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Section 7: Sample Multiple-Choice Questions
WEST–B Mathematics (097)

The sample test questions in this study guide are designed to give you an introduction to the nature of the questions included in the Washington Educator Skills Test–Basic (WEST–B). They represent the various types of questions you may expect to see on the actual test; however, they are not designed to predict your performance on the test as a whole.

Work through the sample questions carefully before referring to the answers. The correct response and test objective being assessed are provided for each question. When you are finished with the sample questions, you may wish to review the test objectives and descriptive statements provided in the test framework for this test field.

In addition to reading and answering the sample questions, you should also utilize the following preparation materials available in this study guide:

Practice Questions

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Mathematics

Objective 0013: Understand and apply concepts and principles of numbers and operations.

1. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree?

  1. 16 feet
  2. 52 feet
  3. 81 feet
  4. 260 feet
Enter to expand or collapse answer.Answer expanded
Correct Response: B. The length of a shadow is proportional to the height of the object casting the shadow. This proportion can be expressed in the following way: height of the student over student's shadow equals height of the tree over tree's shadow. Since the problem asks for the height of the tree, let x equal height of the tree. Using x and the numbers given results in the proportion 4 fifths equals x over 65. This proportion can be solved for x by cross-multiplying. open parenthesis 4 closed parenthesis open parenthesis 65 closed parenthesis equals 5x, or equivalently 5x equals 260, so x equals 260 over 5 equals 52 feet.

2. Simplify the expression 44 minus 4 times 8 plus 4 squared divided 4.

  1. 84
  2. 32
  3. 16
  4. 8
Enter to expand or collapse answer.Answer expanded
Correct Response: C. Simplifying the given expression requires correct application of the rules that specify the order in which operations should be performed. The rules specify the following order: parentheses, exponents, multiplication and division, and addition and subtraction. There are no parentheses in the given problem, but there is an exponent. The operation involving the exponent should be performed first: 44 minus 4 times 8 plus 4 squared divided 4 equals 44 minus 4 times 8 plus 16 divided 4. There is one instance of multiplication (4 times 8) and one instance of division (16 divided 4) in the problem, and these should be performed next: 44 minus 4 times 8 plus 16 divided by 4 equals 44 minus 32 plus 4. The final step in simplifying the expression is to perform addition and subtraction: 44 minus 32 plus 4 equals 12 plus 4 equals 16.

3. Which of the following numbers is the reciprocal of 7 over 100?

  1. 0.93
  2. 7.14285...
  3. 14.2857...
  4. 70
Enter to expand or collapse answer.Answer expanded
Correct Response: C. The reciprocal of 7 over 100 is 100 over 77, which can be written as the mixed number 14 2 sevenths. Converting 2 sevenths to a decimal gives 14.2857.

4. A grocery store orders eggs in cartons that are eight eggs wide by twelve eggs long. The store orders eleven of these cartons. When the order arrives, it turns out that thirty-five of the eggs have been broken in shipping. Which of the following expressions gives the number of eggs that arrived intact?

  1. open parenthesis 8 times 12 closed parenthesis divided by 11 minus 35
  2. open parenthesis 8 plus 12 closed parenthesis times 11 plus 35
  3. open parenthesis 8 plus 12 closed parenthesis plus 11 times 35
  4. open parenthesis 8 times 12 closed parenthesis times 11 minus 35
Enter to expand or collapse answer.Answer expanded
Correct Response: D. Each carton is eight eggs wide by twelve eggs long, so the total number of eggs in a carton should be 8 times 12. Eleven of these cartons will have open parenthesis 8 times 12 closed parenthesis times 11 eggs. If thirty-five eggs in the shipment arrived broken, that amount must be subtracted from the total, giving a final expression of open parenthesis 8 times 12 closed parenthesis times 11 minus 35.

Objective 0014: Understand and apply concepts and procedures of measurement.

5. If a pilot flew a plane from Santa Fe to Tulsa to Houston and then back to Santa Fe along the route indicated below, approximately how many miles did the pilot fly?

Route Map.

A map showing the states of Texas, Oklahoma, and New Mexico, with the cities of Santa Fe in New Mexico, Tulsa in Oklahoma, and Houston in Texas indicated. Straight lines connect the locations of the three cities. A scale of 200 miles to the inch is shown. The distance on the map from Santa Fe to Tulsa is between 2 and 3 inches. The distance on the map from Tulsa to Houston is between 2 and 3 inches. The distance on the map from Houston to Santa Fe is between 3 and 4 inches.

