Z! Prep SAT Math Only Quiz For Tutors

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  • 1/20 Questions

    The table above represents the number of shares of stock purchased on a particular day. What is the average (arithmetic mean)  purchase price , in dollars, of a share of bought that day?         

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Z! Prep SAT Math Only Quiz For Tutors - Quiz
About This Quiz

This quiz is designed to measure a tutor's knowledge and familiarity with the math content on the SAT. In order to be eligible to tutor SAT math students for Club Z!, prospective tutors must be able to successfully answer the following sample questions from the Z! Prep SAT Math Diagnostic test. Your local Area Director will determine the minimum threshold See morefor correct answers. Good luck!

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  • 2. 
    Functions and  are defined as   If a<0 and c<0 for both f(x) and g(x), which of the following could be the graph of both functions? - ProProfs

    Functions and  are defined as   If a<0 and c<0 for both f(x) and g(x), which of the following could be the graph of both functions?

    Correct Answer
    A.
    Explanation
    Medium Difficulty, Multiple Choice, Coordinate Geometry

    Question 9 Strategy: Use process of elimination to remove graphs as possible answers.

    Correct Answer: E. For f(x) = ax + b, a represents the slope. A negative slope must be drawn as a line pointing down as it moves to the right. In g(x) = ax2 + bx + c, a represents the direction of the parabola. Because a is negative, it must be opening down. “c” represents the y-intercept of the parabola. As c is also negative, the parabola must have a y-intercept that is negative. Both the line and parabola in choice E fit these criteria.

    Incorrect Answer: A. The parabola, while opening down, has a positive y-intercept.

    Incorrect Answer: B. The parabola opens up, and the line has a positive slope.

    Incorrect Answer: C. The parabola has a positive y-intercept, and the line has a positive slope.

    Incorrect Answer: D. The parabola opens up.

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  • 3. 

    If AB > BC, which of the following must be true? I. AB > AC II. AB + AC > BC + AC III. AC − AB < AC − BC

    • I only

    • II only

    • III only

    • II and III only

    • I, II, and III

    Correct Answer
    A. II and III only
    Explanation
    Medium Difficulty, Multiple Choice, Answer Data, Logic Problem

    Question 11 Strategy: Draw a triangle and pick numbers that work given that AB > BC.

    Correct Answer: D. II and III only. Pick numbers for AB, AC, and BC. For example: AB = 5, BC = 4, AC = 6. When AC is added to each side of an inequality, the original relationship remains valid (and therefore statement II must be true). When substituting the chosen numbers, 5+6 > 4+6 is a true statement. Statement III must also be true, as 6-5 < 6-4 is also a true statement.

    Incorrect Answer: A. I only. For a triangle, the two smaller sides must have a sum that is greater than the largest side. AB could be the largest side, but so could AC. As such, the relationship between the two is unclear.

    Incorrect Answer: B. II only. Statement II must be true, but so must statement III.

    Incorrect Answer: C. III only. Statement III must be true, but so must statement II.

    Incorrect Answer: E. I, II, and III. If a number smaller than AB is picked for AC, then it seems as statement I must be true. However, statement I is only potentially true, as AC could be either larger or smaller than AB.

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  • 4. 

    The graph of which of the following equations is parallel to line  l  and contains points (5,6)? 

    Correct Answer
    A.
    Explanation
    Medium Difficulty, Multiple Choice, Coordinate Geometry

    Question 13 Strategy: Find the slope of the line between the two points, which must match the slope of the parallel line, then plug in the point (5,6) to make sure it is on that parallel line.

    Correct Answer: C. y – 2/5x = 4. In a line, y = mx + b, the slope (or rate of change) is represented by m. To find the slope from two points: m = (y2 – y1) / (x2 – x1). In this case, m = (7– 1) / (15 – 0) = 6/15. This simplifies to 2/5. The line for answer C has the correct slope. To check and see if the intercept is correct, plug the point (5,6) in and see if the result is valid. 6 – 2(5)/5 = 4 simplifies to 6 – 2 = 4. This is valid.

