Practice Test: Middle School Mathematics/Science (77)

Given that a is irrational and b is rational, which of the following expressions could result in a rational value?

1. a +plus b
2. a ÷divided by b
3. a^ba raised to the power of b
4. a −minus b

Use the diagram below to answer the question that follows.

A diagram shows three groups, each containing one rod and 4 unit squares.

Assuming that a rod represents x and a small square represents 1 unit, the algebra tiles shown in the diagram best represent which of the following expressions?

1. 3x +plus 4
2. 3(x + 4)3 times the quantity x plus 4
3. (x + 4)³the cube of the quantity x plus 4
4. x³ + 4³x cubed plus 4 cubed

If K is both a multiple of x and a factor of y, then which of the following statements must be true?

1. ^K/_yk divided by y is a whole number.
2. ^x/_Kx over k is a whole number.
3. y is a factor of x.
4. y is a multiple of x.

Use the multiplication problem below to answer the question that follows.

The set-up to multiply the number 1, Y, 3 and 24 using the standard algorithm is shown.

The variable Y represents a single-digit number between 0 and 9. Which of the following expressions represents the amount that Y contributes to the total product?

1. 20 •times Y
2. 24 •times Y
3. 40 •times Y
4. 240 •times Y

The division problem 2 × 6⁶ + 10 × 6⁴ + ¹/₂ × 6² ÷ 2pen parentheses 2 times 6 to the sixth power plus 10 times 6 to the fourth power plus one half times 6 squared closed parentheses divided by 2 is equivalent to which of the following expressions?

1. 2 × 3⁶ + 10 × 3⁴ + ¹/₂ × 3²2 times 3 to the sixth power plus 10 times 3 to the fourth power plus one half times 3 squared
2. 2 × 6³ + 10 × 6² + ¹/₂ × 62 times 6 cubed plus 10 times 6 squared plus one half times 6
3. 6³ + 5 × 6² + ¹/₄ × 66 cubed plus 5 times 6 squared plus 1 fourth times 6
4. 6⁶ + 5 × 6⁴ + ¹/₄ × 6²6 to the sixth power plus 5 times 6 to the fourth power plus 1 fourth times 6 squared

Which of the following sets of equations best illustrates the concept that multiplication and division are inverse operations?

1. 4 ×times 1 = 4
   4 ÷divided by (–negative1) = –negative4
2. 4 ×times 0 = 0
   0 ÷divided by 4 = 0
3. 4 ×times 8 = 32
   32 ÷divided by 8 = 4
4. 32 ×times ¹/₄1 fourth = 8
   32 ÷divided by 8 = 4

A submarine is traveling 375 feet below sea level. It rises 183 feet and then dives 228 feet. If the submarine can come safely to the surface at 30 feet per second, approximately how long will it take to reach the surface?

1. 11 seconds
2. 14 seconds
3. 20 seconds
4. 26 seconds

An electronics store applies a 15%15 percent discount on a certain television, which is then followed by a 6.5%6 point 5 percent sales tax. If K represents the final amount a customer pays for the television, which of the following expressions can be used to find the original price of the television?

1. (1 − 0.15)(1.065)Kthe quantity 1 minus 0 point 1 5 times 1 point 0 6 5 k
2. (1 + 0.15)(0.935)Kthe quantity 1 plus 0 point 1 5 times 0 point 9 3 5 k
3. ^K/_{(0.85)(1 − 0.065)}k divided by the product of 0 point 8 5 and the quantity 1 minus 0 point 0 6 5
4. ^K/_{(0.85)(1 + 0.065)}k divided by the product of 0 point 8 5 and the quantity 1 plus 0 point 0 6 5

If x and y are whole numbers whose greatest common factor is 3, which of the following expressions is the least common denominator for ²/_x2 over x +plus ⁵/_y5 over y?

1. 10xy
2. 3xy
3. ^xy/₃1 third x y
4. ^xy/₁₀1 tenth x y

Given that ^a/_ba over b is a proper fraction greater than zero, which of the following inequalities is true for all positive integer values of c?

1. ^{a − c}/_{b − c}the ratio a minus b over b minus c >is greater than ^a/_ba over b
2. ^{a + c}/_{b + c}the ratio a plus c over b plus c >is greater than ^a/_ba over b
3. ^ac/_bcthe ratio a b over b c >is greater than ^a/_ba over b
4. ^{a ÷ c}/_{b ÷ c}the ratio a divided by c over b divided by c >is greater than ^a/_ba over b

Coasting down a hill, a bicyclist's speed increases at a constant rate of 0.750 point 7 5 mile per hour each second. If the bicyclist started timing the ride at the top of the hill when the speed was 5 miles per hour, how many seconds passed before the bicyclist reached a speed of 31 miles per hour?

1. 19¹/₂and 1 half seconds
2. 23¹/₄and 1 fourth seconds
3. 34²/₃and 2 thirds seconds
4. 41¹/₃and 1 third seconds

Which of the following figures describes mixed number A^b/_cwholes plus b over c in simplest form such that Abc = 8?

1. 

   Three congruent bars are divided into fifths. The first bar has the first 3 fifths shaded plus the second bar has all fifths shaded plus the last bar has the last 3 fifths shaded.

2. 

   Five congruent circles are divided into fifths. The first circle has 4 fifths shaded plus the second circle has a different set of 4 fifths shaded plus the final circle has a different set of 4 fifths shaded.

3. 

   Three congruent squares are divided into eighths. Shown is the sum of the three squares where each square has the same 6 eighths shaded.

4. 

   Four congruent circles are divided into fourths. The first circle has one fourth shaded plus the second circle has 3 fourths shaded plus the third circle has one fourth shaded.

Given that the points on each of the number lines shown below are equally spaced, on which of the following number lines does point D correspond with the fraction ¹/₄1 fourth?

1. 

   A number line is shown with 8 uniformly spaced points A through H. A is labeled 2 twenty fourths and H is labeled 2 thirds.

2. 

   A number line is shown with 7 uniformly spaced points A through G. A is labeled 1 eighth and G is labeled 3 eighths.

