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Questions and Answers
What is the simplified form of the algebraic expression $(3x + 5) + (2x - 3)$?
Which of the following is a characteristic of a monomial algebraic expression?
What is the value of x in the quadratic equation $x^2 + 5x + 6 = 0$ when solved using the factoring method?
What is the formula for the standard deviation of a dataset?
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What is the trigonometric ratio of an angle $A$ in a right-angled triangle with an opposite side of length $3$ and a hypotenuse of length $5$?
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What is the equation of the line of best fit for a set of data points?
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What is the nature of the roots of the quadratic equation $x^2 - 4x + 4 = 0$?
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What is the formula for the cosine of an angle $A$ in a right-angled triangle?
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What is the measure of central tendency that is most affected by outliers?
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What is the identity that relates the sine and cosine of an angle $A$?
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Study Notes
Algebraic Expressions
- Definition: An algebraic expression is a combination of variables, constants, and mathematical operations.
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Types of Expressions:
- Monomials: Expressions with one term (e.g. 2x)
- Binomials: Expressions with two terms (e.g. 2x + 3)
- Polynomials: Expressions with more than two terms (e.g. 2x^2 + 3x - 1)
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Operations:
- Addition and subtraction of like terms
- Multiplication of algebraic expressions
- Factorization of algebraic expressions
- Simplification: Combining like terms to simplify an expression
- Expanding and Factorizing: Expanding products of algebraic expressions and factorizing expressions into their simplest form
Quadratic Equations
- Definition: A quadratic equation is a polynomial equation of degree two (e.g. ax^2 + bx + c = 0)
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Types of Quadratic Equations:
- Monic quadratic equations (a = 1)
- Non-monic quadratic equations (a ≠1)
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Solving Quadratic Equations:
- Factoring method
- Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
- Graphical method
- Nature of Roots: Understanding the nature of roots (real, rational, or complex) based on the discriminant (b^2 - 4ac)
Statistics and Graphs
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Measures of Central Tendency:
- Mean
- Median
- Mode
- Range
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Measures of Dispersion:
- Variance
- Standard deviation
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Types of Graphs:
- Bar graphs
- Histograms
- Pie charts
- Line graphs
- Interpreting Graphs: Understanding and interpreting statistical data from graphs
Trigonometry
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Angles and Triangles:
- Measuring angles in degrees
- Understanding trigonometric ratios (sine, cosine, and tangent)
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Trigonometric Ratios:
- Sine (sin): opposite side / hypotenuse
- Cosine (cos): adjacent side / hypotenuse
- Tangent (tan): opposite side / adjacent side
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Identities and Formulas:
- Pythagorean identity: sin^2(A) + cos^2(A) = 1
- Trigonometric formulas for triangles
- Solving Triangles: Using trigonometric ratios to solve problems involving right-angled triangles
Algebraic Expressions
- Algebraic expressions combine variables, constants, and mathematical operations
- Monomials have one term (e.g. 2x)
- Binomials have two terms (e.g. 2x + 3)
- Polynomials have more than two terms (e.g. 2x^2 + 3x - 1)
- Add and subtract like terms
- Multiply algebraic expressions
- Factorize algebraic expressions
- Simplify expressions by combining like terms
- Expand and factorize expressions to their simplest form
Quadratic Equations
- Quadratic equations are polynomial equations of degree two (e.g. ax^2 + bx + c = 0)
- Monic quadratic equations have a leading coefficient of 1 (a = 1)
- Non-monic quadratic equations have a leading coefficient not equal to 1 (a ≠1)
- Solve quadratic equations using factoring, quadratic formula, or graphical method
- Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
- Understand the nature of roots based on the discriminant (b^2 - 4ac)
Statistics and Graphs
- Mean, median, mode, and range are measures of central tendency
- Variance and standard deviation are measures of dispersion
- Bar graphs, histograms, pie charts, and line graphs are types of statistical graphs
- Interpret statistical data from graphs to understand central tendency and dispersion
Trigonometry
- Angles can be measured in degrees
- Sine, cosine, and tangent are trigonometric ratios
- Sine (sin): opposite side / hypotenuse
- Cosine (cos): adjacent side / hypotenuse
- Tangent (tan): opposite side / adjacent side
- Pythagorean identity: sin^2(A) + cos^2(A) = 1
- Use trigonometric formulas to solve problems involving right-angled triangles
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Description
Learn about algebraic expressions, including definitions, types, and operations. Understand monomials, binomials, and polynomials, as well as addition, subtraction, multiplication, and factorization.