    Incorrect Answer: A. y – 5x = 3. The slope of this line is 5, not 2/5.

    Incorrect Answer: B. y – 3x = 5. The slope of this line is 3, not 2/5.

    Incorrect Answer: D. y – 2/5x = 5. While the slope is correct (2/5), checking the point (5,6) results in: 6 – 2(5)/5 = 5, which simplifies to 6 – 2 = 5. Thus (5,6) is not a valid point for this line.

    Incorrect Answer: E. y – 5/2x = 6. The slope of this line is 5/2, not 2/5. The slope formula puts the change of “y” on the top of the fraction, not the change of “x”.

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  • 5. 
      Then all of the following could be values of x EXCEPT - ProProfs

      Then all of the following could be values of x EXCEPT

    Correct Answer
    A.
    Explanation
    Medium Difficulty, Multiple Choice, Answer Data, Functions

    Question 15 Strategy: Consider where x is an invalid input. These usually arise from two issues, either a negative number inside a square root or a zero in the denominator of a fraction. In this case, it is the fraction's denominator that must be considered.

    Correct Answer: B. 5/3. f(x) = (2x + 1) / (3x – 5). If the denominator becomes zero, then the entire fraction results in infinity, a vertical asymptote, or “no solution,” depending on perspective. As such, 3x – 5 cannot = 0. Solving this for x gives 3x cannot = 5, and x cannot = 5/3.

    Incorrect Answer: A. 2/3. The function itself cannot evaluate to 2/3, but an input of 2/3 for x gives a real answer.

    Incorrect Answer: C. -1/2. An input of -1/2 for x gives the real answer of 0.

    Incorrect Answer: D. 0. An input of 0 for x gives the real answer of -1/5.

    Incorrect Answer: E. -3/5. An input of -3/5 for x gives the real answer of 1/34.

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  • 6. 

    Each of the polygons could be folded to form a cube EXCEPT

    Correct Answer
    A.
    Explanation
    Easy Difficulty, Multiple Choice, Answer Data, Logic Problems

    Question 21 Strategy: Visualize the shape being folded step by step into a cube.

    Correct Answer: E. This shape cannot be folded into a cube because the bottom square will overlap the rightmost square, leaving a gap where no fold can cover it.

    Incorrect Answer: A. All sides of the potential cube will be covered.

    Incorrect Answer: B. All sides of the potential cube will be covered.

    Incorrect Answer: C. All sides of the potential cube will be covered.

    Incorrect Answer: D. All sides of the potential cube will be covered.

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  • 7. 

    In the diagram above, square ABCD and semicircles EIH and FJG are inscribed within the larger square EFGH.  If the area of square ABCD is 36, what is the total perimeter of the two shaded regions?

    • Z! Prep SAT Math Only Quiz For Tutors - Quiz

    • Z! Prep SAT Math Only Quiz For Tutors - Quiz

    • Z! Prep SAT Math Only Quiz For Tutors - Quiz

    • Z! Prep SAT Math Only Quiz For Tutors - Quiz

    • Can not be determined from the information given

    Correct Answer
    A.
    Explanation
    Hard Difficulty, Multiple Choice, Geometry

    Question 27 Strategy: Use the area of the square to find the side of the square, which can be used to find the diagonal length with the Pythagorean Theorem, and then the radius. Add the appropriate lengths to find the perimeter of one shaded region. Double it, as there are two shaded regions.

    Correct Answer: A. 12√2 + 3π√2. If the square ABCD's area = 36, s2 = 36, so s (the length of a side) = 6. AD = 6, because it is the side of the square. This means that HD and AH create a right triangle with angles 45-45-90 degrees. Because in a 45-45-90 degree right triangle, the pattern follows as x-x-x√2, and the hypotenuse length AD = 6, AH and AD = 3√2. Alternatively, using the Pythagorean Theorem, x2+x2=36, which can be simplified to x2=18, so x√18, simplifying to x=3√2. As this is the radius of the semicircles, the straight line distances of the shaded area perimeters are also 3√2. There are four of them, so the total straight line distance of the perimeter is 12√2. Because the 90 degree arc on each semicircle is ¼ of a circle, each arc length would be ¼ of the total circumference. As C = 2πr, the total circumference = 2π3√2 = 6π√2. ¼ of that would be 1.5π√2, doubled as there are two semicircles to result in 3π√2. Add this to the straight line distance to find 12√2 + 3π√2.

