Type the equation, read the graph
- Enter the equation exactly as written.
- Read intercepts, maxima, minima, and asymptotes straight off the curve.
- Click any feature to see its coordinates.
Strategy Hub
The fastest, most efficient strategies top SAT and ACT tutors use. Skim a card, learn one rule or trick, then practice it on a real question. Pesty, your AI study buddy, references these same strategies in every hint.
SAT Math · Desmos shortcuts
Desmos is built into the digital SAT. Use it on most algebra, systems, and quadratic problems — it's faster than solving by hand.
Solve systems by graphing
- Put each equation on its own line.
- Click the intersection — Desmos prints (x, y).
- That intersection point IS the solution to the system.
Use a table to evaluate values
- Add a table for f(x).
- Type the candidate x-values down the left column.
- Desmos fills in f(x) — pick the one that matches.
Create sliders for unknown constants
- Type a=1 (or k, b, c). Desmos auto-makes a slider.
- Drag until the graph matches the described behavior.
- Read the constant straight off the slider.
Quadratic roots from x-intercepts
- Graph the quadratic.
- Click each x-intercept to read the root.
- Skip factoring and the quadratic formula entirely.
Default to Desmos for algebra
- Most algebra, systems, and quadratic items are faster on Desmos.
- Reach for paper only when the question is purely conceptual.
- Saves time you can spend on the harder back-half questions.
SAT & ACT · Grammar rules
Almost every writing item is one of these rules in disguise. Name the rule first, then pick the answer.
Subject–verb agreement
- Singular subject → singular verb; plural → plural.
- Ignore prepositional phrases between subject and verb.
- The subject is never inside a phrase like 'of the players'.
Pronoun–antecedent agreement
- Pronoun must match its noun in number.
- If it could refer to two nouns, it's ambiguous — wrong.
- Watch for collective nouns (team, group, jury) — usually singular.
Comma rules
- List of 3+: commas between items.
- After an introductory phrase.
- Around nonessential clauses (info you could cut).
- Before FANBOYS (for, and, nor, but, or, yet, so) joining two independent clauses.
Semicolon vs. colon
- Semicolon joins two complete sentences with no conjunction.
- Colon introduces a list, definition, or explanation.
- What comes before a colon must itself be a complete sentence.
Apostrophes and possessives
- Singular possessive: add 's.
- Plural ending in -s: add only an apostrophe.
- Its = possessive. It's = it is. Their / there / they're.
Dangling and misplaced modifiers
- The word right after an opening modifier must be what it describes.
- 'Running late, the bus was missed' — wrong; the bus wasn't running late.
- Fix: put the right noun right after the comma.
Parallel structure
- Items in a list or comparison share the same form.
- noun/noun/noun, or -ing/-ing/-ing, or to + verb / to + verb.
- Mismatched forms are almost always wrong.
Verb-tense consistency
- Stay in one tense within a sentence or paragraph.
- Only switch when the time frame actually changes.
- Random tense shifts are a classic trap.
Transition-word logic
- Pick by meaning, not sound.
- Addition (also), contrast (however), cause (therefore), example (for instance).
- Read the sentence before and after — the relationship picks the word.
Concision and redundancy
- Shorter is almost always right when meaning is preserved.
- Cut duplicate ideas ('annual yearly tradition').
- Cut filler and phrases that repeat a word already used.
Reading · Tactics that work
Don't read the passage like a novel. Read with a purpose.
Read the question first
- Know what you're hunting for before you read the passage.
- Lets you skim past unrelated paragraphs.
- Cuts reading time roughly in half on detail questions.
Hunt for textual evidence
- Every correct answer is supported by specific lines.
- If you can't point at the words that prove it, it's not the answer.
- Underline the evidence before you choose.
Eliminate extreme and absolute answers
- Watch for always, never, only, must, all, none.
- Passages rarely make absolute claims; answers that do are usually wrong.
- Prefer measured language: often, suggests, may, tends to.
Pacing · Time management per section
Pacing wins more points than any trick. Know your per-question budget cold.
SAT Reading & Writing
- About 1 minute 11 seconds per question on each module.
- Don't camp on one item — flag it and come back.
- Easier items appear first in module 1; module 2 difficulty adapts.
SAT Math
- About 1 minute 35 seconds per question.
- If a question is faster on Desmos, do it on Desmos.
- Flag anything you'd spend more than 2 minutes on — return after the last item.
ACT English
- About 36 seconds per question. Move fast.
- Most items are short — name the rule and answer.
- If two answers look right, the shorter one usually wins.
ACT Math
- About 1 minute per question across 60 items.
- Skip and circle anything that stalls you past ~90 seconds.
- Plug in numbers and back-solve when algebra gets messy.
ACT Reading
- About 8 minutes 45 seconds per passage including questions.
- Skim the passage, then answer with line references.
- Save the hardest passage for last.
ACT Science
- About 53 seconds per question.
- Most questions are data-lookup — go to the figure first.
- Read the experiment summary only when a question forces you to.
Quick references
Open these any time — they're also available from the Reference button during a test.
Desmos Cheat Sheet
The fastest way to handle most SAT Math algebra, systems, and quadratics.
Type the equation, read the graph
Paste or type the equation exactly as written. Drag the graph or pinch-zoom to read intercepts, maxima, and minima straight off the curve.
Systems → graph both, click the intersection
Enter each equation on its own line. Click where the curves cross — Desmos prints the (x, y) intersection coordinates. That is the solution.
Tables to evaluate values fast
Add a table for any function f(x). Type x-values in the left column and Desmos fills the f(x) column. Great for "which value satisfies…" questions.
Sliders for unknown constants
Type k=1 (or a, b, c). Desmos auto-creates a slider. Drag it until the graph matches the described behavior — solved.
Quadratic roots = parabola x-intercepts
Graph the quadratic. Click each x-intercept to read the root. No factoring, no quadratic formula needed.
Default to Desmos
For most algebra, systems, and quadratic problems, Desmos is faster than hand-solving. Reach for paper only when the question is purely conceptual.
Grammar Rules Reference
The exact rules SAT and ACT writing items test, over and over.
Subject–verb agreement
Singular subjects take singular verbs; plurals take plural verbs. Ignore prepositional phrases between subject and verb — the subject is never inside "of ____".
Pronoun–antecedent agreement
A pronoun must match its noun in number and clarity. If the antecedent is singular, the pronoun is singular; if it could refer to two nouns, the sentence is ambiguous.
Comma rules
Use commas: between items in a list of three or more; after an introductory phrase; around a nonessential clause; and before a FANBOYS conjunction (for, and, nor, but, or, yet, so) that joins two independent clauses.
Semicolon vs. colon
A semicolon joins two complete sentences with no conjunction. A colon introduces a list, definition, or explanation — and what comes before the colon must itself be a complete sentence.
Apostrophes and possessives
Singular possessive: add 's. Plural possessive ending in -s: add only an apostrophe. "Its" = possessive, "it's" = it is. "Their/there/they're" — keep them straight.
Dangling and misplaced modifiers
The word right after an opening modifier must be what that modifier describes. "Running late, the bus was missed" is wrong — the bus wasn't running late.
Parallel structure
Items in a list, comparison, or paired construction must share the same grammatical form: noun/noun/noun, or -ing/-ing/-ing, or to + verb / to + verb.
Verb-tense consistency
Keep tense steady within a sentence and paragraph unless the time frame actually changes. Switching tenses without a reason is a classic trap.
Transition-word logic
Pick the transition that matches the logical relationship: addition (also), contrast (however), cause (therefore), example (for instance). Read the sentences before and after — the meaning, not the sound, picks the answer.
Concision and redundancy
Shorter is almost always right when the meaning is preserved. Cut duplicated ideas ("annual yearly tradition"), filler, and phrases that repeat a word already in the sentence.