supports implicit equations such as $2x + 3y = 12$ without needing to solve for $y$ first.

Frage 12: When two lines have no solution in a system of linear equations, what is true about their slopes and y-intercepts?

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They have identical slopes ( $m_1 = m_2$ ) but different y-intercepts ( $b_1 \neq b_2$ ), representing distinct parallel lines.

If both slopes and y-intercepts are identical, the lines coincide and have infinitely many solutions.

Frage 13: What is the exponent rule for negative exponents: $x^{-n}$ ?

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$x^{-n} = \frac{1}{x^n}$ (for $x \neq 0$ ).

A negative exponent indicates the reciprocal of the base raised to the positive power: $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$ .

Frage 14: What is the exponential growth and decay model formula on the SAT?

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$y = a(1 + r)^t$ for growth and $y = a(1 - r)^t$ for decay, where $a$ is initial amount and $r$ is rate.

If an item depreciates by $15\%$ annually, the multiplier is $(1 - 0.15) = 0.85$ , yielding $y = a(0.85)^t$ .

Frage 15: How do dashes (—) function in SAT punctuation?

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A pair of em dashes sets off nonessential parenthetical information; a single dash introduces an emphatic conclusion or elaboration.

Pairs of dashes must match: if an interruption opens with a dash, it must close with a dash before the main clause resumes.

Frage 16: What is the difference between restrictive and non-restrictive relative clauses ('that' vs. 'which')?

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'That' introduces essential restrictive clauses without commas; 'which' introduces nonessential descriptive clauses preceded by a comma.

Example: 'The books that are on the desk belong to Ana' (specific books). 'The books, which are on the desk, belong to Ana' (all books).

Frage 17: In similar triangles, if the ratio of corresponding side lengths is $k$ , what are the ratios of their perimeters and areas?

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Ratio of perimeters is $k$ ; ratio of areas is $k^2$ .

If triangle B has sides 3 times as long as triangle A ( $k=3$ ), its perimeter is 3 times as large and its area is $3^2 = 9$ times as large.

Frage 18: What is the volume formula for a right circular cylinder and a right circular cone?

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Cylinder: $V = \pi r^2 h$ ; Cone: $V = \frac{1}{3}\pi r^2 h$ .

These geometric reference formulas are provided on the SAT reference sheet accessible on the exam screen.

Frage 19: What is the arc length formula $s$ for a central angle $\theta$ in radians?

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$s = r \cdot \theta$ , where $r$ is the radius and $\theta$ is measured in radians.

If angle is given in degrees, convert via $\theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180^\circ}$ . Sector area is $A = \frac{1}{2}r^2\theta$ .

Frage 20: In SAT Reading, what strategy avoids common trap answers in 'Command of Evidence' questions?

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Match exact textual keywords and factual scope without extrapolating beyond what is explicitly stated in the passage or chart.

Distractors often present true real-world claims that are not stated in or supported by the author's argument in the passage.