SAT
MATHS
Heart of Algebra (~35%)
Focus: Linear equations, systems, and inequalities.
Solving, simplifying, and interpreting linear expressions in one or two variables
Solving using substitution, elimination, or graphing. Understanding when a system has no solution (parallel lines), one solution (intersecting), or infinitely many (same line).
Understanding slope (m) as a “rate of change” and the y-intercept (b) as a “starting value” or “constant” in real-world word problems.
Problem Solving and Data Analysis (~15%)
Focus: Ratios, percentages, and statistics.
Solving unit rate problems and scale drawings.
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Calculating percent increase/decrease and successive percentage changes.
Interpreting mean, median, mode, range, and standard deviation (conceptual: how “spread out” is the data?).
Analyzing scatterplots, lines of best fit, and correlation vs. causation.
Calculating conditional probability from two-way tables.
Evaluating if a study’s results can be generalized to a population based on random sampling.
Passport to Advanced Math (~35%)
Focus: The “Hard” Algebra—quadratics, polynomials, and non-linear curves.
Factoring, expanding, and simplifying complex rational expressions.
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witching between Vertex Form $a(x-h)^2 + k$, Factored Form $a(x-r_1)(x-r_2)$, and Standard Form $ax^2 + bx + c$.
Solving a system where one equation is linear ($y = mx + b$) and the other is quadratic ($y = ax^2 + bx + c$).
Understanding $f(t) = a(1 \pm r)^t$ where $r$ is the percent rate.
Understanding zeros (roots) and their relationship to the graph (touches vs. crosses the x-axis).
Additional Topics in Math (~15%)
Focus: Geometry, Trigonometry, and Complex Numbers.
Area and volume of 2D and 3D shapes; properties of triangles (Isosceles, Equilateral, Right).
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Mastery of Sine, Cosine, and Tangent (SOH CAH TOA).
The Circle Equation $(x-h)^2 + (y-k)^2 = r^2$ and converting between degrees and radians.
Operations $(+, -, \times)$ with $i$, where $i = \sqrt{-1}$.
KUMATICS EDUCATION
ENGLISH
The Digital SAT combines Reading and Writing into a single section. It is adaptive, meaning your performance on the first module determines the difficulty of the second.
Information and Ideas (~26%)
Focus: Comprehension, analysis, and reasoning based on text and data.
Central Ideas and Details: Determining the main point of a passage or identifying key supporting facts.
Identifying which piece of textual evidence best supports a specific claim or hypothesis.
Interpreting data in tables, bar graphs, or line graphs to identify the best evidence for a conclusion.
Making logical deductions from the text. This is often the hardest category, requiring you to find the “missing piece” of an argument.
Craft and Structure (~28%)
Focus: Vocabulary, text structure, and cross-textual connections.
Selecting high-level academic vocabulary (e.g., venerable, ephemeral, ubiquitous) that fits the tone and meaning of a sentence.
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Identifying how a passage is organized or why a specific sentence/paragraph was included (e.g., “to challenge a common assumption”).
Comparing two short passages (Text 1 and Text 2) to determine how the authors would view each other’s arguments.
Expression of Ideas (~20%)
Focus: Revision and synthesis of information.
Using a list of bulleted facts to create a sentence that meets a specific goal (e.g., “Summarize the methodology of the study”).
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Choosing the correct logical connector to link ideas.
Contrast: However, Conversely, Nevertheless.
Cause/Effect: Therefore, Consequently, Thus.
Addition: Moreover, Furthermore, Additionally.
Standard English Conventions (~26%)
Focus: Sentence structure, usage, and punctuation.
Correct use of punctuation to separate clauses (semicolons, colons, dashes, and commas).
Mastery of subject-verb agreement, verb tense consistency, and pronoun-antecedent agreement.
Avoiding misplaced or dangling modifiers (e.g., “Running down the street, the tree hit the car” vs “Running down the street, the man hit the tree”).
KUMATICS EDUCATION
SCIENCE
KUMATICS EDUCATION
KUMATICS EDUCATION
KUMATICS EDUCATION
MATHS
Elementary Level (Grades 3–4)
Targeting students aged 8–10. Focuses on foundational arithmetic and conceptual understanding.
Fluency in addition, subtraction, multiplication, and division of whole numbers.
