Algebra CP Final Exam Review Name: THIS PACKET IS INTENDED TO BE USED AS SUPPLEMENTAL REVIEW AND PRACTICE THAT REFLECT THE TOPICS WHICH WILL BE COVERED ON THE FINAL EXAM. IT SHOULD NOT BE USED AS YOUR ONLY REVIEW. Chapter 6: Irrational and Complex Numbers 6-5: Equations Containing Radicals 6-6: Rational and Irrational Numbers 6-7: The Imaginary Number i 6-8: The Complex Numbers Chapter 7: Quadratics Equations and Functions 7-1: Completing the Square 7-: The Quadratic Formula 7-3: The Discriminant 7-4: Equations in Quadratic Form 7-5: Graphing y k = a(x- h) 7-6: Quadratic Functions 7-7: Writing Quadratic Equations and Functions Chapter 8: Variation 8-1: Direct Variation and Proportion 8-: Inverse and Join Variation Chapter 11: Sequences and Series 11-1: Types of Sequences 11-: Arithmetic Sequences 11-3: Geometric Sequences 11-4: Series and Sigma Notation 11-5: Sums of Arithmetic Sequences 11-6: Infinite Geometric Chapter 15: Statistics and Probability 15-1: Presenting Statistical Data 15-: Analyzing Statistical Data 15-5: Fundamental Counting Principles 15-6: Permutations 15-7: Combinations 15-8: Sample Spaces and Events 15-9: Probability Chapter 16: Matrices and Determinants 16-1: Definition of Terms 16-: Addition and Scalar Multiplication 16-3: Matrix Multiplication 16-4: Applications of Matrices 1
Chapter 6 1) Solve. Check your solution(s). Show check used! a) 1 x = 5 b) x 3 x + 7 = [6-5] ) Describe the difference between rational and irrational numbers: [6-6] 3) Find a rational number and an irrational number between 4.1 and 17 : [6-6] R I 4) Simplify. a) 3 3 1 b) 7 4 6i 5i + i i [6-7] c) 87 i d) i 17 [6-7] 5) Simplify. a) (4 + 5 i) + (6 i) b) (6 3 i)(4 + 3 i) c) + 3 i 4 5i [6-8]
Chapter 7 6) Solve by completing the square. a) x 4x + 1 = 0 b) x x 4 0 + + = [7-1] 7) Solve: a) x + 16 = 0 b) x 3x 7 0 = [7-1 to 7-] c) 3x x 8 = d) x + 5x + 4 = 0 [7-4] 4 e) (3x 1) 4(3x 1) 3 0 + = f) (x 1) 7(x 1) 6 0 + + + + = [7-4] 8) Determine the value of discriminant, then state the nature of the roots for each quadratic equation. [7-3] a) m 5m 3 0 + = b) 4y 4y + 1 = 0 Discriminant = Discriminant = Nature of roots: Nature of roots: 3
Write a quadratic equation, then solve the problem. [7-] 9) In a right triangle, one leg is 1 m shorter than the hypotenuse, while the other leg is 8 m shorter than the hypotenuse. Find the measures of all sides of the triangle. 10) A picture frame of uniform width measures 14 cm by 0 cm. and surrounds a picture whose area is 160 sq. cm. Find the width of the frame. 11) A rancher has 00 feet of fencing to enclose three identical adjacent rectangular sections (see diagram). Find the dimensions that will produce that maximum area. 4
a) Graph the function using the coordinate grid provided, b) find the vertex, c) find the equation of the line of symmetry, d) the minimum or maximum value, e) domain, and f) range 1a) f ( x) = 4x + 8x + 1 13a) f ( x) ( x ) = + 1 + 4 [7-6] b) b) c) c) d) d) e) e) f) f) 14) Find all x- and y-intercepts for each function below. [7-6] a) f ( x) = 9x 1x + 4 b) ( ) f x = 3x 6x + 1 x intercepts: y intercepts: x intercepts: y intercepts: 5
