EmSAT Achieve cheat sheet

Arabic is written right to left; letters connect within a word but not after the six non-connecting letters: ا د ذ ر ز و.

The hamza seats follow vowel strength: kasra (ي), damma (و), fatha (ا); a hamza on the line occurs after a long vowel or sukun.

Sun letters (الحروف الشمسية) assimilate the definite article's lam in pronunciation: الشمس is pronounced ash-shams; moon letters keep the lam audible.

Verb–subject agreement: a verb preceding its subject stays singular regardless of subject number (جاء الطلاب).

Case endings: nominative ـُ, accusative ـَ, genitive ـِ; dual raises with ـانِ in nominative and takes ـينِ elsewhere.

Broken plurals (جمع التكسير) are non-human and take feminine singular agreement on verbs and adjectives.

Root-and-pattern analysis: most words reduce to a three-consonant root plus a morphological pattern that fixes meaning and part of speech.

Idafa (إضافة) marks possession by juxtaposition; the first noun takes no definite article and no tanwin.

Present perfect (has/have + past participle) links past action to present relevance; simple past is used with a finished, specific past time.

The passive is formed with be + past participle; only transitive verbs can be passivized.

Subject–verb agreement ignores prepositional phrases: the number of the head noun controls the verb.

Relative clauses: use who/whom for people, which/that for things; a non-defining clause takes commas and cannot use that.

Conditionals: first (if + present, will), second (if + past, would), third (if + had + participle, would have + participle).

Parallel structure requires matching grammatical forms in lists joined by and/or/but.

Inference questions require a conclusion supported by the passage but not stated word for word.

A main-idea answer must cover the whole passage, not one paragraph's detail.

Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a; the discriminant b² − 4ac gives two, one, or no real roots.

Slope m = (y₂ − y₁)/(x₂ − x₁); parallel lines share m, perpendicular lines have m₁·m₂ = −1.

Exponent rules: a^m · a^n = a^(m+n); (a^m)^n = a^(mn); a^(−n) = 1/a^n.

Distance = √((x₂ − x₁)² + (y₂ − y₁)²); midpoint averages the coordinates.

Area formulas: triangle ½bh; circle πr²; trapezoid ½(b₁ + b₂)h; cylinder volume πr²h.

Pythagorean theorem a² + b² = c² applies only to right triangles; c is the hypotenuse.

Percent change = (new − old)/old × 100; percent increase followed by equal decrease does not return to the original value.

Mean is sensitive to outliers, median is not; standard deviation measures spread about the mean.

Newton's second law F = ma; weight equals mg, distinct from mass, which is invariant.

Speed = distance/time; acceleration is the rate of change of velocity and can be negative while speed increases.

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; energy is conserved but transforms.

Ohm's law V = IR; series resistors add, parallel resistors combine as 1/R = 1/R₁ + 1/R₂.

pH below 7 is acidic, 7 neutral, above 7 basic; each unit represents a tenfold change in hydrogen-ion concentration.

Covalent bonds share electrons between nonmetals; ionic bonds transfer electrons between metal and nonmetal.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts.

DNA base pairing: adenine–thymine, guanine–cytosine; the sequence is transcribed to mRNA then translated to protein.

Cell theory: cells are the basic unit of life, arise from existing cells, and all organisms are made of cells.