NOTE TO TEACHERS: Our Pioneer Press Newspapers in Education Graduation-Required Assessment for Diploma (GRAD) Mathematics Test Sampler is designed to offer practice with the format and types of questions students might find in the Graduation-Required Assessment for Diploma (GRAD) Mathematics Test, using the test specifications for the GRAD math and past examples from the MCA Grade 11 Math test.we hope that students, teachers and parents will find it a helpful tool in preparing their students for this test. The Graduation-Required Assessment for Diploma (GRAD) Mathematics Test is one of three tests (written composition, reading and mathematics) which students, who entered grade 8 in the 2005-2006 school year or later, are required to pass in order to graduate from a Minnesota public high school. This is the first year of the Math GRAD Test, which will affect students graduation. The Math GRAD Test was designed to measure students proficiency on the Minnesota Academic Standards and is more extensive and rigorous than the former Math BST. It is our hope you will find these a useful tool in preparing your student(s) for this test. You can find additional information at the Minnesota Department of Education website: http://education.state.mn.us/mde/accountability Programs/Assessment and Testing/ Assessments /GRAD/items Calculators may be used. A formula sheet is provided on pages 7 and 8. Newspapers In Education Use the table below to answer question #1. Year 1985 1988 1990 1991 2004 2008 Price ( ) 22 25 25 29 37 42 1. Pedro collects stamps. He is interested in finding how the cost of a stamp has increased over time. During which interval did the price of a stamp increase at the greatest rate? A. 1985-1988 B. 1988-1990 C. 1990-1991 D. 1991-2004 2. Jimmy has a spinner containing six different colored sides red, orange, yellow, blue, green, and white. What is the probability that when Jimmy spins twice he will get the same color both times? A. 1/36 B. 1/18 C. 1/6 D.1/3 Use the diagram below to answer question #3. 6 cm 4. Four cousins find a box of old baseball cards in their grandfather s cellar. Their grandfather says they can keep the cards if they split them in a ratio of 6:5:3:1. If the box contained 345 cards, how many cards were in the largest share? A. 15 cards B. 23 cards C. 90 cards D. 138 cards 5. Ahmed is growing a colony of bacteria, and they double every hour. If he starts with 8 bacteria, how many will Ahmed have after 10 hours? A. 1,024 bacteria B. 2,048 bacteria C. 4,096 bacteria D. 8,192 bacteria 6. Tom and Mike have a coupon for a free one-topping pizza. Their choices of toppings are pepperoni, sausage, hamburger, onion, bell peppers, mushrooms, and anchovies. What is the probability that they both choose hamburger as a topping? A. 1/7 B. 1/49 C. 2/7 D. 1/42 7. Which of the following is the graph for the equation y = x 2 2x 8? A. B. 3. Find the shaded area. Use 3.14 for π and round to the nearest whole cm 2. A. 8 cm 2 B. 28 cm 2 C. 36 cm 2 D. 44 cm 2 1 C. D.
