Test Information Guide
Field 77: Middle School Mathematics/Science
Sample Multiple-Choice Questions
The following reference material will be available to you during the test:
Formulas
Periodic Table
Calculators will NOT be provided for the Middle School Mathematics/Science test.
Number System and Quantity
Objective 0002
Use rational numbers, ratios, and proportional relationships.
1. Map software suggests that it will take 1 hour and 20 minutes to travel 77 miles on a stretch of roadway if a driver's current speed remains constant. If a driver travels, on average, about 5 miles per hour slower than this speed, how far will the driver have traveled after 30 minutes?
- 21 and seven eighths miles
- 24 and three eighths miles
- 24 and seven twelfths miles
- 26 and seven eighths miles
- Answer
- Correct Response: A.
Correct Response: A.
Algebra, Functions, and Modeling
Objective 0003
Use patterns to model and solve problems
2. Use the diagram below to answer the question that follows.
A diagram showing three patterns of linked polygons. Each pattern consists of a single polygon, followed by two of the same polygon joined along a side, followed by three of the same polygon consecutively joined along sides. The first pattern is labeled 3 gons, and the polygons used are equilateral triangles. The second pattern is labeled 4 gons, and the polygons used are squares. The third pattern is labeled 5 gons, and the polygons used are regular pentagons.
A student arranges regular n-gons, each with a side length measuring 1 unit, as shown in the diagram. The student then calculates the perimeter, P, for each iteration, k, of the given pattern. For any regular n-gon, which of the following equations can be used to calculate the perimeter of the k eth iteration?
- P equals open paren N minus 2 close paren K plus 2
- P equals open paren 2 K plus 2 close paren N
- P equals open paren N minus 1 close paren K plus 1
- P equals open paren K plus 1 close paren N
- Answer
- Correct Response: A.
Correct Response: A.
Objective 0005
Demonstrate knowledge of relations and functions.
3. The function h of x can be defined by h of x = f of g of x where f of x = x to the power of negative 1 half and g of x = open paren 2 minus x close paren squared. What is the domain of h of x?
- open bracket 0 comma infinity close paren
- open interval negative infinity comma infinity
- open interval negative infinity comma 2 union open interval 2 comma infinity
- open bracket 0 comma 2 close paren union open interval 2 comma infinity
- Answer
- Correct Response: D.
Correct Response: D.
Geometry and Measurement
Objective 0010
Apply properties of two- and three-dimensional figures.
4. Use the diagram below to answer the question that follows.
A diagram showing a composite figure consisting of five congruent isosceles triangles that share a single apex and are joined consecutively along their sides, with a regular pentagon sharing a side with the base of the fifth triangle. The diagram is labeled with lowercase letters as follows: a is the distance from the center of the pentagon to a vertex; b is the distance from the center of the pentagon to the middle of a side; c is the length of each of the two congruent sides of every triangle; d is the length of the base of each triangle; e is the length of the altitude of each triangle.
The diagram shows a net of a right solid with a regular base. The height of the solid formed from the net can be computed by evaluating which of the following expressions?
- the root of the quantity c squared minus a squared
- the root of the quantity c squared minus b squared
- the root of the quantity e squared minus a squared
- the root of the quantity e squared minus d squared
- Answer
- Correct Response: A.
Correct Response: A.
Statistics and Probability
Objective 0012
Understand the principles, techniques, and applications of statistics.
5. Medical personnel often use blood tests to determine whether patients have acceptable levels of different substances in their bodies and then use these tests to establish appropriate treatment. For one particular substance, doctors expect to see 4.8 mmol/L with a standard deviation of 0.6 mmol/L of the substance in patients' bodies. A doctor discovers that one patient's level of this substance is 1.2 standard deviations below the mean. How much of the substance is in the patient?
- 3.24 mmol/L
- 4.08 mmol/L
- 5.52 mmol/L
- 6.36 mmol/L
- Answer
- Correct Response: B.
Correct Response: B.
Technology / Engineering
Objective 0014
Apply knowledge of engineering design.
6. A small software engineering firm is working on a new graphical user interface. The firm has come up with three different prototypes. Which of the following approaches would be the best next step in the design process?
- assembling a representative focus group and analyzing feedback
- developing all three prototypes and using the one that is ready first
- distributing prototypes to members of the firm and seeking feedback
- analyzing the production costs and selecting the least expensive option
- Answer
- Correct Response: A.
Correct Response: A.
Objective 0016
Demonstrate knowledge of technological systems.
7. In the internal combustion engine, a mixture of gasoline vapor and air in a cylinder is ignited by a spark. One chemical reaction for this process is given below.
2 c sub 8 H sub 18 plus 25 O sub 2 yields 16 C O sub 2 plus 18 H sub 2 O plus 10,108 kilojoules of heat
Which of the following scientific principles most accurately explains the role of this reaction in the production of energy in an internal combustion engine?
- An increase in the number of moles generates additional kinetic energy.
- Heat from the reaction causes the gases to expand and do work.
- Molecules of carbon dioxide contain more energy than hydrocarbon molecules.
- Energy is released as water vapor changes to the liquid phase.
- Answer
- Correct Response: B.
Correct Response: B.
Earth and Space Science
Objective 0018
Apply knowledge of Earth's geosphere, geologic history, and processes.
8. While traveling a Massachusetts highway, a geologist observed an abundance of metamorphic rock. Which of the following conclusions can be made based on this observation?
- There was a continental collision.
- There was a divergent plate boundary.
- There was a shallow ocean covering the region.
- There was a glaciation event that covered the area.
- Answer
- Correct Response: A.
Correct Response: A.
Life Science
Objective 0022
Apply knowledge of the characteristics of populations, communities, ecosystems, and biomes.
9. Which of the following abiotic factors is the primary limiting factor for reptiles living in a tundra ecosystem?
- quantity of large predators
- temperature
- quantity of small prey
- humidity
- Answer
- Correct Response: B.
Correct Response: B.
Physical Science
Objective 0026
Apply knowledge of the states of matter, particle motion, and heat.
10. Use the diagram below to answer the question that follows.
A piston in a cylinder is shown. The amount of the gas inside the cylinder is 1,000 milliliters.
Students are investigating the effects of passing a bar magnet through a coil of wire atteached to an ammeter, as shown in the diagram. This activity is most appropriate for introducing students to which of the following applications of electromagnetism?
- how to build an electromagnet
- how electric motors operate
- how to build an electric circuit
- how electricity is generated
- Answer
- Correct Response: D.
Correct Response: D.