MATH 190 KHAN ACADEMY VIDEOS

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1 MATH 10 KHAN ACADEMY VIDEOS MATTHEW AUTH 11 Order of operations 1 The Real Numbers (11) Example 11 Worked example: Order of operations (PEMDAS) (7 + 3 (5 2)) Rational + Irrational Example 12 Classifying numbers: rational and irrational Which of the following real numbers are irrational? 8 13 Comparing Fractions 2, π, 50, 0325, 777, 81 2 Example 13 Comparing fractions 2 (unlike denominators) compare the two fractions and 6 14 Adding and subtracting fractions Example 14 Adding fractions with unlike denominators Exponents and Radicals (12) 21 Exponents (skip everything after quiz 3) Example 21 Intro to exponents Example 22 Simplifying square roots Example 23 Simplifying a cube root Find Use <, >, or = to Example 24 Exponent properties with products Use laws of exponents to rewrite (1) (2) (3x) 3 (3) (a 3 ) 4 (4) ( 2xy 2) ( 1x 2 y ) 2 ( 3x 2 y 2) (5) 7 0 Example 25 Exponent properties with quotients Use laws of exponents to rewrite 3 (1) 4 ( 3 10 (2) (3) a 3 b 4 a 2 b ) 3 25xy 6 20y 5 x 2 1

2 2 MATTHEW AUTH Example 26 Powers of products and quotients (integer exponents) Use laws of exponents to rewrite (1) ( ) 2 ( ) 7 2 (2) Rational Exponents Example 27 Evaluating fractional exponents Evaluate (1) (2) (3) ( 8 27 ) 2 3 Example 28 Evaluating fractional exponents: negative unit-fraction Evaluate (1) 1 2 (2) ( 27) 1 3 Example 2 Evaluating fractional exponents: fractional base Evaluate (1) ( 25 (2) ( ) 1 2 ) 1 4 Example 210 Evaluating quotient of fractional exponents Evaluate Example 211 Evaluating mixed radicals and exponents Evaluate ( 5 6 ) 3 Example 212 Simplify higher-index roots Simplify 6 64x 8 31 Polynomials 3 Algebraic Expressions (13) Example 31 The parts of polynomial expressions Identify the terms of 3x 2 8x+7 Example 32 Simplify polynomials Simplify 3x 2 8x x 3 x 2 + 8x 3 Example 33 Adding and subtracting multiple polynomials Simplify (x 3 + 3x 6) + ( 2x 2 + x 2) (3x 4) Example 34 Multiplying monomials by polynomials Multiply 4x 2 ( 3x x 7 ) Example 35 Squaring binomials of the form (ax + b) 2 Simplify (7x + 10) 2 32 Factoring Example 36 More examples of factoring quatratics as (x + a)(x + b) Factor (1) x x + (2) x x + 50 (3) x 2 11x + 24 (4) x 2 + 5x 14 (5) x 2 x 56 (6) x 2 5x + 24 Example 37 Difference of squares intro Factor (1) x

3 MATH 10 KHAN ACADEMY VIDEOS 3 (2) y 2 25 (3) 121 b 2 Example 38 Factoring difference of squares: leading coefficient 1 Factor45x Example 3 Perfect square factorization Factor (1) x 2 + 6x + (2) a a + 4 Example 310 Strategy in factoring quadratics Factor (1) 6x 2 + 3x (2) 4x 2 4x 48 (3) 3x x + 75 (4) 7x 2 63 (5) 2x 2 + 7x Rational Expressions (14) Example 41 Intro to rational expression simplification Simplify x2 +6x+5 x 2 x 2 Example 42 Simplifying rational expressions: common monomial factors Simplify (1) 14x2 +7x 14x (2) 17z3 +17z 2 34z 3 51z 2 Example 43 Multiplying rational expressions Simplify a2 4 a 2 1 a+1 a+2 Example 44 Dividing rational expressions Simplify 2p+6 p p+20 Example 45 Adding rational expressions: unlike denominators Simplify as one fraction 5x 2x 3 + 4x2 3x+1 Example 46 Subtracting rational expressions Find the difference Express the a 2 answer as a simplified rational expression and state the domain a+2 a 3 a 2 +4a+4 51 Solving Equations 5 Equations (15) Example 51 Linear equations with parenthesis Solve (x 6) = 3(4x + 6) for x Example 52 Worked example: number of solutions to equations Solve 8(3x + 10) = 28x 14 4x for x 52 Solving quadratics by taking square roots Example 53 Solving quadratics by taking square roots Solve (1) 2x = 75 (2) 2(x + 4) 2 = Solving quadratics by factoring Example 54 Solve the following (1) s 2 2s 35 = 0 (2) 6x 2 120x = 0 (3) (2x 3) 2 = 4x 6

4 4 MATTHEW AUTH 54 Completing the square Example 55 Solve (1) x 2 4x = 5 (2) 10x 2 30x 8 = 0 Example 56 Worked example: Rewriting expression by completing the square Rewrite x x + in the form (x + a) 2 + b Example 57 Worked example: Solving equations by completing the square Solve x 2 2x 8 = 0 by completing the square Example 58 Worked example: Completing the square (leading coefficient 1) Solve 4x x 300 = 0 by completing the square 55 Solving Rational Equations Example 5 Equations with one rational expression Solve 14x+4 3x 2 = 8 Example 510 Equation with one rational expression (advanced) Solve x 2 x2 4 x 2 = 4 Example 511 Equation with rational expressions Solve x2 10x+21 3x+12 = x 5 x 4 Example 512 Equation with rational expressions (example 2) Solve 2x Solving square-root equations x 1 = 3 x+1 Example 513 Intro to square-root equations and extraneous solutions Solve x = 2x 6 Example 514 Solving square-root equations (basic) Solve 5x 2 8 = 2x for x Example 515 Solving square-root equations: one solution Solve 3 + 5x + 6 = 12 for x Example 516 Solving square-root equations: two solution Solve 6+3w = 2w + 12 for w Example 517 Solving square-root equations: no solutions Solve 3x 7+ 2x 1 = 0 for x 6 Inequalities (18) Example 61 Testing solutions to inequalities Test if x = 0, 1, 2 and 5 solve the following inequalities (1) x + 2 2x (2) 3x + 4 > 5x Example 62 One-step inequality examples Solve each of the following (1) 05x 75 (2) 75x 125 x (3) 3 > 10 x (4) 15 < 8 Example 63 Two-step inequalitites Solve 2 3 > 4y for y

5 MATH 10 KHAN ACADEMY VIDEOS 5 Example 64 Inequalitites with variables on both sides Solve 3p 7 < p + for p Example 65 Inequalitites with variables on both sides (with parentheses) Solve 5x + 7 > 3(x + 1) for x Example 66 Multi-step inequalities Solve each of the following for x (1) 4x + 3 < 1 (2) 5x > 8x + 27 (3) 8x 5(4x + 1) 1 + 2(4x 3) 7 The Coordinate Plane; Graphs of Equations; Circles 71 Equation of Circle Example 71 Graph the circle (x + 5) 2 + (y 5) 2 = 4 Example 72 Graph the circle (x + 1) 2 + (y 1) 2 = Expanded equation of a circle Example 73 Graph the circle x 2 + y 2 + 4x 4y 17 = 0 References address: mauth@ccnycunyedu

Beginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions

Beginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations: