Praxis I PPST: Introduction to the Mathematics Section

The Mathematics section of the Pre-Professional Skills Test is 60 minutes long and usually contains 40 questions. The questions are selected from different areas of mathematics including arithmetic, elementary algebra, basic geometry, measurement, and graph and chart reading. Complex computation is not required, and most of the terms used are general, commonly encountered mathematical expressions (for instance, area, perimeter, integer, and prime number).

This part of the exam tests your ability to use your cumulative knowledge of mathematics and your reasoning ability. Computation is minimal; you are not required to have memorized any specific formulas or equations.

The test is composed of the following content areas and approximate percentages:

  • Conceptual Knowledge: whole numbers, fractions, decimals, place value, ordering of numbers, and properties of numbers and operations; 6 questions, 15%

  • Procedural Knowledge: ratio, proportion, percent, probability, equations, inequalities, algorithms, solving problems, computing, and estimating; 12 questions, 30%

  • Representations of Quantitative Information: interpreting bar graphs, line graphs, pie charts, pictographs, tables, diagrams, and flow charts; seeing trends; making inferences; drawing conclusions; identifying patterns; and making connections; 12 questions, 30%

  • Measurement and Informal Geometry: systems of measurement, appropriate units of measurement, linear/area/volume measurement, geometric properties, reading scales, and solving problems involving geometry; 6 questions, 15%

  • Formal Mathematical Reasoning: interpreting logical statements, using deductive reasoning, evaluating the validity of a conclusion, and identifying appropriate generalizations; 4 questions, 10%

Directions

Each of the questions or incomplete statements below is followed by five suggested answers or completions. Select the best answer or completion of the five choices given and fill in the corresponding lettered space on the answer sheet.

Analysis of Directions

  1. You have 60 minutes to do 40 problems, which averages to just over one minute per problem. Keep that in mind as you attack each problem. Even if you know you can work a problem but that it will take you far longer than one minute, you should skip it and return to it later if you have time. Remember, you want to do all the easy, quick problems first before spending valuable time on the others.

  2. There is no penalty for guessing, so you should not leave any blanks. If you don't know the answer to a problem but you can size it up to get a general range for your answer, you may be able to eliminate one or more of the answer choices. This procedure will increase your odds of guessing the correct answer. But even if you can't eliminate any of the choices, take a guess because there is no penalty for wrong answers.

  3. Above all, be sure that your answers on your answer sheet correspond to the proper numbers on your question sheet. Placing one answer in the incorrect number on the answer sheet could possibly shift all your answers to incorrect spots. Be careful to avoid this problem!

Suggested Approach with Samples

Here are a number of approaches that can be helpful in attacking many types of mathematics problems. Of course, these strategies won't work on all the problems, but if you become familiar with them, you'll find that they'll be helpful in answering quite a few questions.

Mark key words

Circling or underlining key words in each question is an effective test-taking technique. Many times you may be misled because you may overlook a key word in a problem. By circling or underlining these key words, you'll help yourself focus on what you are being asked to find. Remember, you are allowed to mark and write on your testing booklet. Take advantage of this opportunity.

SAMPLE QUESTION: If 3 yards of ribbon cost $2.97, what is the price per foot?

  1. $0.33

  2. $0.99

  3. $2.94

  4. $3.00

  5. $8.91

The key word here is foot. Dividing $2.97 by 3 will tell you only the price per yard. Notice that $0.99 is one of the choices, B. You must still divide by 3 (since there are 3 feet per yard) to find the cost per foot. $0.99 divided by 3 is $0.33, which is choice A. Therefore, it would be very helpful to mark the words price per foot in the problem.

Pull out information

Pulling information out of the wording of a word problem can make the problem more workable. Pull out the given facts and identify which of those facts will help you work the problem. Not all facts will always be needed.

SAMPLE QUESTION: A woman purchased several books at $15 each plus one more for $12. What was the average price of each book?

  1. $12

  2. $13

  3. $14

  4. $15

  5. There is not enough information to tell.

To calculate an average, you must have the total amount and then divide by the number of items, so you'll want to pull out the prices and the number of items at each price. The difficulty here, however, is that several books at $15 does not specify exactly how many books were purchased at $15 each. Does several mean two? Or does it mean three? Several is not a precise mathematical term. Therefore, there is not enough information to pull out to calculate an average. The answer is E.

Work from the answers

At times, the solution to a problem will be obvious to you. At other times, it may be helpful to work from the answers. If a direct approach is not obvious, try working from the answers. This technique is even more efficient when some of the answer choices are easily eliminated.

SAMPLE QUESTION: Barney can mow the lawn in 5 hours, and Rachel can mow the lawn in 4 hours. How long will it take them to mow the lawn together?

  1. 8 hours

  2. 5 hours

  3. 4-1/2 hours

  4. 4 hours

  5. 2-2/9 hours

You may never have worked a problem like this, or perhaps you have worked one but don't remember the procedure required to find the answer. In that case, try working from the answers. Since Rachel can mow the lawn in 4 hours by herself, it will take less than 4 hours if Barney helps her. Therefore, choices A, B, C, and D are not reasonable. Thus, the correct answer — by working from the answers and eliminating the incorrect ones — is E.

Approximate

If a problem involves number calculations that seem tedious and time consuming, round off or approximate the numbers. Replace the given numbers with whole numbers that are easier to work with. Find the answer choice that is closest to your approximated answer.

SAMPLE QUESTION: The value for (0.889 x 55) / 9.97 to the nearest tenth is

  1. 49.1

  2. 17.7

  3. 4.9

  4. 4.63

  5. 0.5

Before starting any computations, take a glance at the answers to see how far apart they are. Notice that the only close answers are C and D, but D is not a possible choice, since it is to the nearest hundredth, not tenth. Now, some quick approximations — 0.889 = 1 and 9.97 = 10 — leave you with 55/10, which equals 5.5.

The closest answer is C; therefore, it is the correct answer. Notice that choices A and E are not reasonable.

Focus on the words of formal mathematical reasoning problems

Some questions will contain formal mathematical reasoning. Be sure to focus on the words used, their meaning, and how they are connected. Don't complicate the problem.

SAMPLE QUESTION: In a drawing with five parallelograms, four of the parallelograms are rectangles and one is a rhombus. If the rhombus is not a square, and at least two of the rectangles are squares, which of the following must be true?

  1. No rhombus is a parallelogram.

  2. Exactly one rectangle is a rhombus.

  3. No rectangles are parallelograms.

  4. Each parallelogram is a rectangle.

  5. At least three of the parallelograms are rhombi.

Since each square is a rhombus, and at least two of the rectangles are squared, then at least three of the parallelograms are rhombi. Choice E is the correct answer.