PSAT MATH Springs and Future Scholars. Math Test Content Specifications Element Redesigned PSAT Time AllottedAmount% of Test Total70 minutes100% Calculator

PSAT MATHSprings and Future Scholars

Math Test Content Specifications

Math Test Content Specifications

Element RedesignedPSAT

Time Allotted Amount % of TestTotal 70 minutes 100%

Calculator Permitted Section 45 minutes 64%

Calculator Not Permitted Section 25 minutes 36%

Questions Number % of TestTotal 48 questions 100%

Multiple Choice (4 options) 40 questions 80%

Student-Produced Response (grid in) 8 questions 20%

Content CategoriesHeart 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

16 questions 33%

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 ScoresAnalysis in Science 7 questions 15%Analysis in History/Social Studies 7 questions 15%

Math Calculator Permitted Section Specifications

Element Redesigned PSATQuestion Type Number % of TestTotal 31 100%Multiple Choice (4 options) 27 87%

Student-Produced Response (grid-in) 4 13%Content CategoriesTotal 31 100%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 PSATQuestion Type Number % of TestTotal 17 100%Multiple Choice (4 options) 13 76%

Student-Produced Response (grid-in) 4 24%Content CategoriesTotal 17 100%Heart of Algebra 8 47%Passport to Advanced Math 8 47%Additional Topics in Math 1 6%

Time Allocated 25 minutes

How to Grid In an AnswerHere 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.

Math Test – No Calculator25 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 # 1Mathematics Sections

Locate the QuestionGo 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.


Circle Needed DataNow, 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,…)

Page 24 of your manual


Test Taking Techniques # 3Mathematics Sections

Eliminate Obviously Wrong Answers1. 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.




Label Figures1. 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




Sketch Figures That Are Not Given1. 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.



Some Figures Will Not Be Drawn to Scale 1. It will be indicated on the figure.

2. Otherwise, assume they are drawn to scale.



Use Your Calculator on the Calculator Section1. 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.




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.



Plug it in! 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.




Know How to Fill in the Griddables1. 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.)

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

Manual

1. Grid the answer correctly, three different ways.

2. Grid the answer 4. correctly, three different ways.

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 AnswerA B C D

2.

Select an AnswerA 2B 4C 6D 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?

2.

Select an AnswerA 2B 4C 6D 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.

Select an AnswerA. 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.

Select an AnswerA. 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 AnswerA B C D

6.

Solids Liquids Gases Total

Metals 77 1 0 78

Metalloids 7 0 0 7

Nonmetals 6 1 11 18

Total 90 2 11 103

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?

7.If what is one possible value of

8.

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

Total 132,948 54,532 27,602 215,082

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 AnswerA 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.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.

Non-Calculator Section: 1.

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Documents

PSAT MATH Springs and Future Scholars. Math Test Content Specifications Element Redesigned PSAT Time AllottedAmount% of Test Total70 minutes100% Calculator