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Term 1

Unit 1 Numbers and operations on them: powers of powers and exponential equations; Unit 2 Algebra: the quadratic function, real zeros of polynomial functions, rational algebraic functions (domain, common domain, equal functions) and operations on rational algebraic fractions; Unit 3 Geometry: similarity of polygons and of triangles, dilation, trigonometric ratios of an acute angle and of the special angles, slopes of parallel and perpendicular lines, equation of the straight line; Unit 4 Statistics: measures of dispersion (range, interquartile range, standard deviation)

1Powers of powers and exponential equationsPowers of powers and exponential equations: the laws of exponents for real bases and integer exponents, and equations of the form a^x = b 2The quadratic functionThe quadratic function: standard form, vertex and axis of symmetry, vertex form, graph and maximum or minimum value 3Zeros of polynomial functionsReal zeros of polynomial functions: degree, zeros from an equation and from a graph, finding an unknown coefficient 4Rational algebraic functionsRational algebraic functions: domain, simplifying, zeros and solving f(x) = k 5Common domain and equal rational functionsCommon domain and equivalent rational algebraic functions 6Operations on rational algebraic fractionsOperations on rational algebraic fractions: add, subtract, multiply, divide, inverses and properties 7Similarity of polygonsSimilarity of polygons: conditions, similarity ratio, special shapes and perimeters 8Similarity of trianglesSimilarity of triangles: the AA, SSS and SAS cases, right triangles and real heights 9DilationDilation: centre and factor, enlargement and reduction, images of triangles and of points in the coordinate plane 10Trigonometric ratios of an acute angleTrigonometric ratios of an acute angle: sine, cosine, tangent, complementary angles and side lengths 11Exact and calculator ratiosTrigonometric ratios of special angles: 30°, 45°, 60°, the calculator, finding the angle and heights 12Slope of a straight lineSlope of a straight line: inclination angle, parallel lines, perpendicular lines and collinear points 13The equation of a straight lineThe equation of a straight line: slope and y-intercept, point and slope, two points, standard form and applications 14Dispersion and standard deviationMeasures of dispersion: range, interquartile range and standard deviation for a list, a frequency table and a table with class intervals 15Term 1 reviewTerm 1 review

☰ Year plan · Mathematics

Egypt›Preparatory 3›Mathematics›Week 5

Common domain and equal rational functions

Week 5 · Common domain and equivalent rational algebraic functions · 3 lessons

Lesson 1 Lesson 2 Lesson 3 Quiz8 Homework5

← PreviousWeek 5 · Equal only on the common domain: proving f(x) = g(x) there, and showing f ≠ g Next →Week 5 · Homework

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