3. 

   A number line is shown with 6 uniformly spaced points A through F. A is labeled 1 twelfth and F is labeled one half.

4. 

   A number line is shown with 5 uniformly spaced points A through E. A is labeled 1 seventh and E is labeled 3 sevenths

Use the table below to answer the question that follows.

The table shows the number of days an offshore oil well has been leaking as a function of the diameter in miles of the oil spill. Assuming that the pattern shown in the table continues, in how many days will the diameter of the oil spill be 8 miles?

1. 50 days
2. 65 days
3. 74 days
4. 82 days

Use the table below to answer the question that follows.

If the sequence of numbers continues using the same pattern, which of the following expressions represents the value of the nth term in the sequence?

1. 2 − 8n2 minus 8 n
2. 10 − 8n10 minus 8 n
3. 8n − 28 n minus 2
4. 8n − 108 n minus 10

A nurse administers 100 milligrams of a medication to a patient at noon. The amount of the medication in the patient's bloodstream decreases at a rate of 10% per hour. Which of the following types of mathematical function best describes the relationship between the number of hours since noon and the amount of medication in the patient's bloodstream at that time?

1. exponential
2. linear
3. proportional
4. quadratic

Use the diagram below to answer the question that follows.

The diagram shows a rectangle surrounded by a stone path, where x represents the narrower path-width along the short sides of the rectangle and 2x represents the wider path width along the long sides of the rectangle. The region containing the stone path and monument is a 20-foot by 12-foot rectangle.

The diagram shows how the rectangular base of a monument is surrounded by a stone path, where x represents the narrower path-width. The width of the stone path on the longer side of the monument is twice the width on the shorter side. If the region containing the stone path and monument is a 20-foot by 12-foot rectangle, which of the following expressions represents the area of the base of the monument in square feet?

1. 2(x² − 22x + 120)2 times the trinomial x squared minus 22 x plus 120
2. 2(x² − 26x + 120)2 times the trinomial x squared minus 26 x plus 120
3. 8(x² − 11x + 30)8 times the trinomial x squared minus 11 x plus 30
4. 8(x² − 13x + 30)8 times the trinomial x squared minus 13 x plus 30

Which of the following equations can be used to determine x, the number of liters of 15%15 percent acid solution that must be added to 3 liters of a 3%3 percent acid solution to obtain a 12%12 percent acid solution?

1. 0.09x + 0.15 = 0.12x0 point 0 9 x plus 0 point 1 5 equals 0 point 1 2 x
2. 0.15x + 0.09 = 0.12x + 30 point 1 5 x plus 0 point 0 9 equals 0 point 1 2 x plus 3
3. 0.15x + 0.09 = 0.12x + 0.360 point 1 5 x plus 0 point 0 9 equals 0 point 1 2 x plus 0 point 3 6
4. 0.09x + 0.15 = 0.12x + 0.360 point 0 9 x plus 0 point 1 5 equals 0 point 1 2 x plus 0 point 3 6

Which of the following graphs displays the solution set for the inequality – ²/₃(3m − 2) < ¹/₂(m + 1)negative 2 thirds times the quantity 3 m minus 2 is less than one half times the quantity m plus 1?

1. 

   A number line is shown with an open circle on negative one third and a shaded line extending to the left.

2. 

   A number line is shown with an open circle on negative one third and a shaded line extending to the right.

3. 

   A number line is shown with an open circle on one third and a shaded line extending to the left.

4. 

   A number line is shown with an open circle on one third and a shaded line extending to the right.

Use the graphs below to answer the question that follows.

Three graphs are shown. The first graph has vertical axis label "height" and horizontal axis label "weight", with point B at approximately 1, 1 and point A at approximately 4, 5. The second graph shows a vertical axis label of weight and a horizontal axis label of price, with point B at approximately 2, 5, and point C at approximately 5, 2. The third graph shows a vertical axis label of price and a horizontal axis label of height, with Point A at approximately 2 3 and Point C at approximately 4 3.

The height, weight, and price of 3 soup cans, A, B, and C, are compared and the results are shown in the graphs. Based on the information in the graphs, which of the following statements is true?

1. Can C weighs the least.
2. Cans A and B are the same height.
3. Can B is the most expensive.
4. Can A is the tallest.

Given that f(x)f of x = x²x squared and g(x)g of x = (x + 5)²the quantity x plus 5 squared, which of the following statements describes the relationship between f(x)f of x and g(x)g of x?

1. The graph of g(x)g of x is equivalent to the graph of f(x)f of x −minus 5.
2. Shifting the graph of g(x)g of x to the left 5 units results in the graph of f(x)f of x.
3. The graph of f(x)f of x is equivalent to the graph of g(x)g of x −minus 5.
4. Shifting the graph of f(x)f of x to the left 5 units results in the graph of g(x)g of x.

The first part of a long car trip is made at highway speed. The driver then reduces the speed of the car in traffic, later resuming highway speed before exiting the highway and following local roads to the destination. The return home is at a steady rate on local roads. Which of the following graphs represents the relationship of distance from home, d, to time, t, for the round trip?

1. 

   The first quadrant of a coordinate plane is shown with "Distance from Home, d" on the vertical axis and "Time, t" on the horizontal axis. The graph shows a line with the following characteristics, starting at the origin: a steep positive slope, then a lesser positive slope, then the initial slope, then a lesser positive slope, then a negative slope to the t axis.

2. 

   The first quadrant of a coordinate plane is shown with "Distance from Home, d" on the vertical axis and "Time, t" on the horizontal axis. The graph shows a line with the following characteristics, starting at the origin: a steep positive slope, then a lesser positive slope, then the initial slope, then a lesser positive slope, then an even lesser positive slope.

3. 

   The first quadrant of a coordinate plane is shown with "Distance from Home, d" on the vertical axis and "Time, t" on the horizontal axis. The graph shows a line with the following characteristics, starting at the origin: a steep positive slope, then a lesser positive slope, then the initial slope, then a lesser positive slope, then a vertical line to the t axis.