  1. 2000 miles
  2. 1700 miles
  3. 1400 miles
  4. 1100 miles
Enter to expand or collapse answer.Answer expanded
Correct Response: B. The scale below the map can be used to determine the distance between the three cities on the map. This involves finding the perimeter of the triangle formed by connecting the three cities. A useful tool can be constructed by transferring the scale to a pencil or other writing device and using a thumbnail as a marker. By using this improvised tool as a ruler, it is possible to estimate the distance as follows:

Distance from Houston to Santa Fe: less than 4 lengths and more than 3 lengths.
Distance from Santa Fe to Houston: less than 3 lengths and more than 2 lengths.
Distance from Tulsa to Houston: less than 3 lengths and more than 2 lengths.

Therefore, the distance must be less than 10 units but more than 7 units. Since each unit represents 200 miles, the distance must be less than 10 open parenthesis 200 miles close parenthesis equals 2000 miles and more than 7 open parenthesis 200 miles close parenthesis equals 1400 miles. Of the choices given, only 1700 miles meets these criteria.

6. Which unit of measurement would be the most appropriate to measure the mass of a concrete block?

  1. grams
  2. kilograms
  3. pounds
  4. tons
Enter to expand or collapse answer.Answer expanded
Correct Response: B. The problem asks for a unit to measure the mass of a concrete block; therefore, pounds and tons are not appropriate. Since a concrete block is fairly heavy, kilograms are a more appropriate measure of mass than grams.

7. The diagram shows a park with buildings on two corners. What is the area of the park if the two buildings are not included?

Route Map.

This is a rectangle, representing a park, which measures four hundred eighty feet wide by two hundred feet tall. In two corners there are smaller rectangles representing buildings. One of the smaller rectangles is one hundred forty feet wide by fifty feet tall. The other smaller rectangle is eighty feet wide by one hundred feet tall.

  1. 81,000 square feet
  2. 89,000 square feet
  3. 96,000 square feet
  4. 111,000 square feet
Enter to expand or collapse answer.Answer expanded
Correct Response: A. The area of the whole park, including the buildings, is the area of the whole rectangle, which is 480 times 200, or 96,000, square feet. The area of the first building is 140 times 50, or 7,000, square feet. The area of the second building is 80 times 100, or 8,000, square feet. The combined area of the two buildings is 15,000 square feet. The area of the park not including the buildings is 96,000 minus 15,000, or 81,000, square feet.

Objective 0015: Understand concepts and principles of geometry and solve related problems.

An isosceles triangle with a base measuring 4 units and sides measuring 5 units each.

8. Which triangle is similar to the triangle shown above?

  1. An isosceles triangle with a base measuring 4 units and sides measuring 6 units each.
  2. An isosceles triangle with a base measuring 2 units and sides measuring 2 point 5 units each.
  3. An isosceles triangle with a base measuring 4 units and sides measuring 3 units each.
  4. An isosceles triangle with a base measuring 5 units and sides measuring 5 units each.
Enter to expand or collapse answer.Answer expanded
Correct Response: B. Two triangles are similar if they have corresponding sides that are proportional. The triangle shown in the item has sides of length 5 units, 5 units, and 4 units. The triangle shown in Response B is similar to this triangle because each of its sides (2.5 units, 2.5 units, 2 units) is 1 half length of the corresponding side in the given triangle.

9. What are the coordinates of point D?

Coordinates.

A coordinate grid with a point labeled D plotted 3 units below the X axis and 2 units to the right of the Y axis.

  1. (3, negative 2)
  2. (negative 2, 3)
  3. (2, negative 3)
  4. (negative 3, 2)
Enter to expand or collapse answer.Answer expanded
Correct Response: C. A point on a Cartesian plane can be described by an ordered pair that specifies the point's value on the x-axis and the point's value on the y-axis. The value of point D on the x-axis can be found by noting that the point directly above point D on the x-axis is labeled 2. Point D's value on the y-axis can be found by noting that the point directly to the left of point D on the y-axis is labeled –3. The ordered pair that describes point D is therefore (2, –3) (Response C). Response A reverses the positions and the signs of the numbers in the ordered pair. Response B reverses only their signs. Response D reverses only their positions.

10. Angle BAC measures 45°. Angle ABC measures 75°. The whole angle ACD measures 130°. What is the measure of angle BCD?

Coordinates.

A coordinate grid with a point labeled D plotted 3 units below the X axis and 2 units to the right of the Y axis.