Understanding ones, tens, hundreds, and thousands; rounding to the nearest ten or hundred.
Basic concepts (parts of a whole), naming fractions, and comparing simple fractions with like denominators.
Comparing numbers using greater than (>), less than (<), and equal to (=) symbols.
Identifying even and odd numbers.
Recognizing 2D shapes (circles, squares, rectangles, triangles) and their basic attributes (sides, corners).
Identifying cubes, spheres, and cylinders.
Basic understanding of the distance around a shape.
Understanding units of time (clocks), money (coins/bills), and basic length/weight.
Reading and interpreting simple bar graphs and pictographs.
Solving for a “missing number” in a simple equation (e.g., 5 + x = 12).
Identifying and extending simple repeating or increasing sequences.
Middle Level (Grades 5–7)
Targeting students aged 10–13. Transitioning from arithmetic to pre-algebraic concepts.
All four operations with fractions and decimals; converting between them.
Calculating the percent of a number and simple interest.
Understanding unit rates and solving simple proportions.
Rounding and estimating results for multi-step problems.
KUMATICS EDUCATION
KUMATICS EDUCATION
KUMATICS EDUCATION
KUMATICS EDUCATION
READING
Elementary Level (Grades 3–4)
Targeting students aged 8–10.
Focus: 28 questions in 30 minutes. Usually 7 short passages.
Simple stories or fables with a clear beginning, middle, and end.
Basic “how-it-works” or biographical passages (e.g., a passage about bees or George Washington).
What is this story mostly about?
Finding a specific fact mentioned in the text
Identifying what happened first, second, or last.
What does a simple word mean in the context of the sentence?
Reading and interpreting simple bar graphs and pictographs.
Solving for a “missing number” in a simple equation (e.g., 5 + x = 12).
Identifying and extending simple repeating or increasing sequences.
Middle Level (Grades 5–7)
Targeting students aged 10–13.
Focus: 40 questions in 40 minutes. Usually 7–9 passages.
Excerpts from novels or short stories (often 19th or 20th century).
Articles about art, history, or biography.
Passages about natural phenomena, biology, or space.
At least one short poem is usually included.
Upper Level (Grades 8–11)
Targeting students aged 13–17
Focus: 40 questions in 40 minutes. Usually 7–9 passages of high complexity.
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Sophisticated prose (e.g., Dickens, Austen, or Thoreau).
Dense, academic articles on sociology, economics, or complex physics/biology.
Essays that argue a specific point of view.
Poems with heavy symbolism and abstract imagery.
Identifying the “claim” and the evidence used to support it.
“The author mentions all of the following EXCEPT…” (These require scanning the whole text).
Understanding the “vibe” or underlying philosophy of a passage.
How does paragraph 2 relate to paragraph 3? (e.g., It provides an example of a theory mentioned earlier).
SSAT Reading "Big Two" Categories
Regardless of level, all questions fall into one of two categories:
Focuses on characters, setting, and plot.
Questions ask about: Character motivations, feelings, and the “lesson” of the story.
Focuses on facts, theories, and arguments.
Questions ask about: Main ideas, supporting details, and the logical structure of the text.
VERBAL
Elementary Level (Grades 3–4)
Targeting students aged 8–10.
Focus: 30 questions in 20 minutes.
Words commonly found in 3rd/4th-grade literature and social studies (e.g., Massive, Ancient, Fragile)
Identifying if a word is a noun, verb, or adjective to find its match.
Using basic sentences to determine which word “fits” best.
Hot : Cold :: Up : Down
Finger : Hand :: Toe : Foot
Painter : Brush :: Carpenter : Hammer
Apple : Fruit :: Carrot : Vegetable
Middle Level (Grades 5–7)
Targeting students aged 10–13.
Focus: 60 questions in 30 minutes (30 Synonyms, 30 Analogies).
Introduction of “Tier 2” academic words (e.g., Alleviate, Nebulous, Resilient).
Testing words that have several definitions (e.g., Grave meaning a burial site vs. Grave meaning serious).
Using prefixes (e.g., un-, pre-, re-) and suffixes (e.g., -less, -ful) to decode meanings.