    Incorrect Answer: B. 19 + π√2. Because the straight line distance involves √2, both parts of the answer will involve √2 as well.

    Incorrect Answer: C. 24 + 6π. 36 is the area of the smaller square.

    Incorrect Answer: D. 12 + 3π. 36 is the area of the smaller square.

    Incorrect Answer: E. Cannot be determined. Using the area of the square to give the side length of 6, both the hypotenuse and radius can be found.

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  • 8. 
    If m and n are positive integers and   ,  what is the value of m? - ProProfs

    If m and n are positive integers and   ,  what is the value of m?

    • 2

    • 3

    • 4

    • 5

    • 6

    Correct Answer
    A. 3
    Explanation
    Hard Difficulty, Multiple Choice, Algebra

    Question 28 Strategy: Distribute the exponents. Remember that (xa)b = xab. Simplify the terms by combining like terms, recalling that xnxm = xn+m.

    Correct Answer: B. 3. With distribution, (m1/2n1/3)24 (m-3n-4)2 becomes m12n8m-6n-8. Combining the exponents on like terms results in m12-6n8-8. Therefore, m6=729. The sixth root of 729 is three, so m = 3.

    Incorrect Answer: A. 2. This would be an incorrect guess.

    Incorrect Answer: C. 4. This would be an incorrect guess.

    Incorrect Answer: D. 5. This would be an incorrect guess.

    Incorrect Answer: E. 6. This is the exponent of m, not the answer.

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  • 9. 
    The figure above shows point B, (5.5, b), on the graph of  and point D, (-5.5, d), on the graph of   where   is constant. If the perimeter of rectangle ABCD is 38, what is the value of   ? - ProProfs

    The figure above shows point B, (5.5, b), on the graph of  and point D, (-5.5, d), on the graph of   where   is constant. If the perimeter of rectangle ABCD is 38, what is the value of   ?

    Correct Answer
    3.5, 7/2
    Explanation
    Hard Difficulty, Student Response, Coordinate

    Question 35 Strategy: Plug the point (5.5,b) in to the parabola f(x) = (x-a)2 to find a.

    Correct Answer: 3.5 or 7/2. If the perimeter is 38, and the length of the bottom and top sides of the rectangle are 11, then the remaining two heights must sum to 38 – 2(11) = 38 – 22 = 16. Each side must thus have a height of 8. Because the height is distributed evenly across the x axis, the distance from the x axis to B must be half of the rectangular height, or 4. Thus, B is (5.5,4). Putting this point into f(x) gives: 4 = (5.5 – a)2. To solve this for a, first square root each side. 2 = 5.5 – a. After subtracting 5.5, we find that -3.5 = -a. Therefore, a = 3.5.

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  • 10. 

    A collegiate track team plans to enter the 400m relay race. the relay team will consist of four runners, each of whom will run 100m. Based on the scatterplot above, how many possible teams of runners could be chosen to run in the relay, if only runners with qualifying times below 10.3 seconds will be considered for the relay team?

    Correct Answer
    5
    Explanation
    Medium Difficulty, Student Response, Word Problem, Statistics

    Question 34 Strategy: Give the runners names “ABCDE” and write out combinations if needed.

    Correct Answer: 5. Based on the scatterplot there are five possible athletes that could run in the relay. As the relay requires four runners, the fifth runner would not be chosen. As there are only five runners, there can only be five patterns, each with a different runner not chosen. ABCD, ABCE, ACDE, ABDE, BCDE.

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  • 11. 

    If f(x) = x - 1,    g(x) = xf(x) + 2, and g(f (a)) = 32, what is the sum of all possible values of a?