8. Simplify the following expression: 5(3x + 7) 4(4 + 2x) A. x + 27 B. 7x + 19 C. 23x + 51 D. 31x + 43 9. The centripetal force of an object moving in a circle is given by the formula F = mv 2 /r, where m = the mass of the object, v = velocity, and r = the radius of the circle. Suppose James is swinging a bucket of water over his head. If James arms are 0.6 meters long, the bucket has a mass of 5 kg, and he is swinging it with a velocity of 15 m/s, what is the centripetal force on the bucket of water? A. 45 N B. 125 N C. 675 N D. 1,875 N Use the table below to answer questions #10 & #11. Height (cm) 150 152 163 167 168 171 175 178 184 186 189 193 Weight (kg) 43 48 47 54 58 63 71 65 83 94 90 89 10. The table above describes the heights in cm and weights in kg of 12 students in Mr. Calderon s class. Find Q 1 and Q 3 of the weights. A. Q 1 = 48, Q 3 = 89 B. Q 1 = 48, Q 3 = 83 C. Q 1 = 51, Q 3 = 86 D. Q 1 = 54, Q 3 = 89 Use the diagram below to answer question #12. 12. The city of St. Paul is looking to build a ski ramp parallel to the hill above. If the ski ramp is to start at point S and R represents (0,0), what is an equation that represents the ski ramp? A. y = -5/6x + 6 B. y = -6/5x + 6 C. y = -5/6x + 9 D. y = -6/5x + 9 13. Ali bought a car four years ago for $12,000. It is now worth $5,000. What was the percent decrease (rounded to the nearest percent) in the price of the car? A. 42% B. 58% C. 71% D. 140% Use the diagram below to answer question #14. 11. Find the mean of the heights, rounded to the nearest cm. A. 172 cm B. 173 cm C. 174 cm D. 175 cm 2 18 ft 48 o x ft 14. Xai is leaning a ladder up against a wall. The ladder is 18 ft long, and he places the base of the ladder away from the base of the wall (see diagram). How far is the ladder from the base of the wall (round to the nearest foot)? A. 13 ft B. 15 ft C. 12 ft D. 20 ft
15. Soua goes to her friend s house for dinner. They are making hamburgers or chicken patties on either a whole wheat or white bun with side options of fries, tater tots, or baked potatoes. How many total different meals are possible from the two types of meat, two types of bun, and three side orders? A. 7 meals B. 12 meals C. 24 meals D. 64 meals 16. Find the intercepts of the graph of the following equation: 2x + 3y = 6. A. x = 2; y = 3 B. x = 3; y = 2 C. x = -2; y = -3 D. x = -3; y = -2 17. Teresa is doing an experiment in physics class. She sets a ball at the top of a ramp that is 4 feet high and 12 feet long (along the ground). What is the actual distance that the ball travels down the ramp? A. 11.31 feet B. 12.65 feet C. 128 feet D. 160 feet Use the Box-and-Whisker Plot below to answer question #18. 19. Yessenia started selling kitchen knife sets a couple of weeks ago. Her weekly income (I) is a combination of a constant salary per week plus a certain amount per set she sells. In her first week on the job, Yessenia sold 35 sets and earned $600. A few weeks later, she sold 50 sets and earned $750. Write an equation to represent Yessenia s income (I) in terms of the number of knife sets (k) she sells. A. I = 10k + 250 B. I = 15k + 150 C. I = 35k + 600 D. I = 50k + 750 Use the diagram below to answer question #20. 20. The new Central Corridor Light Rail Line will be going in along University Ave. connecting downtown Minneapolis to downtown St. Paul. A footbridge is being planned to go over the tracks, so pedestrians can move back and forth with ease. Which of the following statements is true? A. m<1 = m<2 B. m<1 = m<3 C. m<1 = m<4 D. m<1 = m<5 18. Ms. Adeeb created a box-and-whisker plot so her students could see how they did on their last math test. What does the score at 80 represent on this box-and-whisker plot? A. upper quartile B. mode C. mean D. median 21. Gina is hoping to invite some of her friends over to watch the Final Four. She has 11 friends that enjoy watching basketball, but only five other spots in her living room to sit. How many different combinations of five friends from the 11 can she choose to invite over to watch the Final Four? A. 55 ways B. 110 ways C. 330 ways D. 462 ways 3
