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Whittier Tech Grade 10: Honors Algebra II/Geometry Summer Project Grade 10 Honors Algebra II/Geometry Name: Date: 1. Right triangles ABC and AED are shownon the coordinate grid below. Which single transformation, with respect to the line y = x, maps ^ABC → ^AED ? A. dilation B. reflection C. rotation D. translation 2. The distance along the walking trail behind Jessica’s school is approximately 6,290 feet. Jessica calculated the mean length of her walking steps to be 2.9 feet. Which of the following is closest to the number of steps Jessica would take to walk the entire trail? A. 200 steps B. 1,800 steps C. 2,000 steps D. 18,000 steps 3. Sandra created the line plot shown below to display data on the shoe sizes of her classmates. Based on the data given in the line plot, what is the median shoe size of Sandra’s classmates? A. 7 B. 8 C. 10 D. 19 4. In the figure below, ^HIJ ∼= ^LKJ. If m∠L = 50◦, what is m∠IJH ? A. 35◦ B. 40◦ C. 45◦ D. 50◦ page 1 5. Which of the following best represents the graph of a line with an undefined slope? A. B. C. D. 6. Andrew used a wooden stick to estimate the length of a couch. Andrew, who is approximately 6 feet tall, measured his height to be about 1 12 sticks in length. He measured the couch to be about 2 sticks in length. Based on Andrew’s measurements, which of the following is closest to the length of the couch? A. 8 feet B. 9 feet C. 12 feet D. 18 feet 7. The following box-and-whisker plot shows the ages of players on a neighborhood baseball team. a) What is the range of the data set? 8. A landscape artist plans to create a garden on the front lawn of an art museum. The garden will be in the shape of a trapezoid. If the height of the trapezoid is 15 feet, and its bases measure 14 feet and 20 feet, what is the area, in square feet, of the trapezoid? 9. Andy’s Housecleaning Service charges a fixed fee of $40 per job, plus $15 per half-hour that a job requires. a) If c represents Andy’s total charges, write an equation that expresses c in terms of h, the number of half-hours that a job requires. b) What is the total charge for Andy’s services when a job requires 5 12 hours? Show all your work. Hannah’s Homemaids, another housecleaning service, charges no fixed fee but charges $25 per half-hour that a job requires. c) If c represents Hannah’s total charges, write an equation that expresses c in terms of h, the number of half-hours that a job requires. d) The Jordans plan to have their house cleaned, and they like Andy’s and Hannah’s services equally well. For what number of half-hours would the charges for the two services be identical? Show or explain how you got your answer. page 2 Grade 10 Honors Algebra II/Geometry 10. The value of all of the quarters and dimes in a parking meter is $18. There are twice as many quarters as dimes. What is the total number of dimes in the parking meter? 11. Ms. Vargas is analyzing the scores her 10 chemistry students earned on their last test. To make her calculations easier, she reduced each score by 80 points and arrived at the simplified data set shown below. {0, 4, 4, 5, 6, 7, 7, 7, 7, 9} a) For the simplified data set, find each of the measures listed below. Show or explain how you got each answer. • mean • median • mode • range b) For the set of actual scores on the chemistry test, find each of the measures listed below. Show or explain how you got each answer. • mean • median • mode • range 12. Two real numbers have coordinates w and t as shown on the number line below. a) What are the two real numbers represented by w and t on the number line? b) The coordinate of Point A on the number line is w + t. Plot and label Point A on the number line and explain how you decided upon its location. c) The coordinate of Point B on the number line is w − t. Plot and label Point B on the number line and explain how you decided upon its location. d) The coordinate of Point C on the number line is w · t. Plot and label Point C on the number line and explain how you decided upon its location. 13. If 4 more than twice a number is 18, find the number. 