    Correct Answer
    3
    Explanation
    Hard Difficulty, Student Response, Functions

    Question 36 Strategy: Find g(x), then input f(a) into g(x). This sets up a quadratic equation that can be factored or solved using the quadratic formula.

    Correct Answer: 3. If f(x) = x – 1, then g(x) = x(x – 1) + 2. g(x) = x2 – x + 2. f(a) = a – 1, so g(f(a)) = g(a – 1) = (a – 1)2 – (a – 1) + 2. = (a – 1)(a – 1) – a + 1 + 2 = a2 – 2a + 1 – a. This simplifies to a2 – 3a + 4. Therefore, a2 – 3a + 4 = 32, and a2 – 3a – 28 = 0. This factors to (a – 7)(a + 4) = 0, so a can be 7 or -4. The sum of these factors is 3.

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  • 12. 

    If a diagonal of a figure is defined as a line segment joining any 2 non-adjacent vertices, how many diagonals exist in a cube?

    Correct Answer
    16
    Explanation
    Hard Difficulty, Student Response, Word Problem, Logic Problem

    Question 37 Strategy: Draw a cube, connect the vertices to make diagonals.

    Correct Answer: 16. A cube is a six sided shape, with each face a square. When connecting the vertices to make diagonals, be sure to not double count diagonals that have already been drawn!

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  • 13. 
    In the figure above, the smaller circle has a radius .  The larger circle has a radius  .  What is the ratio of the area of the smaller circle to the area of the shaded region? - ProProfs

    In the figure above, the smaller circle has a radius .  The larger circle has a radius  .  What is the ratio of the area of the smaller circle to the area of the shaded region?

    Correct Answer
    .125, 1/8
    Explanation
    Hard Difficulty, Student Response, Word Problem, Arithmetic

    Question 38 Strategy: Find the area of the two regions, divide them in a ratio as smaller/larger.

    Correct Answer: .125 or 1/8. The area of a circle is A = πr2. For the smaller circle, its Area = π(1/3)2 = π/9. The larger circle has an Area = π(1)2 = π. The area of the shaded region would thus be the area of the larger circle minus the area of the smaller circle: π – π/9 = 8π/9. To find the ratio of the area of the smaller circle to the area of the shaded region, take (π/9) / (8π/9), which simplifies to 1/8.

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  • 14. 

    Sara rides her bike from her house at point A to her friend's house at point E. If she were able to travel directly in a straight line to her friend's house, how many miles would she travel?

    Correct Answer
    A.
    Explanation
    Medium Difficulty, Multiple Choice, Word Problem, Geometry

    Question 10 Strategy: Draw a straight line distance between start and end, set up a right triangle.

    Correct Answer: B. √41. By considering the straight line distance as the hypotenuse of a right triangle, the Pythagorean Theorem can be applied. a2 + b2 = c2 where c is the hypotenuse. In this case, 52 + 42 = c2. So 25 + 16 = c2. By simplification (combining like terms) 41 = c2. To solve a squared variable, the opposite order operation is conducted (which is to square root each side). Therefore, c = +/- √41. As this is a geometry (distance) problem, only the positive root is a reasonable answer.

    Incorrect Answer: A. 3. If the Pythagorean Theorem is set up incorrectly, with the distance not as the hypotenuse, 52 = 42 + c2. In this case, 25 – 16 = c2, so 9 = c2 and c = 3.

    Incorrect Answer: C. 5. This is the total horizontal distance traveled.

    Incorrect Answer: D. √11. When finding the hypotenuse, the two smaller sides must be added. Also, the horizontal distance is 5, but the vertical distance is only 4 (due to doubling back on the path: 5 – 1 = 4).

    Incorrect Answer: E. √10. See above.

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  • 15. 

    Which of the following has the same surface area as the square pyramid shown above with a slant height of 13.5 and a base edge of  6π  ?