4. 

   The first quadrant of a coordinate plane is shown with "Distance from Home, d" on the vertical axis and "Time, t" on the horizontal axis. The graph shows a line with the following characteristics, starting at the origin: a steep positive slope, then a zero slope, then the initial slope, then a zero slope, then the initial slope, then a zero slope, followed by a lesser positive slope.

A local school requires 3 teachers as chaperones for every 20 students attending a field trip. Which of the following graphs best relates x, the number of students, to y, the number of teachers, on any given field trip?

1. 

   A graph of the line is shown in the first quadrant of the coordinate plane. The line has a y intercept of 12 and an x intercept of 80.

2. 

   A graph of the line is shown in the first quadrant of the coordinate plane. The line has a y intercept of 60 and an x intercept of 9.

3. 

   A graph of the line is shown in the first quadrant of the coordinate plane. The line has passes through the origin and the point 30, 200.

4. 

   A graph of the line is shown in the first quadrant of the coordinate plane. The line passes through the origin and the point 100, 15.

Two points, (–2 , k + 8)negative 2, k plus 8 and (2, k)2, k, lie on line ℓL. Which of the following expressions represents the x-intercept of line ℓL in terms of k?

1. k + 4k plus 4
2. –k − 4negative k minus 4
3. ^{k + 4}/₂1 half the quantity k plus 4
4. ^{k − 4}/₂1 half the quantity k minus 4

Two lines, k and p, are parallel. If the equation for line k is 3x + Ay = B3 x plus A y equals B, and line p passes through the point (–4 , 0)negative 4, 0, which of the following equations represents line p?

1. y = ³/_A(x − 4)y equals 3 over A times the quantity x minus 4
2. y = ^3x/_A − 4y equals 3 x divided by A all minus 4
3. y = – ³/_A(x + 4)y equals negative 3 over A times the quantity x plus 4
4. y = – ^3x/_A + 4y equals negative 3 x divided by A all plus 4

Use the graph below to answer the question that follows.

A coordinate plane is shown. A series of lines intersect through the point 2 negative 3 on the graph.

Given that k is a slope value, the family of lines shown in the graph can be described using which of the following equations?

1. y + 3 = kx − 2y plus 3 equals k x minus 2
2. y + 3 = k(x − 2)y plus 3 equals k times the quantity x minus 2
3. y = kx + 2 − 3y equals k x plus 2 minus 3
4. y = k(x + 2) − 3y equals k times the quantity x plus 2 all minus 3

A farmer triples the area of a square chicken pen by increasing its length by 4 meters and its width by 2 meters. Which of the following equations could be a step in the process of finding x, the side length of the original pen?

1. x² − 3x − 4 = 0x squared minus 3 x minus 4 equals 0
2. x² + 6x + 8 = 0x squared plus 6 x plus 8 equals 0
3. 2x² + 6x − 8 = 02 x squared plus 6 x minus 8 equals 0
4. 3x² − 2x − 4 = 03 x squared minus 2 x minus 4 equals 0

The graph of a parabola of the form y = x² + bx + cy equals x squared plus b x plus c crosses the y-axis at –negative36 and the x-axis at x = 3. At what other point does the graph cross the x-axis?

1. x = –negative12
2. x = –negative9
3. x = 9
4. x = 12

Use the diagram below to answer the question that follows.

A net for a right cone is shown that depicts a sector for a large circle connected to a smaller circle. The sector for the large circle has a central angle of 60 degrees and a radius of 10 centimeters.

The diagram shows the net of a right cone. Which of the following expressions represents the area of the cone's base in square centimeters?

1. ²⁵/₃ π25 pi over 3
2. ²⁵/₆ π25 pi over 6
3. ²⁵/₉ π25 pi over 9
4. ²⁵/₃₆ π25 pi over 36

The edges of a small cube are scaled by a factor of 4. How does the surface area–to-volume ratio for the larger cube compare to that of the smaller cube?

1. The ratio is smaller by a factor of 4.
2. The ratio is smaller by a factor of 2.
3. The ratio is larger by a factor of 2.
4. The ratio is larger by a factor of 4.

The edge of a cube measures 10 inches, rounded to the nearest inch. Using the rounded length, a student calculates the volume of the cube to be 1000 cubic inches. Which of the following computations is most relevant to establishing the maximum amount of error in the student's reported volume?

1. (10.49 − 10)³the cube of the difference 10 point 4 9 minus 10
2. (10.49 − 9.5)³the cube of the difference 10 point 4 9 minus 9 point 5
3. 10³ − 9³10 cubed minus 9 cubed
4. 10.49³ − 10³10 point 4 9 cubed minus 10 cubed

Use the diagram below to answer the question that follows.

Two horizontal lines are shown. Triangle A B C is drawn between them such that vertex B is on the top line and vertices A and C are on the bottom line. There is a line segment B D that connects vertex B to a point D that is between A and C on the bottom line. There is also point E on the top line, to the right of vertex B.

Which of the following assumptions can be made about the figure shown?

1. Point A is on
2. ACline A C ≅is congruent to BCline B C
3. ∠ADBangle A D B is a right angle
4. ∥is parallel to

Triangle ABCA B C is a right triangle with hypotenuse ABA B. Segment MNM N is drawn parallel to side ACA C with M on hypotenuse ABA B and N on side CBC B. If ACA C = 20, CNC N = 12, and MNM N = 12, what is the length of side CBC B?

1. 16
2. 18
3. 20
4. 30

Use the diagram and information below to answer the question that follows.

Quadrilateral A B C D is shown with diagonals A C and B D. The intersection of the diagonals forms an angle of x degrees.

If ADsegment A D ≅is congruent to ABsegment A B and DCsegment D C ≅is congruent to BCsegment B C, then which of the following statements must be true?

1. DXsegment D X ≅is congruent to BXsegment B X
2. AXsegment A X ≅is congruent to CXsegment C X
3. ∠DAXangle D A X ≅is congruent to ∠ADXangle A D X
4. ∠DBCangle D B C ≅is congruent to ∠BDAangle B D A

Use the information below to answer the question that follows.

