1. PSAT MATH Springs and Future Scholars

2. Math Test Content Specifications Element Redesigned PSAT Time AllottedAmount% of Test Total70 minutes100% Calculator Permitted Section45 minutes64% Calculator Not Permitted Section25 minutes36% QuestionsNumber% of Test Total48 questions100% Multiple Choice (4 options)40 questions80% Student-Produced Response (grid in) 8 questions 20%

3. Content Categories Heart of Algebra Analyzing and fluently solving equations and systems of equations Creating expressions, equations, and inequalities to represent relationships between quantities and to solve problems Rearranging and interpreting formulas 16 questions33% Problem Solving and Data Analysis Creating and analyzing relationships using ratios, proportions, percentages, and units Describing relationships shown graphically Summarizing qualitative and quantitative data 16 questions33% Passport to Advanced Math Rewriting expressions using their structure Creating, analyzing, and fluently solving quadratic and higher-order equations Manipulating polynomials purposefully to solve problems 14 questions29% Additional Topics in Math * Making area and volume calculations in context Investigating lines, angles, triangles, and circles using theorems Working with trigonometric functions 2 questions4% Contribution of Items to Cross-Test Scores Analysis in Science7 questions15% Analysis in History/Social Studies7 questions15%

4. Math Calculator Permitted Section Specifications ElementRedesigned PSAT Question Type Number% of Test Total31100% Multiple Choice (4 options)27 87% Student-Produced Response (grid-in) 4 13% Content Categories Total31100% Heart of Algebra8 26% Problem Solving and Data Analysis16 52% Passport to Advanced Math6 19% Additional Topics in Math 1 3% Time Allocated 45 minutes

5. Math Calculator Not Permitted Section Specifications ElementRedesigned PSAT Question Type Number% of Test Total17100% Multiple Choice (4 options)13 76% Student-Produced Response (grid-in) 4 24% Content Categories Total17100% Heart of Algebra 8 47% Passport to Advanced Math 8 47% Additional Topics in Math 1 6% Time Allocated 25 minutes

6. How to Grid In an Answer

7. Math Test – No Calculator 25 Minutes, 17 Questions Directions: For questions 1-13, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 14-17, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 14 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work. Notes: 1. The use of a calculator is not permitted. 2. All variables and expressions used represent real numbers unless otherwise indicated. 3. Figures provided in this test are drawn to scale unless otherwise indicated. 4. All figures lie in a plane unless otherwise indicated. 5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f (x) is a real number.

9. Test Taking Technique # 1 Mathematics Sections Locate the Question Go to the end of the question and underline the question being asked. It is usually the last sentence of the problem. Look for the question mark.

10. Test Taking Technique # 2 Mathematics Sections Circle Needed Data Now, look at the problem and… 1.Circle numbers you need to answer the problem. 2.Circle words that describe how to do the problem. (Sum, Product, Factor, Squared,…)

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13. Test Taking Techniques # 3 Mathematics Sections Eliminate Obviously Wrong Answers 1.Distance, speed, height, age, … can not be negative or imaginary numbers. 2.Some answer choices will not make sense for the question being asked. 3.Very large or small answers, outside the range of possibilities for the question can be eliminated.

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16. Test Taking Technique # 4 Mathematics Sections Label Figures 1.Label vertices, ordered pairs, scales for axes,... 2.Write in the lengths of sides, distances, angle measures, … 3.Mark congruent angles or sides and similar parts. 4.Write the formula next to the figure

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19. Test Taking Technique # 5 Mathematics Sections Sketch Figures That Are Not Given 1.It is much easier to work the problem if you can see what you are talking about. 2.Do not waste a lot of time making your picture. 3.Label all parts and write the formula, as we discussed previously.

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21. Test Taking Technique # 6 Mathematics Sections Some Figures Will Not Be Drawn to Scale 1.It will be indicated on the figure. 2.Otherwise, assume they are drawn to scale.

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23. Test Taking Technique # 7 Mathematics Sections Use Your Calculator on the Calculator Section 1.There are 31 questions (out of 48) that allow you to use a calculator. 2.Not having to depend on your brain to do all the calculations will reduce your stress level. 3.Working fractions and decimals on the calculator is usually faster and easier than doing them in your head. 4.Take a quick moment to check that you punched the problem into the calculator correctly.

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26. Test Taking Technique # 8 Mathematics Sections Show Your Work! 1.Doing all the calculations in your head, increases the chance of making a mistake and increases your stress level. 2.If you write down all your work you can leave that problem if you need to and return to it without having to start over from the beginning. 3.Writing down your steps allows you to locate any mistakes you might make much quicker.

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28. Test Taking Technique # 9 Mathematics Sections Plug it in! 1.When it is appropriate, plug the answer choices into the problem to see which one is correct. 2.Start with letter choice D and work your way up to letter choice A. College Board knows most students start with letter A. They use this fact to cause you to waste time.

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31. Test Taking Technique # 10 Mathematics Sections Know How to Fill in the Griddables 1.You should only get positive answers for the FRQ’s because there is no negative sign on the grids. Do NOT add a negative sign. 2.There are only four boxes on the grid. The greatest correct answer is 9999. 3.Grid correctly. (See instructions on page 28 of your manual.)

34. Practice Gridding in the Blank Response Grids on Page 29 of Your Manual

37. It’s time to do some practice problems on your own. On the PSAT you are given 45 minutes to complete 31 calculator questions. That comes out to 1 minute, 27 seconds per question. You will now have 32 minutes to complete 22 questions. Use your strategies.

38. Calculator Section: 1. The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone? Select an Answer A B C D

39. 2. Select an Answer A 2 B 4 C 6 D 9 The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown. How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

40. 2. Select an Answer A 2 B 4 C 6 D 9 The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown. How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

41. 3. Select an Answer A. The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone B. The predicted first metacarpal bone increase in centimeters for every centimeter increase in height C. The predicted height in centimeters of a person with a first metacarpal bone length of 0 centimeters D. The predicted first metacarpal bone length in centimeters for a person with a height of 0 centimeters The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown. Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?

42. 4. Select an Answer A.168 centimeters B. 169 centimeters C. 170 centimeters D. Th171 centimeters The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown. Based on the line of best fit, what is the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters?

43. 5. Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying x nights? Select an Answer A B C D

44. 6. SolidsLiquidsGasesTotal Metals771078 Metalloids7007 Nonmetals611118 Total90211103 The table below classifies 103 elements as metal, metalloid, or nonmetal and as solid, liquid, or gas at standard temperature and pressure. What fraction of all solids and liquids in the table are metalloids?

45. 7. If what is one possible value of

46. 8. Reported Voting by Age (in thousands) VotedDid Not VoteNo ResponseTotal 18- to 34-year-olds30,32923,2119,46863,008 35- to 54-year-olds47,08517,7219,47674,282 55- to 74-year-olds43,07510,0926,83159,998 People 75 years old and over 12,4593,5081,82717,794 Total132,94854,53227,602215,082 A survey was conducted among a randomly chosen sample of U.S. citizens about U.S. voter participation in the November 2012 presidential election. The table below displays a summary of the survey results. According to the table, for which age group did the greatest percentage of people report that they had voted? Select an Answer A 18- to 34-year-olds B 35- to 54-year-olds C 55- to 74-year-olds D People 75 years old and over

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61. Now lets do some non-calculator practice problems. On the PSAT you are given 25 minutes to complete 17 non- calculator questions. That comes out to 1 minute, 28 seconds per question. You will now have 15 minutes to complete 10 questions. Use your strategies.

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