October 22 2025 DSAT – Test 10J: Sample Questions & Full Analysis

Expert Breakdown of the October 2025 US School Day SAT (Test 10J)

Welcome to the allsatpapers.com expert analysis! As specialists in official test materials, we know that success on the Digital SAT comes from practicing with real, official exams. The October 22, 2025 US School Day DSAT (Test 10J) is a key test form from this month's administrations. It provides a crucial look at the types of questions, vocabulary, and mathematical reasoning skills the College Board is currently using to challenge students.

Expert Note: This test form (10J) has a unique Module 1, but its adaptive Module 2 (both Reading/Writing and Math) is identical to the "hard" module seen on other October test dates (like 10C, 10E, 10F, etc.). This makes it an essential tool for high-scoring students who want to master the most challenging questions.

This post will provide a deep dive into this specific test, quoting key passages that customers often search for to identify the exam they need. Let's analyze what makes Test 10J a vital study tool.

Section 1: Reading & Writing Module 1 (Key Passages)

The first R&W module is designed to set your baseline. As requested, we have quoted the first two questions in full, as these are the most common passages users search for to identify this test.

Section 1: Reading & Writing Module 2 (Adaptive) Analysis

This module's difficulty adapts based on your performance in Module 1. The questions in 10J's second module are noticeably more complex, with challenging vocabulary and nuanced passages.

Section 2: Math Module 1 Analysis

The first math module on Test 10J is very straightforward and focuses on foundational skills. It is designed to be accessible and quickly assess core competencies.

Core Concepts on Display

• One-Step Equations (Question 1): The module starts with $6x = 30$. This is a basic test of solving for $x$. $x = 30 / 6 = 5$.
• Linear Functions (Question 2): A simple substitution. The equation is $p = 10n$. The question asks for the value of $p$ when $n = 9$. $p = 10(9) = 90$.
• Data Analysis (Question 3): A simple bar graph reading. "How many more... comedy than drama?" The graph shows 25 for comedy and 20 for drama. The answer is $25 - 20 = 5$.
• Geometry (Question 12): A parallel lines problem. Two parallel lines are cut by a transversal. An exterior angle is $41^\circ$. The corresponding interior angle is also $41^\circ$. This angle and the angle $x$ form a straight line, making them supplementary. $x + 41 = 180$. Solving gives $x = 139$.

Section 2: Math Module 2 (Adaptive) Analysis

This module is significantly more difficult than the first. It tests complex, multi-step problems that require a deep understanding of algebra and functions.

Advanced Applications

• Quadratic Equations (Question 7): $x^2 - 12x + 27 = 0$. This requires factoring. You need two numbers that multiply to 27 and add to -12. These are -3 and -9. The factored form is $(x - 3)(x - 9) = 0$. The solutions are $x=3$ and $x=9$. The question asks for the sum of the solutions: $3 + 9 = 12$.
• Finding the Equation of a Parabola (Question 12): This question shows a graph of a parabola with x-intercepts at -1 and 3, and a y-intercept at 3.
  1. Use the x-intercepts (roots) to write the factored form: $y = a(x - r_1)(x - r_2)$.
  2. $y = a(x - (-1))(x - 3) \rightarrow y = a(x + 1)(x - 3)$.
  3. Use the y-intercept $(0, 3)$ to find $a$. Plug in $x=0$ and $y=3$.
  4. $3 = a(0 + 1)(0 - 3)$
  5. $3 = a(1)(-3) \rightarrow 3 = -3a$
  6. $a = -1$.
  7. The full equation is $f(x) = -1(x + 1)(x - 3)$.
• Quadratic Formula (Question 19): "What is the positive solution to... $x^2 + 2x - 11 = 0$?" This cannot be factored easily.
  1. Use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
  2. $x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-11)}}{2(1)}$
  3. $x = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-2 \pm \sqrt{48}}{2}$
  4. The question asks for the positive solution: $\frac{-2 + \sqrt{48}}{2}$.
  5. Simplify the radical: $\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$.
  6. $x = \frac{-2 + 4\sqrt{3}}{2} = -1 + 2\sqrt{3}$.
• Discriminant (Question 21): "The equation $3x^2 - 10x + k = 0$ has no real solutions... what is the least possible integer value for k?"
  1. "No real solutions" means the discriminant ($b^2 - 4ac$) must be less than 0.
  2. Here, $a = 3$, $b = -10$, and $c = k$.
  3. $(-10)^2 - 4(3)(k) < 0$
  4. $100 - 12k < 0 \rightarrow 100 < 12k$
  5. $100/12 < k \rightarrow 25/3 < k$
  6. $8.33... < k$. Since $k$ must be an integer, the least possible value is 9.

Overall Difficulty and Analysis of Test 10J

After a comprehensive review of all four modules, here is our expert assessment of the October 22, 2025 (10J) US School Day DSAT:

• Overall Difficulty: Hard.
• Analysis: This test is another "hard path" form from the October 2025 administrations. Its Module 1 R&W is unique ("sand wasp," "St. Juliana"), but its Module 2 (both R&W and Math) is content-identical to the other hard forms (10C, 10E, 10F, 10G, 10H). This confirms that the College Board has a very specific set of challenging passages and problem types for students who perform well on Module 1.
• Reading & Writing: This section is Hard. While Module 1 is relatively standard, Module 2 (which is shared with the 10C/E/F/G/H forms) features more advanced vocabulary (e.g., "amalgam," "asserted," "predominant") and more complex, nuanced passages.
• Math: This section is Hard. Just like the other "hard" forms, this test features an extreme difficulty jump. Module 1 is exceptionally easy. Module 2, however, is a significant challenge. It is packed with advanced algebra, including multiple questions requiring the quadratic formula (and radical simplification), discriminant inequalities, and finding the equation of a parabola from its intercepts.

Why This Practice Test is Essential For Your Prep

DSAT Test 10J (October 22, 2025) is a perfect example of the "hard path" on the Digital SAT. It clearly shows the test's emphasis on:

• Advanced Vocabulary: This test form moves beyond basic context clues to test higher-level vocabulary (e.g., "amalgam," "asserted"). Students must have a strong vocabulary base.
• Algebra Mastery: The Math section is not just about calculation; it's about knowing which advanced algebraic tool to use. The hard module (M2) requires you to be fluent in factoring, the quadratic formula, and the discriminant, and to know when to use each one.
• Multi-Step Problem Solving: The hardest math questions combine multiple concepts. The parabola question (M2 Q12) is a perfect example, blending graphical analysis (finding intercepts) with algebra (solving for $a$).

Studying with an official past paper like Test 10J is the single best way to simulate the most challenging version of the Digital SAT. If you can score well on this test, you are prepared for anything the DSAT can throw at you.