1. PSAT MATH
Future Scholars

2. 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%

3. 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

4. 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) %
Content Categories
Heart of Algebra 8
26%
Problem Solving and Data Analysis 16
52%
Passport to Advanced Math 6
19%
Additional Topics in Math %
Time Allocated
45 minutes

5. 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) %
Content Categories
Heart of Algebra 8
47%
Passport to Advanced Math
Additional Topics in Math %
Time Allocated
25 minutes

6. 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  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.

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…
Circle numbers you need to answer the problem.
Circle words that describe how to do the problem. (Sum, Product, Factor, Squared,…)

11. Page 28 of your manual

12. Page 28 of your manual

13. 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.

14. Page 28 of your manual

15. This question is not in your manual

16. 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

17. Page 29 of your manual
Example 6

18. Page 30 of your manual
Example 7

19. 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.

20. Page 30 of your manual
Example 8

21. 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.

22. Page 30 of your manual
Example 9

23. 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.

24. Page 31 of your manual
Example 11

25. Page 31 of your manual
Example 12

26. 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.

27. This Example is not in your manual

28. 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.

29. Page 32 of your manual
Example 14

30. Page 32 of your manual
Example 15

31. 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.)

34. Practice Gridding in the Blank Response Grids on Page 29 of Your Manual
Grid the answer correctly, three different ways.
Grid the answer correctly, three different ways.

37. 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.

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.
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?

40. 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?

41. 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?

42. 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?

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.
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

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

46. D People 75 years old and over8.
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

47. 9.

48. 10.

49. 11.

50. 12.

51. 13.

52. 14.

53. 15.

54. 16.

55. 17.

56. 18.

57. 19.

58. 20.

59. 21.

60. 22.

61. 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.

62. Non-Calculator Section: 1.

63. 2.

64. 3.

65. 4.

66. 5.

67. 6.

68. 7.

69. 8.

70. 9.

71. 10.