أوراق عمل الوحدة السابعة Rational Functions والتاسعة Trigonometric Functions بحسب الصف الثاني عشر العام في مادة الرياضيات – الفصل الثالث

أوراق عمل الوحدتين السابعة و التاسعة

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Chapter 7: Rational Functions
Chapter 9: Trigonometric Functions
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Chapter 7: Rational Functions

M7L1 – Multiplying and Dividing Rational Expressions

· Simplify rational expressions.
· Multiply and divide rational expressions.
· Simplify complex fractions.

M7L2 – Adding and Subtracting Rational Expressions

· Add and subtract rational expressions (like and unlike denominators).
· Simplify complex fractions using the LCD.

M7L3 – Graphing Reciprocal Functions

· Identify excluded values (vertical asymptotes).
· Graph reciprocal functions using tables and transformations.
· Determine domain, range, and asymptotes.

M7L4 – Graphing Rational Functions

· Graph rational functions with vertical and horizontal asymptotes.
· Identify oblique (slant) asymptotes.
· Recognize point discontinuity (holes).

M7L6 – Solving Rational Equations and Inequalities

· Solve rational equations in one variable.
· Identify extraneous solutions.
· Solve rational inequalities.
· Real-life applications: mixture, work, and distance problems.

Chapter 9: Trigonometric Functions

M9L1 – Angles and Angle Measure

· Draw angles in standard position.
· Find positive and negative coterminal angles.
· Convert between degrees and radians.
· Find arc length using s = r\theta .

M9L2 – Trigonometric Functions of General Angles

· Find trig values for acute angles in right triangles.
· Find trig values for general angles using a point (x, y).
· Use reference angles to evaluate trig functions.

M9L3 – Circular and Periodic Functions

· Use the unit circle to find \sin\theta and \cos\theta.
· Find exact trig values for special angles.
· Identify the period of a periodic function.

M9L4 – Graphing Sine and Cosine Functions

· Identify amplitude, midline, and period from graphs and equations.
· Graph sine and cosine functions.
· Model real-world situations (springs, electricity, Ferris wheels).

M9L5 – Graphing Other Trigonometric Functions

· Graph tangent functions (period, asymptotes, zeros).
· Graph reciprocal trig functions: cosecant, secant, cotangent.
· Identify asymptotes, relative extrema, and midline.

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