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EST High-Frequency Grammar Rules and Math Formulas

Core grammar conventions, punctuation rules, algebraic relationships, and geometric formulas for the Egyptian Scholastic Test (EST I & II).

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Semicolon Usage Rule
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1
Semicolon Usage Rule
A semicolon connects two closely related independent clauses without a coordinating conjunction (Clause 1; Clause 2).
2
Comma Splice Error and Fix
Joining two independent clauses with only a comma is an error. Fix with: period, semicolon, or comma + coordinating conjunction (FANBOYS).
3
Dangling Modifier Rule
An introductory participial phrase must be followed immediately by the noun that actually performs the action.
4
Non-Restrictive vs Restrictive Clauses
Non-restrictive (non-essential) clauses are enclosed by commas. Restrictive (essential) clauses take no commas and often use 'that'.
5
Subjunctive Mood for Contrary-to-Fact Conditions
Use 'were' instead of 'was' with singular subjects for hypothetical or unreal conditions ('If I were you...').
6
Faulty Comparison Rule
Compare equivalent entities. Use 'that of' (singular) or 'those of' (plural) to avoid comparing a feature to a whole object.
7
Colon Usage Rule
A colon must be preceded by a complete independent clause. Never place a colon directly after a verb or preposition.
8
Fewer vs Less Distinction
'Fewer' is used with plural countable nouns (fewer books). 'Less' is used with singular uncountable mass nouns (less water).
9
Slope Formula Between Two Points
m = (y2 - y1) / (x2 - x1). Parallel lines have m1 = m2; perpendicular lines have m1 * m2 = -1.
10
Standard Form and Vertex of a Parabola
y = ax^2 + bx + c has vertex x-coordinate x_v = -b / (2a). Vertex form is y = a(x - h)^2 + k with vertex (h, k).
11
Discriminant (Delta) and Number of Real Solutions
Delta = b^2 - 4ac. If Delta > 0: 2 distinct real roots; if Delta = 0: 1 repeated real root; if Delta < 0: 2 complex roots (no real x-intercepts).
12
Equation of a Circle in the xy-Plane
(x - h)^2 + (y - k)^2 = r^2, with center (h, k) and radius r.
13
Exponential Growth and Decay Formula
A(t) = P (1 + r)^t for growth; A(t) = P (1 - r)^t for decay, where r is the fractional rate.
14
Fundamental Trigonometric Identity
sin^2(theta) + cos^2(theta) = 1, and tan(theta) = sin(theta) / cos(theta).
15
Special Right Triangle Ratios (30-60-90 and 45-45-90)
30-60-90: sides in ratio 1 : sqrt(3) : 2. 45-45-90: sides in ratio 1 : 1 : sqrt(2).
16
Area of an Equilateral Triangle
Area = (sqrt(3) / 4) * s^2, where s is side length.
17
Sum of Interior Angles of an n-Sided Polygon
Sum = (n - 2) 180 degrees. Each interior angle of a regular n-gon is [(n - 2) 180] / n.
18
Arc Length and Sector Area Formulas
Arc length s = (theta / 360) 2pir. Sector Area = (theta / 360) pi*r^2 (for theta in degrees).
19
Volume of a Cylinder and Cone
V_cylinder = pi r^2 h. V_cone = (1/3) pi r^2 * h.
20
Surface Area and Volume of a Sphere
Surface Area = 4 pi r^2. Volume = (4/3) pi r^3.
21
Empirical Rule for Normal Distribution (68-95-99.7)
68% of data lies within +/-1 sigma, 95% within +/-2 sigma, and 99.7% within +/-3 sigma of the mean mu.
22
Logarithmic Product, Quotient, and Power Rules
log(xy) = log x + log y; log(x/y) = log x - log y; log(x^k) = k * log x.
23
System of Linear Equations: Inconsistent vs Coincident
Parallel lines (same slope, different intercept) = no solution. Identical lines (same slope and intercept) = infinite solutions.
24
Triangle Inequality Theorem
The length of any side must be strictly less than the sum and strictly greater than the difference of the other two sides.
25
Distance and Midpoint Formulas in 2D
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2). Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Egyptian Scholastic Test (EST) in Egypt

In Egypt, Egyptian Scholastic Test (EST) is part of: University entrance.

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