    • A cylinder with a height of 3π and a radius of 9

    • A cylinder with a height of 2π and a radius of 9

    • A cylinder with a height of 2π and a diameter of 12

    • A rectangular prism with edges of 9π, 2π, and 8

    • A rectangular prism with edges of 6π, 3π, and 8

    Correct Answer
    A. A cylinder with a height of 2π and a radius of 9
    Explanation
    Medium Difficulty, Multiple Choice, Word Problems, Geometry

    Question 11 Strategy: Find the surface area of the square pyramid, then test the surface areas of the given cylinders and rectangular prisms one by one until a correct match is found.

    Correct Answer: B. Cylinder with height of 2π and radius of 9. The surface of the pyramid can be found by adding the areas of the four triangular faces and the square base. Each triangular face (A = ½bh) has an area of ½(13.5)(6π) = 40.5π. As there are four of them, the total triangular surface area is 40.5π x 4 = 162π. The area of the base is 6π x 6π = 36π2. Thus the total surface area = 162π + 36π2. A cylinder has a surface area = 2πrh + 2πr2. For this cylinder, the surface area = 2π(9)(2π) + 2π(9)2 = 36π2 + 162π.

    Incorrect Answer: A. Cylinder with height of 3π and radius of 9. The surface area of this cylinder = 2π(9)(3π) + 2π(9)2 = 54π2 + 162π.

    Incorrect Answer: C. Cylinder with a height of 2π and a diameter of 12. If the diameter is 12, then the radius is half that, or 6. The surface area of this cylinder = 2π(6)(2π) + 2π(6)2 = 24π2 + 72π.

    Incorrect Answer: D. Rectangular prism with edges 9π, 2π, 8. A rectangular prism has a surface area that adds up all six rectangular faces. If the prism has dimensions of length (l), width (w) and height (h), then the surface area = 2lw + 2lh + 2wh. In this case, surface area = 2(9π)(2π) + 2(9π)(8) + 2(2π)(8) = 36π2 + 144π + 32π = 36π2 + 176π.

    Incorrect Answer: E. Rectangular prism with edges 6π, 3π, 8. In this case, surface area = 2(6π)(3π) + 2(6π)(8) + 2(3π)(8) = 36π2 + 96π + 48π = 36π2 + 144π..

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  • 16. 

    A baseball glove was originally priced at n dollars. During a holiday sale, the price of the glove was lowered by d dollars, resulting in a sale price of p dollars.  What percentage of the original cost was discounted for the sale?

    Correct Answer
    A.
    Explanation
    Hard Difficulty, Multiple Choice, Word Problems, Arithmetic

    Question 12 Strategy: Pick numbers that are easy to work with and substitute for n, d, p. Common sense says that 100 must be on the top of the fraction, not the bottom, to multiply the decimal into a percent.

    Correct Answer: D. 100(n – p) / n. Pick n = 100, d = 10, p = 100 – 10 = 90. Note that p is a dependent variable that is derived from n and d. Clearly the discount should be 10%. Plug the numbers into the expression to find that 100(100 – 90) / 100 = 100(10)/100 = 10%.

    Incorrect Answer: A. (n – d) / 100n. 100 is in the denominator, which will not make this a percent.

    Incorrect Answer: B. (n – p) / 100n. 100 is in the denominator, which will not make this a percent.

    Incorrect Answer: C. 100(n – d) / n. Plugging in the chosen numbers results in 90%. This is the “percent cost” of the original, not the discount.

    Incorrect Answer: E. 100n / (n – p). Plugging in the chosen numbers results in 10000/10. 1000% discount is not reasonable.

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  • 17. 

    A line of voters outside a polling site consists of 7 Democrats, 8 Republicans, and 2 Independents. If three voters are selected from the line at random, what is the probability that all three voters will be Democrats?

    Correct Answer
    A.
    Explanation
    Hard Difficulty, Multiple Choice, WP, Statistics

    Question 13 Strategy: Find the total number of voters, then take the proportion of Democrats. Repeat three times, reducing both the total number and the number of Democrats by one each time to represent selection.