Quadrilaterals are placed in the appropriate sections of a Venn diagram based on the properties of their diagonals, as shown below.

A Venn diagram is shown with three overlapping circles. One circle is labeled "diagonals are congruent", another circle is labeled "Diagonals bisect each other", and the third circle is labeled, "diagonals are perpendicular". The overlapping region that represents the intersection between "Diagonals bisect each other" and "diagonals are perpendicular" but not "diagonals are congruent" is shaded.

Which of the following quadrilaterals is included in the shaded section?

1. kite
2. rectangle
3. rhombus
4. parallelogram

Use the diagram below to answer the question that follows.

A diagram shows a sphere inscribed in a cube. The radius of the sphere is r, and the side lengths for the cube are 2r.

A sphere is inscribed in a cube as shown in the diagram above. If the volume of the cube is 64 cubic inches, what is the approximate volume of the sphere?

1. 19 cubic inches
2. 33 cubic inches
3. 41 cubic inches
4. 50 cubic inches

Use the diagram below to answer the question that follows.

A vertical line, L, is the axis of revolution for a composite shape that is formed by a rectangle connected to a quarter of a circle. The rectangle has dimensions z and 2z, and the radius of the quarter circle is equal to the length of the shared side with the rectangle, z.

The diagram shows a figure made up of a quarter of a circle adjacent to a rectangle that has dimensions z × 2zz times 2 z. If the figure is rotated about line ℓL, which of the following expressions represents the volume of the rotated figure?

1. ^7πz3/₃7 pi z cubed over 3
2. ^8πz3/₃8 pi z cubed over 3
3. ^10πz3/₃10 pi z cubed over 3
4. ^14πz3/₃14 pi z cubed over 3

Use the graph below to answer the question that follows.

Triangle A B C is graphed in the first quadrant of a coordinate plane. Vertex A is located at 8 8, Vertex B is located at 0 4, and Vertex C is located at 2 0.

Which of the following expressions represents the area of the circle that circumscribes △ABCtriangle A B C, given that ACA C is the diameter of the circle?

1. 5π5 pi
2. 10π10 pi
3. 20π20 pi
4. 25π25 pi

For any triangular region, the center of mass is located at the intersection of its three medians. If the center of mass of triangle A(0, 0)0, 0, B(14, 0)14, 0, C(4, 12)4, 12 is located at (k, 4)k, 4, what is the value of k?

1. ⁸/₃8 thirds
2. ¹⁰/₃10 thirds
3. 6
4. 7

Use the diagram below to answer the question that follows.

A trapezoid is shown in the first quadrant of the coordinate plane with vertex A at (1, 1), vertex B, vertex C at (5, 8), and vertex D located at (1, 8) There is a vertical line segment with endpoints E and F that is parallel to segment CB and bisects segment E C and segment A B. Another horizontal line segment connects point F to a point, G, located on segment A D.

Quadrilateral ABCDA B C D is constructed on a coordinate plane, as shown in the diagram. EFsegment E F bisects DCsegment D C and ABsegment A B, and triangle AGFA G F is isosceles. What is the area of the rectangle DEFGD E F G?

1. 10
2. 12
3. 14
4. 20

A bar graph would be the best choice for displaying which of the following sets of data?

1. the percentage of total pieces of carry-on luggage that fall within various weight ranges for a particular airline
2. the relationship between the number of hours a group of students spend reading and their scores on a standardized verbal skills test
3. the number of pairs of sneakers of each of six brands sold in a season by a particular sporting goods store
4. the average weekly earnings for construction workers over the last 20 years

Use the stem-and-leaf plot below to answer the question that follows.

A stem and leaf plot is shown with stems 0, 1, 2, 3, and 4. Stem 0 has leaves 7 7 9 9 9. Stem 1 has leaves 0 0 3 4 4 8 8 9 9. Stem 2 has leaves 0 2 5 5 8 8 9 9. Stem 3 has leaves 2 5 5 8. Stem 4 has leaves 0 2 2 4. Key 1 to 0 equals 10

An athletic team plays ten games per season. The team's scores for the last three seasons are shown in the stem-and-leaf plot. What are the median score and interquartile range for these scores?

1. median = 21, interquartile range = 19
2. median = 23, interquartile range = 19
3. median = 21, interquartile range = 37
4. median = 23, interquartile range = 37

Use the data set below to answer the question that follows.

0, 0, 1, 1, 1, 2, 4, 4, 4, 4, 5, 6, 6, 7, 8

A human resources manager is compiling data on the number of sick days taken by employees during the previous year. The data are shown above. Which of the following statistics will be  start bold least end bold  affected if an employee who took 15 sick days is included in the data set?

1. maximum
2. mean
3. median
4. range

In a particular study, the heights of 50,000 16-year-old students were found to be normally distributed with a mean height of 168 cmcentimeters and standard deviation 5 cmcentimeters. Approximately how many students had a height of at least 173 cmcentimeters?

1. 8,000
2. 16,000
3. 34,000
4. 42,000

A state representative tracks constituents' communications by phone, mail, or e-mail regarding a bill to be voted on. The representative counts 1500 total communications, with 70 percent in favor of the bill. Which of the following statements describes the validity of these results in representing the opinions of all constituents?

1. The results must be valid because a large number of people made the effort to communicate with their representative.
2. The results must be valid because all constituents have access to at least one of these methods of communication.
3. The results may not be valid because a special interest group or groups may have been responsible for most of the favorable communications.
4. The results may not be valid because the outcome of the vote for the bill is not yet known.

A student surveyed peers about two movies that were released over the weekend, a comedy movie and an animated movie. Of the peers the student surveyed, 55%55 percent of them had seen the comedy movie, 28%28 percent had seen the animated movie, and 14%14 percent had seen both movies. If the survey is representative of all students at the school, what is the probability that a randomly selected student saw neither movie?

1. 13%13 percent
2. 17%17 percent
3. 31%31 percent
4. 41%41 percent

Use the diagram below to answer the question that follows.

A diagram is shown with an initial point labeled "box of markers". Three lines branch out from the initial point labeled "red", "green", and "blue". At the end of each of those lines there are two branches labeled "dry" and "not dry" for a total of 6 branches at the end of the diagram.

The diagram above shows the composition of a box of used color markers in a classroom. There are 2 red markers, 4 green markers, and 6 blue markers. One-half of the red markers have dried out, 25%25 percent of the green markers are dry, and 50%50 percent of the blue markers are dry. What is the probability that a marker randomly selected from the box will be dried out?

1. ³/₁₂3 twelfths
2. ⁵/₁₂5 twelfths
3. ⁶/₁₂6 twelfths
4. ⁷/₁₂7 twelfths

A student places in a bag a blue number cube and two red number cubes, each with 6 faces numbered from 1 to 6. A friend will select two number cubes at random and then roll them. What is the probability that the result will be two red number cubes with a sum of 3?

1. ¹/₅₄1 fifty-fourth
2. ¹/₃₆1 thirty-sixth
3. ¹/₂₂1 twenty-second
4. ¹/₁₈1 eighteenth

In a bag containing only red and green grapes, there are 25 red grapes. After a child eats 5 green grapes, the probability of randomly choosing a green grape is less than 25%25 percent. What is the largest number of grapes that the bag could have contained originally?

1. 43
2. 39
3. 38
4. 31

A statistician is interested in determining the probability of getting at least one vowel (A, E, I, O, U) in random samples of the English alphabet. Which of the following simulations would generate data to answer this question?

1. using a computer to randomly select 1000 five-letter words from a dictionary
2. assigning the numbers 1–through 26 to the letters A–to Z and using a calculator or computer to generate 100 random sets of five numbers
3. designating each side of five coins as either vowel or consonant and flipping the set of five coins 100 times
4. writing each letter of the alphabet on pieces of paper and randomly drawing a group of five-letter samples until a sample is drawn with only one vowel

Use the information below to answer the question that follows.

Students conduct an experiment to examine how the materials used to build a levee affect the ability of the levee to prevent flooding. As a first step, they use a water table to examine how quickly running water erodes model levees built out of sand, gravel, or soil.

Which of the following questions should the students consider to help determine which material would be most effective at preventing running water from breaching a levee?

1. How does the material used to build the levee affect the shape and dimensions of the levee?
2. What are the costs per truckload of each of the materials under consideration for building the levee?
3. Which materials are readily available near the site of the levee versus which need to be transported from elsewhere?
4. How does the material used to build the levee affect the ability of the levee to support vehicles on a road built along its surface?

Use the information below to answer the question that follows.

Scientists are working to develop an early warning system for volcanic eruptions. The system will rely on the existing seismic network that is already in place to monitor seismic activity surrounding active volcanoes. The seismic stations will automatically communicate their data to the relevant government agencies, where it will be immediately analyzed and formulated into three levels of warnings.

Which component of the engineering design process must be considered to finalize this warning system?

1. defining the problem to be solved
2. brainstorming and selecting a solution
3. modeling and testing prototypes
4. researching criteria and constraints

When evaluating an engineering design for a structure such as a bridge, it would be most important to take which of the following actions first?

1. comparing the load-bearing strength of a variety of different materials that are being considered for the components
2. calculating the necessary strength of components based on extreme, rather than normal, loads
3. selecting materials for components based on the mean load expected on each component, rather than the mode or median load
4. testing the strength of components by subjecting a physical model to a variety of loads

Students are designing a single-axis mechanical arm for a simulated Mars rover. The arm should be able to grasp and lift objects. Which of the following tests would appropriately evaluate the effectiveness of each prototype, based on the project's goals?

1. determining how large of an object can be raised to a set distance and height
2. calculating the durability of the component materials in the arm
3. moving the arm to perform various typical tasks
4. timing the arm as it holds up one object

Patio furniture that is meant to be left outside can be made from several different types of materials: aluminum, steel, molded plastic resin, wicker, or rot-resistant woods, such as cedar or redwood. Compared with the other options listed, steel possesses which of the following design feature advantages?

1. superior resistance to rain and sunlight
2. wider range of shapes and colors
3. better comfort during all seasons
4. greater strength and sturdiness

An auto repair shop has a number of tools, including a rivet gun for fastening body parts to the frame and a wrench for removing and replacing lug nuts on a tire. The shop also uses a large block and tackle for raising an engine block out of the engine compartment and a mallet to pound out dents in the car frames. Being able to measure the torque produced when using the tool would be most important when using which of these tools?

1. mallet
2. wrench
3. block and tackle
4. rivet gun

Which of the following scientific principles relating to the structure of materials most directly explains why diamond-dust drill bits are used to drill holes in tile, porcelain, glass, or stone?

1. The coefficient of friction between two materials depends on the smoothness of the surfaces that are in contact.
2. The hardness of a material depends on the structure of its molecular lattice and the type of bonds between its atoms.
3. The durability of a material and its resistance to fracture depends on the direction of cleavage planes within the material.
4. The melting point of a material depends on the amount of energy needed to break the bonds between the molecules in the material.

Use the information below to answer the question that follows.

Hot-dip galvanizing is the process of immersing steel in a bath of molten zinc. While the steel is immersed in the zinc, a metallurgical reaction occurs between the iron and the zinc. The end result is a multilayer coating on the surface of the object consisting of zinc and zinc-iron alloy, which is resistant to oxidation and corrosion.

Hot-dip galvanizing is an example of which of the following secondary processes of manufacturing?

1. conditioning
2. finishing
3. assembling
4. forming

Use the table below to answer the question that follows.

Which line in the table matches a tool with the proper safety procedure to handle it in a workspace?

1. Line 1
2. Line 2
3. Line 3
4. Line 4

Advances in which of the following areas have most led to improvements in efficiency and reduction of emissions of internal combustion engines produced since the 1980s 19 eighties ?

1. thermodynamics
2. extraction of fuels
3. aerodynamics
4. embedded electronic microcontrollers

Cell-phone technology has spread to many parts of the world that never previously had landline-based telephone service. Which of the following qualities of cell-phone technology is likely most responsible for this phenomenon?

1. It provides the combined functionality of televisions, radios, and computers.
2. It does not require an extensive on-the-ground infrastructure.
3. It is able to transmit text, images, and videos in addition to voice.
4. It has interchangeable software components.

Airlines use systems engineering to model the supply of and the demand for flights between various cities at various dates and times. These models require a variety of data inputs to determine what flights will be made available at what dates and times. Which of the following examples of quantitative information would most likely be a type of input data needed for such a model?

1. passenger capacities of different airplanes in the fleet
2. number of flights to be scheduled on a particular day
3. net profits earned each day, broken down by region
4. how much to charge for each seat on a flight

Use the diagram below to answer the question that follows.

An arrow diagram is shown with a microcontroller in the center. The photo re zis tor, power supply, and photoelectric sensor all point to the microcontroller. From the microcontroller, arrows point to the relay and then from the relay to a light bulb.

A person installs a system in their home that automatically turns certain lights off during the day and on during the night. Which of the following components of this system is a processing device in this system?

1. microcontroller
2. power supply
3. photoresistor photo re zis tor 
4. light bulb

Use the table below to answer the question that follows.

Which of the following factors best explains the difference in orbital velocity among the three planets shown in the table?

1. the reduction in the density of each planet with increased distance from the Sun
2. the decline in the gravitational force between the Sun and the planet with increased distance from the Sun
3. the greater tilt of the orbit of each planet with increased distance from the Sun
4. the greater length of the orbit and increased length of the year for each planet with decreased distance from the Sun

Which of the following statements best explains why a lunar eclipse occurs rarely instead of every time that there is a full moon?

1. Earth, the Moon, and the Sun are seldom in alignment because the plane of the Moon's orbit is tilted relative to that of Earth.
2. Earth, the Moon, and the Sun are usually lined up only during the day when Earth does not cast a shadow on the Moon.
3. Earth only casts a shadow on the Moon at the points in its elliptical orbit when it is nearest to the Sun.
4. Earth's shadow is usually too small to be seen on the disk of the Moon when it is full.

Which of the following statements most accurately describes why there are few fossils present in the fossil record from the Archean and Proterozoic eons?

1. Populations of organisms in the Archean and Proterozoic eons were too small to be preserved in groups.
2. Organisms in the Archean and Proterozoic eons inhabited environments that did not favor preservation.
3. Individual organisms in the Archean and Proterozoic eons were too small in size to be preserved.
4. Organisms in the Archean and Proterozoic eons generally lacked easily preserved hard body parts.

Growing salt crystals in a middle school earth science laboratory exercise would best help students understand the formation of which of the following types of rock?

1. inorganic limestone
2. sandstone
3. metamorphic granite
4. basalt

Which of the following provides the best example of chemical weathering?

1. the slumping of unconsolidated sediments during a rainstorm
2. the breakup of a granite outcrop from temperature changes
3. the dissolution of limestone by groundwater
4. the formation of talus slopes from frost wedging

The deflection of winds and the formation of ocean gyres are primarily caused by:

1. the transfer of heat from the tropics to the poles.
2. the back-and-forth movement of tides.
3. the evaporation of surface water.
4. the Coriolis effect.

Use the diagram below to answer the question that follows.

A diagram entitled “Atmospheric layer” shows a stacked bar graph with a y-axis of altitude above sea level in kilometers. At the bottom of the bar graph, from 0 to 10 is the troposphere. Next, from 10 to 50 is the stratosphere and from 50 to 80 is the mesosphere. Above this from 80 to an undefined point is the ionosphere. Then, from the undefined point to 500 is the thermosphere. At the very top, from 500 until the top of the chart is the exosphere.

A scientist collects air samples to determine the degree to which the ozone layer has recovered from the damage caused by chlorofluorocarbon aerosols in the past. The altitude from which a scientist needs to collect the samples is approximately:

1. 5 kilometers above sea level.
2. 25 kilometers above sea level.
3. 70 kilometers above sea level.
4. 85 kilometers above sea level.

Which of the following is most directly caused by differential heating of the land surface and ocean surface?

1. the changing strength of the trade winds in different seasons
2. the early spring tornadoes that occur along the Gulf Coast
3. the varying speeds of the jet stream over the course of the year
4. the onshore breezes that develop on warm summer afternoons

During late February in southern New England, a warm precipitation-producing air mass moves into the region. Although the temperature of air aloft is well above average for the time of year, a thin layer of extremely cold air remains trapped at the bottom of valleys in the interior. Under these conditions, it is most likely that if steady precipitation falls in these valleys, it will be in the form of:

1. snow pellets.
2. wet snow that accumulates rapidly.
3. heavy sleet.
4. rain that freezes on impact.

During the 1990s 19 nineties , Doppler radar replaced the radar systems that had been in place for many decades. One of the primary advantages of Doppler radar over conventional radar is that it can be used to:

1. estimate the water equivalent of falling frozen precipitation.
2. measure the horizontal velocity of falling precipitation.
3. calculate the total precipitation that falls over an area.
4. measure precipitation intensity over a particular area.

Which of the following statements best explains why most potential sites for development of geothermal power plants in the United States are in the western part of the country, such as Nevada, Colorado, Arizona, and California?

1. The western states have higher groundwater temperatures due to their drier and hotter climate.
2. The western states have higher groundwater temperatures due to the greater tectonic activity there.
3. Locating sites and drilling wells is easier and less costly in the western states because the crust is thinner there.
4. Locating sites and drilling wells is easier and less costly in the western states because they lack thick vegetation covering the land.

Which of the following effects of global climate change is the best example of a "positive feedback loop" in the global climate system?

1. Increased Antarctic Ocean temperatures lead to local increases in atmospheric water vapor, which falls as snow in the interior of the continent.
2. Higher levels of carbon dioxide increase the rate of growth of forests, which increases the sequestering of carbon dioxide in wood.
3. Warming temperatures melt Arctic permafrost, which releases methane and carbon dioxide from decomposing vegetation.
4. Melting of the Greenland glacier causes fresh water to flow into the North Atlantic, which slows thermohaline circulation.

In a unit about natural disasters and their effects on communities, students are learning how to build a water purification filtration system using common materials. Which of the following strategies would be most effective in removing toxic compounds from the water?

1. boiling the water
2. bubbling the water with oxygen
3. exposing the water to strong sunlight
4. percolating the water through activated charcoal

Which of the following statements best describes one difference between the end result of meiosis and the end result of mitosis?

1. Mitosis produces four daughter cells, while meiosis produces two daughter cells.
2. Mitosis produces daughter cells that are considerably larger in size than the daughter cells produced by meiosis.
3. Daughter cells produced by mitosis have both sets of chromosomes, while those produced by meiosis have only one set of chromosomes.
4. Daughter cells produced by mitosis contain all the organelles of the parent cell, while those produced by meiosis only contain the parent cell's nucleus.

Which of the following characteristics of an unknown object would provide the best evidence that the object is a living organism?

1. It possesses carbon-containing molecules.
2. It is able to reproduce.
3. Its temperature is higher than that of the surrounding air or water.
4. It has a highly ordered structure.

Use the diagram below to answer the question that follows.

A diagram of a cell is shown. The cell has a number of different membrane-bound compartments. One of these is a structure labeled X. X is roughly egg-shaped, sits in the center of the cell, and is much larger than any of the other structures. X also has a small dark circle within it.

One of the primary roles of the structure labeled X in the generalized cell shown in the diagram above is to:

1. control the concentration of ions in the cellular fluids.
2. store nutrients necessary for cell functioning.
3. contain the genetic material between cell divisions.
4. provide a site for the breakdown of cellular waste products.

Whether the products of glycolysis undergo fermentation or cellular respiration during glucose metabolism is dependent on which of the following factors?

1. the surface area of the cell
2. the cell's immediate energy needs
3. the presence or absence of oxygen
4. the availability of light

Use the table below to answer the question that follows.

A teacher watches for different species of birds with their class outside their classroom window and records the number of bird sightings each day in the table shown. Which of the following graphs best represents the trend in the data over time?

1.  A graph of the number of birds sited for each day on the x-axis is shown. The slope appears exponential. 


2. A graph of the number of birds sited for each day on the x-axis is shown. The slope has a positive linear trend.


3. A graph of the number of birds sited for each day on the x-axis is shown. The slope goes up, curves and turns back down.


4. A graph of the number of birds sited for each day on the x-axis is shown. The slope has a negative linear trend.

Use the passage below to answer the question that follows.

A field in central New England where corn was grown is abandoned and left undisturbed. Initially grasses and weed species take over the field. Gradually, woody shrubs and species such as sumac and poplar become established, followed by white pines. After several decades, the area is characterized by a stable community of mixed hardwood trees dominated by oaks.

Which of the following processes is described in the passage?

1. evolution
2. biological magnification
3. exponential growth
4. succession

Which of the following structures in a flowering plant is best adapted for the function of receiving pollen?

1. petal
2. anther
3. stigma
4. ovary

The fur color of a rodent species is determined by a single gene with two possible alleles. The allele for black fur, B big B , is dominant, and the white fur allele, b little B , is recessive. A rodent with genotype Bb big B little b  is bred with a rodent with genotype bb little B little B . What is the expected phenotypic ratio of the offspring from this cross?

1. 25% black fur
   75% white fur
2. 50% black fur
   50% white fur
3. 75% black fur
   25% white fur
4. 100% black fur
   0% white fur

A DNA molecule is about to undergo replication. The base sequence of a small section of one of the original DNA strands is shown below.

A–A–G–C–G–T–A

What will be the base sequence of the corresponding section of the new complementary DNA strand that is formed?

1. A–A–G–C–G–T–A
2. T–T–C–G–C–A–T
3. U–U–C–G–C–A–U
4. C–C–T–A–T–G–C

Which of the following statements best explains how a given variant gene can be maintained in a large portion of a population, even if that gene does not directly confer an advantage?

1. Genetic drift leads to the maintenance of variant genes through chance alone.
2. Mutations can occur over and over at the same site and constantly feed new variation into a population.
3. Recessive genes are not expressed in the phenotype of heterozygous individuals.
4. Natural selection facilitates the spread of some genes in a population at the expense of others.

The fact that mitochondria and chloroplasts have their own DNA provides the strongest support for which of the following hypotheses?

1. Organic molecules formed spontaneously under the conditions found on the early Earth.
2. Aerobic organisms evolved after anaerobic organisms.
3. Eukaryotes evolved as a result of endosymbiotic relationships among prokaryotes.
4. Life on Earth first arose in the oceans rather than on land.

Which of the following observations provides support for the theory of evolution?

1. A snowshoe hare's coat turns from brown to white as the winter approaches.
2. A young lion becomes a more skilled hunter during its first years of life.
3. A tree seedling develops a root system that allows it to cling to the rocky hillside where it germinated.
4. A population of insects develops resistance to a particular pesticide over several generations.

Which of the following is an example of a pure substance as opposed to a mixture?

1. alcohol
2. milk
3. gasoline
4. blood

Water has a significantly higher surface tension than most other substances. Which of the following factors is directly responsible for this characteristic of water?

1. the size of atoms in a water molecule
2. the solvent properties of water
3. the hydrogen bonding between water molecules
4. the specific heat capacity of water

Use the reaction equation below to answer the question that follows.

HCl(aq) + NaOH(aq) → H₂O(l) + X  H C L aqueous plus N A O H aqueous yields H 2 O liquid plus X 

According to the principle of conservation of matter, which of the following is the chemical formula for the reaction product X in the equation shown?

1. NaOH(aq) N A O H aqueous 
2. HCl(aq) H C L aqueous 
3. NaCl(aq) N A C L aqueous 
4. O₂(g) O 2 gas 

Use the information below to answer the question that follows.

