Name: Algebra 1 9.3 & 9.4 Midterm Review Sheet January 2019 The Midterm format will include 35 Part I multiple choice questions that will be worth 1 point each, 10 Part II short answer questions that will be worth 2 points each and 9 Part III open response questions that will be worth 5 points each. There will be no partial credit on the Part I. Partial credit will be given on Parts II and III. You must place your final answer choice number to Part I on the answer sheet provided. The midterm must be done in PEN. Graphs or drawings may be done in pencil. This is not a comprehensive review. You should also study previous worksheets and your notes. 1. Using the data given find the value of Q 1 and Q 3. 85, 74, 92, 100, 75, 88, 95, 78, 89 2. List the property used in each of the examples below: (a) (-7x)(1) = -7X (a) (b) 7 + 4 = 4 + 7 (b) (c) 5(x 3) = 5(x) 5(3) (c) (d) If 3a + 5 = 11 and 11 = 3x - 8 then 3a + 5 = 3x - 8 (d) (e) 6 + (2 + y) = (6 + 2) + y (e) 3. Find the rate of change of each piece in the graph given below. Rate of Change Piece A: Rate of Change Piece B: Rate of Change Piece C: 1
4. Give an example of a rational number and an irrational number. 5. Find the sum of the following expression: (3x + 5) + 4(x - 5) + (x + 5) 6. Find the difference of the following expression: (6x + 7) - 4(x + 3) - (x - 4) 7. Simplify the polynomial: 4xyz + 2x 2 + 5xyz - x 2 8. What type of polynomial expression is your answer to question 7? 9. Using this polynomial state the following: -5x + 7x 2-6 + 8x 3 + 9x 4 a) What is the leading coefficient? b) What is the leading term? c) What is the degree of the polynomial? d) Write the polynomial in standard form. 10. What is the IQR for this box plot? 11. Find the product of the following: a) (3x - 5)(2x + 4) b) (3x 2 + 2x - 5)(2x - 5) c) (3x - 5) 2 d) (2x 2-4x + 3)(3x 2-2x + 1) e) Subtract (4x 2 3x + 2) from (8x 2 + 2x 5) 2
12. Translate the following word into expressions: a) 6 more than a number b) the product of 5 and a number increased by 5 c) twice a number decreased by 8 13. What value is the best representation of the data for the following distributions? a) Skewed distribution b) Symmetrical distribution 14. How is this box and whisker plot skewed? 15. Solve the following inequality and write your solution in set builder notation: 5x + 7 < 6x 16. Graph the solution of each of the following: a) x < 2 b) x > 3 c) x > -1 17. How is this histogram skewed? If so, state the type of skewness. 3
18. Simplify the expression. Assume the denominator does not equal zero. Your final answer must be expressed with positive exponents. (4g 5 h -3 ) 3 (2g 2 h 2 ) -3 19. Solve the following equation: 6(x - 5) = 3(10 + 3x) 20. Compute the value of (-4) 0 + 6(3) -3 21. Simplify the following expression and place your answer in standard form. 2(4x 2-5x - 2) - 6(x 2-3x + 5) 22. Solve the following inequality: 3 + 5x < 4(x+ 5) - 2 23. Graph this compound inequality: -2 < x < 4 4
24. Justify each step used to simplify each expression by indicating the property that was used. a) (x + 3) + 2 = x + (3 + 2) (a) = x + 5 b) 3( x + 5) + 2(x- 5) = 3(x) + 3(5) + 2(x) 2(5) (b) = 3x + 15 + 2x 10 = 5x + 5 25. Volunteering The two-way table below shows the location of places that males and females volunteered in the last month. Complete the two-way table. Males Females Animal Shelter 26 21 Hospital 13 17 Library 9 14 a) Find the relative frequency for the two way table given above and round your answers to the nearest thousandths. Males Females Animal Shelter 26 21 Hospital 13 17 Library 9 14 5
b) Find the conditional frequency using gender as the condition. Males Females Animal Shelter 26 21 Hospital 13 17 Library 9 14 c) Find the conditional frequency using location as the condition. Males Females Animal Shelter 26 21 Hospital 13 17 Library 9 14 26. The table shows the heights (in feet) of the waves at a beach and the numbers of surfers at the beach. a) Plot the data on the graph. b) Find the equation of the line of best fit and draw it in the graph. c) Find the correlation coefficient. e) How many surfers might be at the beach if the waves were 2 feet high? 6
27. What is the average rate of change of the following intervals? a) Between 0 and 4 seconds b) [10, 12) 28. Use a graphing calculator to construct a box-and-whisker plot for the data. Draw the box-and whisker plot and describe the center and spread of the data using the mean and standard deviation or the five number summaries. 21, 28, 16, 30, 25, 34, 21, 47, 18, 36, 24, 28, 30, 15, 33, 24, 32, 22 27, 38, 23, 29, 15, 27, 33, 19, 34, 29, 23, 26, 19, 30, 25, 13, 20, 25 5 10 15 20 25 30 35 40 45 50 Description of the center and spread of the data: 7
29. a. What is the median of the junior data distribution? b. Calculate the mean of the distribution and state if the mean number of miles walked by a junior less than, approximately equal to or greater than the median number of miles? If they are different, explain why. If they are approximately the same explain why. c. How would you describe the typical number of miles walked by a junior? *** You can also be asked to draw a dot plot from a set of numbers. 30. Find the solution set for each equation and state your answer in set builder notation: a) x(x + 6) - 5(x + 6) = 0 b) 2 + x > 6 or 2x - 5 < -7 8
31. Solve for x and check: rx + 5y = 9z 32. The larger of two numbers is 6 more than twice the smaller. If the sum of the numbers is 18, find the numbers. 9
33. John wants to buy a new video game that costs $50. He has already saved $22. He has agreed to wash cars to earn the extra money. He earns $3.50 for every car he washes. What is the minimum number of cars John must wash to have at least $50 this week? 34. Rewrite the inequality below as a compound sentence. a) -4 < x < 2 b) Graph the inequality on the number below. c) What is the smallest possible value for x? Explain. 35. Using this set of data find the mean, median, mode, range and standard deviation. 68, 57, 65, 25, 32, 38, 42, 44, 45, 58, 57, 65, 81, 79, 55, 60, 61, 62, 68, 65, 40, 51, 47, 46, 45, 78, 73, 72, 49, 48, 54, 52, 30, 34, 36, 35, 42, 27, 20, 65 10