ورقة مفاهيم Differential and integral calculus للصف الثالث الثانوي 2026.. حملها الآن pdf

أعلنت وزارة التربية والتعليم والتعليم الفني رسميا إتاحة ورقة مفاهيم Differential and integral calculus and solid geometry للصف الثالث الثانوي عبر موقعها الإلكتروني المعتمد لمساعدة طلاب مدارس اللغات في مراجعة القواعد والاشتقاقات الرياضية المعقدة المقررة في منهج الرياضيات البحتة وتوفير الدعم التعليمي اللازم لهم قبيل انطلاق ماراثون امتحانات نهاية العام الدراسي.

ورقة مفاهيل تفاضل وتكامل لغات تالتة ثانوي 2026

تهدف وزارة التربية والتعليم من خلال نشر هذه الكراسات والمجلدات الرسمية إلى توفير مرجع قانوني موحد للطلاب يعفيهم من حفظ المعادلات والاشتقاقات الرياضية الطويلة داخل لجان الامتحانات، حيث يتضمن المحتوى المفرغ بدقة من الأوراق الرسمية المعتمدة في ورقة المفاهيم:

Pure Mathematics Differential & Integral Calculus
Unit One: Differentiation and it's Applications
Derivatives of the trigonometric function
Function: Sine function sin x -> Derivative: cos x
Function: Cosine function cos x -> Derivative: - sin x
Function: Tangent function tan x -> Derivative: sec^2 x
Function: Cotangent function cot x -> Derivative: - csc^2 x
Function: Secant function sec x -> Derivative: sec x tan x
Function: Cosecant function csc x -> Derivative: - csc x cot x
Implicit Differentiation

Differentiating the implicit relation f(x, y) = 0 requires to differentiate both sides of the relation with respect to one of the two variables x or y according to the chain rule to get dy/dx or dx/dy respectively.
Parametric Differentiation
The curve given in the parametric form y = f(t) , x = g(t), then dy/dx = dy/dt * dt/dx = dy/dt / dx/dt where f and g are two differentiable functions with respect to t
Higher - Derivatives of a functions
If y = f(x) where f is a differentiable function with respect to x, then the derivatives starting from the second derivative (if found) are called the higher derivatives and they are denoted the symbol d^2y/dx^2 or y'' , the third derivative is denoted by the symbol y''' or d^3y/dx^3 and the n^th derivatives is denoted by the symbol y^(n) or d^ny/dx^n or f^(n)(x) where n is a positive integer number.
The two equations of the tangent and the normal to a curve
If m the slope of the tangent to the curve y = f(x) at the point (x_1 , y_1) which lies on it, then: the equation of the tangent to the curve at point (x_1 , y_1) is:
y - y_1 = m (x - x_1)
the equation of the normal at point (x_1 , y_1) is:

y - y_1 = -1/m (x - x_1)
Related time Rates
If y = f(x) , x changes over time t , then y changes over time t.
i.e. y is a composite function of the time t and dy/dt = dy/dx * dx/dt and this relation relates the time rate of change x with the time rate of change y.
The rate is positive if the variable increases with the increase of time.
The rate is negative if the variable decreases with the increase of time.
Pure Mathematics Algebra and solid geometry concepts
Unit one permutations, Combination and Binomial theorem
(1) ^nP_r = n(n - 1)(n - 2) ... (n - r + 1) , n >= r , n in Z^+
(2) ^nP_r = |n / |n-r
(3) |1 = |0 = 1
(4) ^nC_r = ^nP_r / |r = |n / ( |r * |n-r )
(5) ^nC_n = ^nC_0 = 1
(6) ^nC_r = ^nC_n-r
(7) If ^nC_X = ^nC_Y then X = Y or X + Y = n
(8) ^nC_r / ^nC_r-1 = (n - r + 1) / r
(9) ^nC_r + ^nC_r-1 = ^+1C_r
(10) (X + a)^n = X^n + ^nC_1 * X^(n-1) * a + ^nC_2 * X^(n-2) * a^2 + ... + a^n
(X - a)^n = X^n - ^nC_1 * X^(n-1) * a + ^nC_2 * X^(n-2) * a^2 - ... + (-a)^n
(11) (X + a)^n + (X - a)^n = 2(Sum of odd ordered terms) from (X + a)^n
(12) (X + a)^n - (X - a)^n = 2(Sum of even ordered terms) from (X + a)^n
(13) (1 +- X)^n = 1 +- ^nC_1 * X + ^nC_2 * X^2 +- ^nC_3 * X^3 + ... + (+- X)^n
(14) The general term in the expansion of (X + a)^n is T_r+1 = ^nC_r * X^(n-r) * a^r
The middle term in the expansion (X + a)^n
(a) If n is odd , there are two middle terms of orders (n+1)/2 , (n+3)/2
(b) If n is even , there is one middle term of order (n+2)/2
(15) In the expansion of (X + a)^n, The ratio between two consecutive terms
T_r+1 / T_r = [(n - r + 1) / r] * (a / X)