  1. 15°
  2. 50°
  3. 60°
  4. 70°
Enter to expand or collapse answer.Answer expanded
Correct Response: D. The angles in a triangle add up to 180°. Since angle BAC measures 45°, and angle ABC measures 75°, the measure of angle ACB must be 180° minus the sum of the other two angles. This works out to 180 degrees minus open parenthesis 45 degrees plus 75degrees closded parenthesis equals 180 degrees minus 120 degrees equals 60 degrees. Since angle ACD measures 130°, the measure of angle BCD must be 130° minus the measure of angle ACB. This works out to 130 degrees minus 60 degrees, or 70 degrees.

Objective 0016: Understand concepts and principles of probability and statistics and solve related problems.

11. A box contains 20 red marbles, 15 blue marbles, 25 yellow marbles, and 2 black marbles. If a person selects a marble at random from the box, what is the probability that the marble will be black?

  1. 1 over 62
  2. 1 over 61
  3. 1 over 31
  4. 1 over 30
Enter to expand or collapse answer.Answer expanded
Correct Response: C. The probability of an event such as the one described in the item can be expressed as a fraction whose numerator is the total number of favorable cases and whose denominator is the total number of possibilities. In the item, the favorable case is the drawing of a black marble. Since there are 2 black marbles, the numerator is 2. The total number of possibilities is the total number of marbles, or 62. The fraction representing the probability of drawing one of the 2 black marbles from the bag of 62 marbles is therefore 2 over 62 or 1 over 31.

12. A salesperson works from a company's main office between 9:00 a.m. and 1:00 p.m. from Monday through Thursday. The schedule shows times that the salesperson is unavailable to receive phone calls from clients due to meetings. An assistant will receive phone calls during these times. Which of the following values best describes the likelihood that a customer's call will be received by the assistant for the days shown?

A schedule showing meetings planned for four mornings in a week (detailed in table below). On Monday there is a sales meeting scheduled from nine thirty to ten thirty, another sales meeting from ten thirty to eleven, and a lunch meeting from twelve to one. On Tuesday there is a scheduling meeting from nine to ten, a client call from eleven to twelve, and a lunch meeting from twelve to one. On Wednesday there is a sales meeting scheduled from nine to ten thirty and another meeting scheduled from eleven thirty to twelve thirty. On Thursday a roundtable meeting with clients is scheduled from nine to twelve.

blank Monday Tuesday Wednesday Thursday
9 o'clock blank scheduling meeting sales meeting roundtable meeting with clients
9:309:30 sales meeting
10:0010 o'clock blank
10:3010:30 sales meeting blank blank
11:0011 o'clock blank client call blank
11:3011:30 blank meeting
12:0012 o'clock lunch meeting lunch meeting blank
12:3012:30 blank blank
  1. 31%
  2. 45%
  3. 55%
  4. 69%
Enter to expand or collapse answer.Answer expanded
Correct Response: D. The calendar contains 32 half-hour blocks of time across 4 days.The salesperson's assistant will need to receive phone calls for 22 of the half-hour blocks scheduled for meetings and appointments. The likelihood of the assistant receiving the call is 22 over 33, or approximately 69%.

13. The operators of a parking lot recorded the lengths of time, in minutes, that seven cars were parked at the lot. These data are shown below:

22, 95, 56, 100, 13, 156, 48.

What is the difference between the mean and the median of these data?

  1. 8
  2. 14
  3. 26
  4. 30
Enter to expand or collapse answer.Answer expanded
Correct Response: B. The mean is obtained by adding the values of all the data and dividing by the number of data points. The sum of all the values is 490; there are seven data points, so the mean is 490 divided by 7 equals 70. The median is obtained by sorting the values from least to greatest and choosing the middle value. In order from least to greatest, the values are 13, 22, 48, 56, 95, 100, 156, so the median is 56. The difference between the mean and the median is 70 minus 56 equals 14.

Objective 0017: Understand concepts and principles of algebra and solve related problems.

14. Which equation describes the relationship between the x and y values in the table below?

xy
13
25
37
49
  1. y equals 3x
  2. y equals x plus 2
  3. y equals 3x minus 1
  4. y equals 2x plus 1
Enter to expand or collapse answer.Answer expanded
Correct Response: D. To find the correct equation, substitute each x-value into each equation to determine if the resulting number equals the corresponding y-value in the table. Start by substituting x equals 1 into each equation. Note that for Response C, y equals 3 open parenthesis 1 close parenthesis minus 1 equals 2 does not equal 3, so that response can be eliminated. Next, substitute x equals 2 into responses A, B, and D. Note that Responses A and B can be eliminated since for A, y equals 3 open parenthesis 2 close parenthesis equals 6 does not equal 5, and for B, y equals open parenthesis 2 close parenthesis plus 2 equals 4 does not equal 5. Response D is the only remaining choice, and it can be further verified by substituting x equals 3 and x equals 4 into the equation y equals 2 x plus 1 (Response D).

