HONORS GEOMETRY Summer Skills Set

Size: px

Start display at page:

Download "HONORS GEOMETRY Summer Skills Set"

Lesley Horn
5 years ago
Views:

1 HONORS GEOMETRY Summer Skills Set Algebra Concepts Adding and Subtracting Rational Numbers To add or subtract fractions with the same denominator, add or subtract the numerators and write the sum or difference over the denominator. Simplify, if necessary = = = = = To add or subtract fractions with different denominators, first find the least common denominator (LCD). Rewrite each fraction with the LCD, and then add or subtract. Simplify, if necessary = + = (improper fraction) or 1 (mixed number) Find each sum or difference. Write in simplest form

2 Order of Operations Evaluate within grouping symbols. Evaluate powers (exponents) Multiply and divide in order (L R) Add and subtract in order (L R) Simplify as needed * A number next to a grouping symbol means multiply. Examples: 3 3 (5 3) + 3 = () 3 = 9(8) + 3 = = = = 40 = 38 Evaluate each expression (7 5) + 5. (4 + 5) 8 + (3) (6 3) (5 1) 4 + 5(7 4) ( 3) 3 7(8) + 4() (6 + 1) Evaluate each expression for s = 3 and v = sv (sv) s +s 4 1 s v 1 (s v) s v

3 Factoring Factor out the greatest common factor (GCF) first Look for special cases next the difference of two squares (two terms only) or a perfect square trinomial (three terms) Look for a pair of binomial factors ( reverse-foil ) If there are four or more terms, try grouping to find common binomial factors As a final check, be sure there are no common factors other than 1 Factor completely. x + 9x x 6x + 9 x 5x 4. x + 3x 70 18x + 57x +4 x 4 10x + 9 p + 8p 66 16y 1 x 9x 5 10x 9x + 1 0q 13q + x 4 x p 3 1p + 8p v v + 1v

4 Solving Quadratic Equations The solutions of a quadratic equation are the x-intercepts of the graph of the corresponding parabola. There can be two real solutions, one real solution, or no real solution. First bring everything to one side (set the equation equal to 0). When there is no linear term (b = 0), get x by itself and take the square root. Two answers result. If the quadratic expression can be factored easily, then factor, set each factor equal to zero and solve. When factoring is not easy or not possible, use the quadratic formula or solve by calculating the zeros on your graphing calculator. The quadratic formula: If ax + bx + c = 0, then ± x = b b 4ac a Solve each equation by the indicated method. When necessary, round answers to two decimal places. Solve questions 1-3 by using square roots. k = 16. x + 7 = 5 m + 4 = 10. Solve questions 4-6 by factoring. p + 3p 18 = 0 n + 8n = 15 r 7 14r = 7 Solve questions 7-9 by using the quadratic formula. Check your answers by graphing. 4g + 8g + 7 = 4 5x = 18 n 9 7n 4 = 0 Solve questions 10-1 by an appropriate method. x + x 1 = 1 8x + 4x 16 = x 10x + = 9 1

5 Solving Equations in One Variable To solve an equation in one variable, use inverse operations to isolate the variable. 5 ( r + 6) = 1 5 r 1 = 1 Distributive Property r 7 = 1 Combine like terms r = 1+ 7 Add 7 to each side r = 8 Simplify r 8 Divide both sides by = Simplify r = 4 Solve each equation. x 6 = 10. x =15 5 8x = x = a = 3y 4 = 0 t + = 1 3r (r + 1) = 1 44 = 5y 8 y c = c n + = n 1 (16 y ) = (4c + 1) (c 3) = 3 1 x ( 4x + ) = 13

6 Solving a System of Equations To solve a system of equations use the substitution method..

7 Solving a System of Equations To solve a system of equations using linear combinations..

8 Writing equations of lines..

9 Writing equations of lines..

10 Simplifying Radicals To simplify radicals, look for perfect squares that divide evenly into the radicand. Perfect squares: 1, 4, 9, 16, 5, 36, 49, 64, 81, 100, 11, et cetera 56 = 4i14 = 4i 14 = 14 Use the product or quotient rule to simplify radicals. Multiply rational parts separately. 7i3 14 = i3 7i14 = 6 7i7i = 6 7 i = 6i 7 = 4 3 6z w 6z w 6 z w 3z zw = zw = 1 zw = To add or subtract radicals, the radicand must be the same. Simplify individual radicals first = = + 11 Simplify each expression. Write in simplest radical form i i

Geometry Concepts Coordinate System/Ordered Pairs Ordered pairs can be graphed on a coordinate plane. The first number of an ordered pair shows how to move across. It is called the x-coordinate.

11 Geometry Concepts Coordinate System/Ordered Pairs Ordered pairs can be graphed on a coordinate plane. The first number of an ordered pair shows how to move across. It is called the x-coordinate. The second number of an ordered pair shows how to move up or down. It is called the y-coordinate. To locate point B, move left (backward) to and up to Give the coordinates of the following labeled points. A. B C D E. Match the coordinates to the corresponding point labeled on the above graph. ( 3, 4) (5, 4) (0, 5) (, 3) (, )

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: