PSAT MATH Future Scholars

Math Test Content Specifications Element Redesigned PSAT Time Allotted Amount % of Test Total 70 minutes 100% Calculator Permitted Section 45 minutes 64% Calculator Not Permitted Section 25 minutes 36% Questions Number 48 questions Multiple Choice  (4 options) 40 questions 80% Student-Produced Response  (grid in) 8 questions   20%

Analyzing and fluently solving equations and systems of equations 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 questions 33% Problem Solving and Data Analysis Creating and analyzing relationships using ratios, proportions, percentages, and units Describing relationships shown graphically Summarizing qualitative and quantitative data 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 questions 29% Additional Topics in Math * Making area and volume calculations in context Investigating lines, angles, triangles, and circles using theorems Working with trigonometric functions 2 questions 4% Contribution of Items to Cross-Test Scores Analysis in Science 7 questions 15% Analysis in History/Social Studies

Math Calculator Permitted Section Specifications Element Redesigned PSAT Question Type Number % of Test Total 31 100% Multiple Choice  (4 options) 27 87% Student-Produced Response  (grid-in) 4 13% Content Categories Heart of Algebra 8 26% Problem Solving and Data Analysis 16 52% Passport to Advanced Math 6 19% Additional Topics in Math 1 3% Time Allocated 45 minutes

Math Calculator Not Permitted Section Specifications Element Redesigned PSAT Question Type Number % of Test Total 17 100% Multiple Choice  (4 options) 13 76% Student-Produced Response  (grid-in) 4 24% Content Categories Heart of Algebra 8 47% Passport to Advanced Math Additional Topics in Math 1 6% Time Allocated 25 minutes

How to Grid In an Answer Here are the gridding rules: Mark no more than one circle in any column. Only answers entered in the ovals in each grid area will be correct. Students do not receive credit for anything written in the boxes above the ovals. It doesn't matter in which column students begin entering their answers; as long as the correct answer is gridded, students will receive credit. The grid can hold only four places and can accommodate only positive numbers and zero. Unless a problem indicates otherwise, an answer can be entered on the grid as a decimal or a fraction. You don't have to reduce fractions like  3 24 to their lowest terms. Convert all mixed numbers to improper fractions before gridding the answer. If the answer is a repeating decimal, you must grid the most accurate value the grid will accommodate.

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.

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.

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

Page 28 of your manual

Page 28 of your manual

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

Page 28 of your manual

This question is not in your manual

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

Page 29 of your manual Example 6

Page 30 of your manual Example 7

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

Page 30 of your manual Example 8

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

Page 30 of your manual Example 9

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

Page 31 of your manual Example 11

Page 31 of your manual Example 12

Test Taking Technique # 8 Mathematics Sections Show Your Work! Doing all the calculations in your head, increases the chance of making a mistake and increases your stress level. 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. Writing down your steps allows you to locate any mistakes you might make much quicker.

This Example is not in your manual

Test Taking Technique # 9 Mathematics Sections Plug it in! Plug it in! When it is appropriate, plug the answer choices into the problem to see which one is correct. 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.

Page 32 of your manual Example 14

Page 32 of your manual Example 15

Test Taking Technique # 10 Mathematics Sections Know How to Fill in the Griddables 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. There are only four boxes on the grid. The greatest correct answer is 9999. Grid correctly. (See instructions on page 28 of your manual.)

Practice Gridding in the Blank Response Grids on Page 29 of Your Manual Grid the answer 8 2 3 correctly, three different ways. Grid the answer 4. 7 correctly, three different ways.

It’s time to do some practice problems on your own 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.

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

2. 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. Select an Answer A 2 B 4 C 6 D 9 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?

2. 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. Select an Answer A 2 B 4 C 6 D 9 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?

3. 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. 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 Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?

4. 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. Select an Answer 168 centimeters B. 169 centimeters C. 170 centimeters D. Th171 centimeters 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?

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

6. 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?   Solids Liquids Gases Total Metals 77 1 78 Metalloids 7 Nonmetals 6 11 18 90 2 103

If what is one possible value of 7. If    what is one possible value of 

D People 75 years old and over 8. 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? Reported Voting by Age (in thousands)   Voted Did Not Vote No Response Total 18- to 34-year-olds 30,329 23,211 9,468 63,008 35- to 54-year-olds 47,085 17,721 9,476 74,282 55- to 74-year-olds 43,075 10,092 6,831 59,998 People 75 years old and over 12,459 3,508 1,827 17,794 132,948 54,532 27,602 215,082 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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Now lets do some non-calculator practice problems 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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