15. Solve for x.

2 x plus 7 is greater than 15

  1. x is greater than 4
  2. x is greater than 8
  3. x is greater than 11
  4. x is greater than 22
Enter to expand or collapse answer.Answer expanded
  1. Correct Response: A. This inequality can be solved as follows:
  2. First, subtract 7 from each side. 2x plus 7 is greater than 15
  3. 2x is greater than 15 minus 7
  4. 2x is greater than 8
  5. Next, divide both sides of the inequality by 2. 2x is greater than 8
  6. x is greater than 4 (Response A)

16. Ohm's law is written as I equals V over R, where I is the electric current flowing through a conductor (in amperes), V is the voltage, and R is the resistance of the conductor (in ohms). What is the amount of current when the voltage is 120 volts and the resistance is 0.6 ohms?

  1. 20 amperes
  2. 72 amperes
  3. 200 amperes
  4. 720 amperes
Enter to expand or collapse answer.Answer expanded
Correct Response: C. According to the formula, if the voltage is 120 volts and the resistance is 0.6 ohms, the current will be 120 divided by 0.6, or 200, amperes.

Objective 0018: Apply mathematical reasoning, problem-solving, and communication skills.

17. Which piece of information is extraneous for the solution of the problem below?

A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is 287 dollars and 50 cents per bus. The cost of food for each person is 18 dollars and 75 cents.

  1. number of people on the trip
  2. cost of each bus
  3. number of miles the buses will travel
  4. cost of food for each person
Enter to expand or collapse answer.Answer expanded
Correct Response: C. The total cost for the trip includes both the cost of transportation and the cost of food. The total transportation cost can be calculated by multiplying the cost of each bus (Response B) and the number of buses needed. The cost of food can be calculated by multiplying the number of people on the trip (Response A) and the cost of food per person (Response D). The two products must be added to find the total cost of the trip. Since Responses A, B, and D were all used in the calculation, only Response C is extraneous.

18. Which pair of numbers provides a counterexample to the statement below?

The product of two numbers is always greater than either of the two numbers.

  1. 1 half and 3 fourths
  2. negative 4 and negative 3
  3. 62 and 43
  4. 3.2 and 2.5
Enter to expand or collapse answer.Answer expanded
Correct Response: A. To find a counterexample to the statement, "The product of two numbers is always greater than either of the two numbers," it is necessary to find two numbers with a product that is not greater than either number. Response A provides a counterexample because the product of 1 half and three fourths is three eighths, which is less than either 1 half or 3 fourths. The other responses are not counterexamples because their products are greater than both of the original numbers.

19. Which of the following statements is equivalent to the inequality 5n minus 7 is greater than 12?

  1. Seven less than five times a number is more than twelve.
  2. Five less than seven times a number is more than twelve.
  3. Seven more than five times a number is more than twelve.
  4. Five more than seven times a number is more than twelve.
Enter to expand or collapse answer.Answer expanded
Correct Response: A. If n is an unknown number, the expression 5n represents five times that number. Subtracting 7, as in 5n minus 7, results in a value that is seven less than five times the number. So 5n minus 7 is greater than 12 states that seven less than five times a number is more than twelve.

20. Angle A in the polygon shown is 55 degrees, and angle B is 50 degrees. A student states that since the angles must add up to 180 degrees, angle C must be equal to 75 degrees. Which of the following errors is the student most likely to have made?

concave quadrilateral

A concave quadrilateral, labeled A B C D, with three acute angles at points A, B, and C. The fourth interior angle, at point D, is greater than one hundred eighty degrees.

  1. The student failed to treat angle D as a negative angle.
  2. The student assumed that the angles of all polygons must add to 180 degrees.
  3. The student ignored angle D and treated the polygon as a triangle.
  4. The student didn't continue the pattern shown by angles A and B.
Enter to expand or collapse answer.Answer expanded
Correct Response: C. The student is determining the measure of angle C given the measures of angles A and B, without reference to angle D. Given this, it is most likely that the student is treating the polygon as a triangle and ignoring angle D. (If the student had assumed that the four angles of the polygon added to 180 degrees, the conclusion would have been that angles C and D together added to 75 degrees.)