Use the diagram below to answer question #22. This graph represents the number of students who completed 1, 2, 3, 4, and 5 assignments last week in Ms. Xiong s class. Number of Students Completing Assignments on Time 22. AC = BC, BD = AD, m<abd = 27 o, and AD, BD, & CD are angle bisectors. Find m<adc A. 27 o B. 72 o C. 117 o D. 126 o 23. The expression 5x 3(7x 2) + 9 is equivalent to A. 16x + 3 B. -16x + 15 C. -26x + 3 D. 26x + 15 Use the diagram below to answer question #24. 24. Patty is standing by a flagpole outside her school. The sun is casting a shadow of both Patty and the flagpole. If Patty is 5 6 tall and her shadow is 9 long, and if the shadow of the flagpole is 54 long, how tall is the flagpole (rounded to the nearest foot)? A. 33' B. 34' C. 88' D. 89' Number of Students Number of Assignments 25. What percentage of students completed 4 or more assignments on time last week? A. 12% B. 13% C. 48% D. 52% 26. Determine the equation of the line that passes through (2, 1) and (-2, 9). A. y = -1/2x + 2 B. y = -2x + 5 C. y = -1/2x + 8 D. y = -2x 3 27. Aziza is designing a new pyramid-shaped box for a toy company. In order to make the box properly, she would have to make a cutout like which of the following? A. B. C. D. Students 4
28. Ying hits a golf ball from an elevated tee. The equation for the golf ball s height h is modeled by the equation h = -5t 2 + 5t + 30, where t is the time in seconds after the golf ball is hit. How many seconds did it take the golf ball to land? A. 1 second B. 2 seconds C. 3 seconds D. 4 seconds 29. Solve the following system of equations: 3x + 5y = 16 4x 5y = -37 A. (3, -5) B. (3, 5) C. (-3, -5) D. (-3, 5) 30. Which of the following tables corresponds to the equation y = 2x 7? A. B. C. D. 31. It takes Faith 3/4 of an hour to walk to school. How many seconds does it take her to walk to school? A. 45 seconds B. 1,080 seconds C. 2,700 seconds D. 3,600 seconds 32. Jane has decided to save some money as a precaution in these troubling economic times. Jane has $1,200 that she is going to put into a savings account with an annual interest rate of 8%. Using the formula I = prt (where I = interest earned, p = principal, r = interest rate, and t = time), how much money will she have in her account at the end of one year? A. $96 B. $1,104 C. $1,296 D. $9,600 The following is a list of shoe sizes for students in Mr. Thompson s class. Use this data for questions 33 & 34. 5, 6, 8, 7, 6, 9, 10, 8, 9, 13, 10, 11, 10, 9, 5, 9, 11, 5, 7, 12 33. Find the mean of the data set. A. 8 B. 8.5 C. 9 D. 9.5 34. Find the range of the data set. A. 8 B. 8.5 C. 9 D. 9.5 35. Evaluate the following expression: 6 3 + 3 5 x 5 A. -24 B. -20 C. 0 D. 30 5 36. Which of the following expressions is equivalent to 2x +13? A. 3(2x + 9) 5(x + 5) B. 2(3x + 9) (5x + 5) C. 9(3x + 2) 5(5x + 1) D. 9(2x + 3) 5(x + 5)
37. Yer flips a quarter 3 times. What is the probability that she gets 2 or more heads? A. 1/4 B. 3/8 C. 1/2 D. 5/8 38. Solve the following equation for x: 3(2x + 7) = 4x + 11 A. -5 B. -1 C. 3.2 D. 16 39. Deandre is making water balloons with which to soak his little sister. He has 15 balloons that when filled with water, approximate a sphere with a diameter of 6 inches. To the nearest cubic inch, how much water will Deandre need to fill all 15 balloons and thoroughly soak his little sister? (Use 3.14 for π ) A. 113 in. 3 B. 565 in. 3 C. 1,696 in. 3 D. 5,097 in. 3 40. Carlos is baking a cake. The recipe calls for 2 1/4 cups of flour. Carlos decided he doesn t want the full cake, instead he will make a cake only 2/3 the size. How much flour does Carlos need for his smaller cake? A. 1-1/2 cups B. 1-7/12 cups C. 2-11/12 cups D. 4-1/2 cups 6
Formula Sheets The formulas below may be used to solve problems on this test NOTES 7
Formula Sheets The formulas below may be used to solve problems on this test NOTES 8