14. The cost of a long-distance telephone call is determined by a flat fee for the first 5 minutes and a fixed amount for each additional minute. If a 15-minute telephone call costs $3.25 and a 23-minute call costs $5.17, find the cost of a 30-minute call. 15. James is four years younger than Austin. If three times James’ age is increased by the square of Austin’s age, the result is 28. Find the ages of James and Austin. 16. What is the slope of the line that passes through the points (4, 5) and (7, 3)? 17. a) On the same set of coordinate axes, graph the following system of inequalities: y ≤ −3x + 2 y − x > 0 b) Write the coordinates of a point not in the solution set of the inequalities graphed in part a. 18. Find an equation of the line passing through the point (6, 5) and perpendicular to the line whose equation is 2y + 3x = 6. 19. The expression (m − n) − (n − m) is equivalent to A. 2m − 2n B. 2m C. −2n D. m − n 20. A set of data consists of 3, 3, 6, 4, and 9. The median for these data is A. 6 B. 5 C. 3 D. 4 21. Pat’s grades on Course I tests were 90, 75, 98, 82, 90, and 87. The mode of her grades is A. 90 B. 89 C. 87 D. 82 page 3 Grade 10 Honors Algebra II/Geometry 22. The set of scores on a mathematics test is 72, 80, 80, 82, 87, 89, and 91. The mean score is A. 84 B. 83 C. 82 D. 80 23. The accompanying histogram shows the distribution of the number of children in the families of the students in a ninth-grade class. The mode of the set of data in the histogram is A. 5 B. 2 C. 3 D. 7 24. A student’s four test scores were 88, 91, 93, and 86. What score would be needed on a fifth test to obtain a mean of 90 for all five tests? A. 90 B. 92 C. 95 D. 96 25. What was the median high temperature in Middletown during the 7-day period shown in the accompanying table? Daily High Temperature in Middletown Day Temperature (F◦ ) Sunday 68 Monday 73 Tuesday 73 Wednesday 75 Thursday 69 Friday 67 Saturday 63 A. 69 B. 70 C. 73 D. 75 26. For a set of scores, 80 is the score for the 75th percentile. Which statement is true? A. Eighty scores are at or below 75. B. Seventy-five scores are at or below 80. C. Seventy-five percent of the scores are at or below 80. D. Eighty percent of the scores are at or below 75. 27. Which measure is always the same as the 50th percentile? A. mean B. median C. mode D. lower quartile 28. The freshman class held a canned food drive for 12 weeks. The results are summarized in the table below. Canned Food Drive Results Week 1 2 3 4 5 6 7 8 9 10 11 12 Number of Cans 20 35 32 45 58 46 28 23 31 79 65 62 Which number represents the second quartile of the number of cans of food collected? A. 29.5 B. 30.5 C. 40 D. 60 29. The accompanying diagram shows a box-and-whisker plot of student test scores on last year’s Mathematics A midterm examination. What is the median score? A. 62 B. 71 C. 81 D. 92 page 4 Grade 10 Honors Algebra II/Geometry 30. Jorge made the accompanying stem-and-leaf plot of the weights, in pounds, of each member of the wrestling team he was coaching. What is the mode of the weights? A. 145 B. 150 C. 152 D. 168 31. The box-and-whisker plot below represents students’ scores on a recent English test. What is the value of the upper quartile? A. 68 B. 76 C. 84 D. 94 32. Which pair of angles x and y are supplementary? A. m∠x = 113 m∠y = 67 B. m∠x = 76 m∠y = 14 C. m∠x = 140 m∠y = 190 D. m∠x = 180 m∠y = 180 33. In the accompanying diagram, −−→ BD ⊥ ←−→ABC at B and−→ BE ⊥ −→BF at B. If m∠FBC = 20, what is m∠EBD ? A. 20 B. 70 C. 90 D. 110 34. In the accompanying diagram, line a intersects line b. What is the value of x? A. −10 B. 5 C. 10 D. 90 35. The measures of two angles of a triangle are 70 and 55. This triangle is A. a right triangle B. a scalene triangle C. an obtuse triangle D. an isosceles triangle 36. In the diagram below, ^LMO is isosceles with LO = MO. If m∠L = 55 and m∠NOM = 28, what is m∠N? A. 27 B. 28 C. 42 D. 70 37. In the accompanying diagram of isosceles triangle ABC, −−−AB ∼= −−−BC, m∠BAC = x, and m∠ABC = x + 30. What is the value of x ? A. 80 B. 75 C. 50 D. 30 page 5 Grade 10 Honors Algebra II/Geometry 38. In the diagram below of ^ABC, −−−AB ∼= −−−AC, m∠A = 3x, and m∠B = x + 20. What is the value of x? A. 10 B. 28 C. 32 D. 40 39. In the accompanying diagram, ∠ACD is