15) Find an equation for the parabola that has the following properties: [7-5] a) Has vertex (, -3) and contains (-, -35) b) Has vertex (-1, -5) and contains (1, 3) 16) Find a quadratic equation having the following roots: [7-7] a) 3 3 and 3+ 3 b) 1 4i and 1+ 4i Chapter 8 [8-1 & 8-] 17) Find the equation of variation when y varies jointly as x and w and inversely as the square of z, and y = 9 when x = 3, w = 6, and z =. 18) If t varies inversely as the cube of z and directly as the square of r, and t = 4 when z = 3 and r = 6, find t when z = 6 and r = 9. Chapter 11 19) Consider the following sequence: 11, 1, 31, 41, [11- & 3] a) Find the common difference / ratio. b) Find the next three terms c) Find a 34 6
0) Consider the following sequence:, -1, 7, -43, [11- & 3] a) Find the common difference / ratio. b) Find the next three terms c) Find a 8 1) a) Find the missing terms of the following arithmetic sequence: 0,,,, 8 [11-] b) Find the missing terms of the following geometric sequence:,,,, 59 [11-3] ) a) Write the following series in expanded form [11-4] b) find its sum. 5 n = 1 ( 5n 3) 3) a) Find the common difference d of the arithmetic series below [11-4] b) write the arithmetic series using sigma notation. 1 + 5 + 9 + 13 + 17 + 1 + 5 4) a) Find the common ratio r of the geometric series below, and [11-4] b) find the sum. 6 k = 1 3 k + 7
5) Find the sum of each geometric series described. [11-5] 1 a) t 1 = 3, r = 0.5, n = 5 b) t 1 = 81, r =, n = 4 3 6) Find the sum of each infinite geometric series, if it exists. [11-6] a) 1 1 4... 1 + 9 + 7 + b) t = 7, r = 1 3 Chapters 15 For Questions 6-8 use the following data: Alex s scores on 60-point reading tests are: 53, 55, 57, 54, 57, 60, 48, 36, 46, 56, 57, 54, 60, 59, 49, 50, 5, and 47 7) Find the mean, median, and mode of Alex s test scores. [15-1] Mean: Median: Mode: 8) Find Q1, Q and range. Use these values to create a box-and-whisker plot. [15-] Q1: Q3: Range: 8
9) a) In what interval does the bottom 5% of the data lie in? [15-] b) In what interval does the top 5% of the data lie in? c) In what interval does the middle 50% of the data lie in? 30) What group of students has a greater median height? [15-1] 31) How many ordered 4-digit numerical codes can be formed from the numbers 1,, 3, 4, 5, 6 if: [15-5] a) the digits are not repeated? b) the digits are repeated? c) the digits are not repeated but must begin with the number 1? 3) Compute the value of (using an appropriate formula): [15-6 & 15-7] a) 11 P 7 b) 9 C 7 c) 7 C 7 d) 4 P 4 33) a) Find the number of ways the letters of word HEXAGON can be arranged? [15-6] b) Find the number of ways the letters of word SUBSTITUTE can be arranged? [15-6] 34) Manny is completing a social studies test and he must answer 3 out of the first 4 questions correctly, and 7 of the last 10 questions correctly. In how many ways can this be done? Show all work necessary. [15-7] 9
35) a) Determine the probability of rolling a sum of 8 using two 6-sided dice: [15-9] b) Determine the probability of rolling a product of 6 using two 6-sided dice: c) Determine the probability of rolling a sum of 13 using two 6-sided dice: 36) There are 4 red, 3 white, and orange balls in the bag. Four balls are drawn at random. [15-9] What is the probability that one will be white and three will be red? Chapter 16 37) Solve for matrix X: [16-] a) [ 13 1] 3X [ 10 3] = b) 13 9 7 9 = 3X 1 18 3 6 38) Let 1 A = 3 4 and B 6 = 1 3 Find: a) A + 3B b) 3B A [16-] c) Ai B d) Bi A [16-3] 10