Chilly : Freezing :: Warm : Hot
Glass : Brittle :: Rubber : Flexible
Famine : Hunger :: Rain : Flood
Recipe : Chef :: Blueprint : Architect
Upper Level (Grades 8–11)
Targeting students aged 13–17
60 questions in 30 minutes (30 Synonyms, 30 Analogies).
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Words often found in classical literature or GRE-style prep (e.g., Recalcitrant, Ephemeral, Pragmatic)
The test often avoids the primary definition of a word to see if the student knows the obscure one (e.g., Pedestrian meaning “dull/ordinary” rather than “walker”).
Deep reliance on Greek and Latin roots (e.g., anthrop-, bene-, mal-, chron-) to solve high-difficulty questions.
Coward : Bravery :: Philanthropist : Greed
Lighthouse : Guidance :: Dam : Containment
Prune : Tree :: Edit : Manuscript
Seed : Plant :: Foundation : Building
KUMATICS EDUCATION
KUMATICS EDUCATION
PSAT
MATHS
PSAT 8/9 (Grades 8–9)
Targeting students aged 13-14.
Focus: Mastering the “Heart of Algebra” and foundational proportions.
Solving for x in one-variable equations
Understanding y = mx + b and interpreting slope/intercepts in context.
Solving two linear equations using substitution or elimination.
Graphing and solving linear inequalities.
Using rates, ratios, and percentages to solve “real-world” problems.
Converting measurements (e.g., feet to meters, hours to seconds).
Reading tables, scatterplots, and line graphs.
Basic understanding of mean, median, and range.
Basic formulas for rectangles, triangles, and prisms
Understanding vertical, supplementary, and complementary angles.
Introduction to the Pythagorean Theorem (a^2 + b^2 = c^2)
PSAT 10 & PSAT/NMSQT (Grades 10–11)
Targeting students aged 15-17.
Focus: Increasing complexity in Algebra and the introduction of “Passport to Advanced Math.”
Systems with no solution, one solution, or infinite solutions.
Creating equations from dense text descriptions.
Solving |x – a| = b and interpreting it as distance.
Calculating probability based on table data.
Conceptual understanding (not calculation) of data spread.
Understanding margin of error and sample bias in surveys.
Distinguishing between linear growth (y = mx + b) and exponential growth (y = ab^x).
Factoring, completing the square, and using the Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$.
Finding the vertex and intercepts of a quadratic graph.
Working with radicals, rational exponents ($x^{a/b}$), and polynomial division.
Composite functions like $f(g(x))$.
SOH CAH TOA (Sine, Cosine, Tangent).
(x – h)^2 + (y – k)^2 = r^2.
Calculating the length of a “slice” of a circle using radians or degrees.
Operations with i (where i^2 = -1).
KUMATICS EDUCATION
Reading & Writing
PSAT 8/9 (Grades 8–9)
Targeting students aged 13-14.
Focus: Clear, direct information and foundational grammar.
Identifying the main point of a short informational text.
Choosing the quote that best supports a researcher’s claim.
Interpreting simple tables or bar graphs to complete a statement.
Identifying the meaning of a word based on surrounding clues (Grade 8-9 tier).
Explaining what a specific sentence does (e.g., “It introduces a counterargument”).
Basic punctuation (commas, periods), subject-verb agreement, and verb tense.
Choosing the best connecting word (However, Therefore, For example).
Taking a list of “notes” provided and choosing the sentence that achieves a specific goal (e.g., “Summarize the findings of the study”).
PSAT 10 & PSAT/NMSQT (Grades 10–11)
Targeting students aged 15-16.
Focus: Subtle logic, sophisticated vocabulary, and complex sentence structures.
Making a logical leap based on the text (the answer is not explicitly stated but is the only logical conclusion).
Interpreting scatterplots with best-fit lines or multi-variable tables.
Reading two very short snippets (Text 1 and Text 2) and determining how the authors would agree or disagree with each other.
Testing words that have “academic” nuance (e.g., underscore, corroborate, ambivalent).
Identifying a narrator’s specific attitude toward a subject in literary excerpts.
Advanced use of semicolons, colons, and dashes to join complex thoughts.
Ensuring descriptive phrases are next to the correct noun (avoiding “dangling modifiers”).
Mastering pronoun-antecedent agreement and parallel structure in long lists.