Several materials are selected to test as thermal insulators in an investigation, whose steps are as follows:

1. Boiling water is poured into a flask, which is then closed with a rubber stopper that holds a thermometer.
2. The flask is placed into a box containing the first material.
3. A timer is set and measurements are recorded every minute for ten minutes.

This procedure is repeated for the other materials being tested. The same flask, box, and amount of water are used for each trial.

In this investigation, the dependent variable is the:

1. insulated material.
2. time each trial takes.
3. volume of heated water.
4. amount of heat conserved.

Use the diagram below to answer the question that follows.

When 1.0 mol of helium at 298 K kelvins  is placed in the 10.0 L liters  container shown above, it exerts a pressure of 2.4 atm atmospheres . Which of the following changes to this system would lead to a decrease in pressure?

1. increasing the temperature of the system
2. adding additional helium to the container
3. moving the piston to a lower position within the container
4. removing some of the helium from the container

Use the table below to answer the question that follows.

The table shows the results of an experiment when four objects are dropped from different heights. Which object has the greatest gravitational potential energy when dropped? (PE = mgh P E = m g h , where g is the acceleration due to gravity at Earth's surface and g = 9.8 m/s² meters per second squared )

1. object A
2. object B
3. object C
4. object D

Use the graph below to answer the question that follows.

A graph of displacement in meters on the y-axis is shown versus time in seconds on the x-axis. The trend line starts at (0, 0), goes up in a linear manner to (6, 6), flattens out until (12, 6), then decreases in a linear manner until (14, negative 5), where it flattens out to (20, negative 5) and increases in a linear manner until (28, 5). From there it flattens out to (32, 5) and decreases linearly past (36, negative 2) and off the graph.

The graph represents the displacement of a truck at a construction site. Which of the following statements about the truck's movement is true?

1. The truck stops moving at 24 seconds.
2. The truck starts moving forward at 36 seconds.
3. The truck has a constant acceleration at 6 seconds.
4. The truck starts moving in a reverse direction at 12 seconds.

Which of the following dogs would be expected to put in the most amount of work to climb a flight of stairs?

1. the largest dog
2. the fastest dog
3. the smallest dog
4. the slowest dog

Use the diagram below to answer the question that follows.

Two students hold a rope taut between them such that it appears to be a straight line. Above their heads, there is an arrow pointing towards each of the students.

The classroom activity shown in the diagram would be most appropriate for demonstrating which of the following physical science concepts?

1. entropy
2. net forces
3. energy transfers
4. conservation of matter

Use the information below to answer the question that follows.

A free-body diagram of a person pushing on a box along the ground is shown. The person is on the left of the box. Arrow 1 points from the left toward the right of the box. Arrow 2 points from the center to above the box. Arrow 3 points from the center to below the box. Arrow 4 points from the right to the left of the box.

In the free-body diagram shown above, a person applies a force to a box in order to slide it across the floor. If the box is sliding at a constant velocity, which of the following forces in the free-body diagram must be equal in magnitude?

1. I and III  1 and 3  
2. I and IV  1 and 4  
3. II and IV  2 and 4  
4. III and IV  3 and 4  

Which of the following explains why white light separates into the different colors of the spectrum as it travels through a prism?

1. Different frequencies of light move through a prism at different speeds, causing them to refract differently as they cross air-glass boundaries.
2. The prism magnifies the amplitude of high-frequency wavelengths more than low-frequency wavelengths.
3. Variable reflection of light entering the prism at different angles splits the light into different wavelengths.
4. The prism polarizes the light waves as they travel through the glass, dividing them into distinct wavelengths.

Several lights are connected in a parallel circuit and one of the lights burns out. Which of the following statements best describes how the burning out of the light affects the other lights in the parallel circuit?

1. Charge still flows through the burned-out light, providing the lights in the other branches of the circuit with electricity.
2. The other lights continue to draw the same current since neither resistance nor voltage is affected in those branches of the circuit.
3. Current is increased in the other branches of the circuit, so the lights will brighten as a result of the increased flow of charge.
4. The branches of the circuit draw less charge overall because the burned-out light no longer draws a charge, reducing the brightness of the lights.

Use the information below to complete the assignment that follows.

A business is deciding whether to fulfill a customer's order for highly customized devices by using the services of their own manufacturing department or by arranging to have another manufacturer create the devices. The business will sell each device for $3500 regardless of who manufactures them.

In the process used by this business:

• $700700 dollars worth of labor and materials is required to begin the first stage of manufacturing for each device. Upon completion of this stage, the device is tested for quality.
• The company expects that 80%80 percent of the devices created will meet quality standards and proceed to the second stage. The rest are discarded.
• An additional $500500 dollars worth of labor and materials is required to begin the second stage of manufacturing for each device. Upon completion of this stage, the device is again tested for quality.
• The company expects that 75%75 percent of the devices that get to the second stage will meet quality standards and be sold to the client. The rest are discarded.

Use your knowledge of probability to develop a response of approximately 150–300 words, or 1–2 pages, in which you analyze the probabilities of specified outcomes. In your response:

• draw a tree diagram of the situation, including all appropriate labels, and use it to summarize the net profit or loss associated with every possible outcome in attempting to manufacture a single device;
• predict how many total manufacturing attempts will be needed to create 3 devices that can be sold;
• recommend whether the business should attempt to create the devices through their own manufacturing department or purchase 3 completed devices from another manufacturer for $90009000 dollars total; and
• discuss any influences that can cause variations in your recommendation.

Be sure to show your work and explain the reasoning you use in analyzing and solving the problem.

Use the information below to complete the exercise that follows.

Environmental and genetic factors can affect the size and growth of a pea plant.

Use your knowledge of life science to write an essay of approximately 150– to 300 words, or 1– to 2 pages, in which you:

• explain two key scientific concepts related to environmental and genetic factors that influence the growth of the pea plant;
• use a representative graph, formula, and/or diagram with all proper labels to model factors that influence the growth of the pea plant; and
• discuss the cause-and-effect relationship between environmental and/or genetic factors and the growth of the pea plant.