    Correct Answer: E. 7 / 136. There are 17 total voters, so the first selection should be 7 / 17. One voter has already been picked so the second selection will be 6 / 16. The third selection will be 5 / 15. Multiplying these three numbers and simplifying gives 7 / 136. A useful time-saving measure is to multiply all three fractions using a calculator, and either check the decimal against the answer, or convert the decimal using a calculator function back into a fraction.

    Incorrect Answer: A. 3 / 7. Probability must be considered as the “choice” or “selection” as a proportion of the whole. 3 / 7 would indicate three selections over the “selection” number, which does not identify the proportion of the whole that Democrats represent.

    Incorrect Answer: B. 7 / 17. This is only the probability of the first voter selected being a Democrat.

    Incorrect Answer: C. 5 / 51. See above explanation.

    Incorrect Answer: D. 5 / 119. See above explanation.

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  • 18. 
    If m and n are positive integers and   ,  what is the value of m? - ProProfs

    If m and n are positive integers and   ,  what is the value of m?

    • 2

    • 3

    • 4

    • 5

    • 6

    Correct Answer
    A. 3
    Explanation
    Hard Difficulty, Multiple Choice, Algebra

    Question 14 Strategy: Distribute the exponents. Remember that (xa)b = xab. Simplify the terms by combining like terms, recalling that xnxm = xn+m.

    Correct Answer: B. 3. With distribution, (m1/2n1/3)24 (m-3n-4)2 becomes m12n8m-6n-8. Combining the exponents on like terms results in m12-6n8-8. Therefore, m6=729. The sixth root of 729 is three, so m = 3.

    Incorrect Answer: A. 2. This would be an incorrect guess.

    Incorrect Answer: C. 4. This would be an incorrect guess.

    Incorrect Answer: D. 5. This would be an incorrect guess.

    Incorrect Answer: E. 6. This is the exponent of m, not the answer.

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  • 19. 

    The ratio of seniors to juniors on the varsity basketball team is 5 to 3. If there are 16 players on the team, how many fewer juniors are there than seniors

    • 2

    • 4

    • 6

    • 8

    • 10

    Correct Answer
    A. 4
    Explanation
    Medium Difficulty, Multiple Choice, Word Problem, Arithmetic

    Question 9 Strategy: Set up a ratio using either 5/3 or 5/8. A counting method could also be employed.

    Correct Answer: B. 4. This can be set up as a ratio problem. 5 / 3 = x / (16 – x). In this case, x represents the number of seniors and 16 – x represents the number of juniors (as 16 itself is the total of both seniors and juniors, the remainder once seniors are subtracted must be juniors). Alternatively, 5 / 8 = x / 16. In this second case, the 8 represents (5 + 3) = the total number of students in the ratio. In either case, cross multiplication will result in 8x = 80, so x = 10. The difference between 10 seniors and 6 juniors is thus 4.
    Alternatively: 5 to 3 scales up to 10 to 6. These add to 16, so they are the correct numbers for the team.

    Incorrect Answer: A. 2. A straight subtraction of 5 – 3 would result in the difference of the ratio between juniors and seniors, not the actual difference of the total number in a 16 person group.

    Incorrect Answer: C. 6. Should the ratio have been set up correctly and solved for the number of juniors, 16 – x = 10. However, the prompt requests the difference between the number of juniors and seniors.

    Incorrect Answer: D. 8. A mistaken addition of 5 + 3 would result in 8. The prompt, however, does not ask for the total number of students in the ratio.

    Incorrect Answer: E. 10. Should the ratio have been set up correctly and solved for the number of seniors, x = 10. However, the prompt requests the difference between the number of juniors and seniors.

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  • 20. 

    When the sum of n and 5 is subtracted from twice n, the result is 7. What is the value of n?

    • -12

    • -2

    • 0

    • 2

    • 12

    Correct Answer
    A. 12
    Explanation
    Easy Difficulty, Multiple Choice, Word Problem, Algebra

    Question 8 Strategy: Translate the expression into algebra using a variable.

    Correct Answer: E. 12. The algebra should be set up as: 2n – (n + 5) = 7. Solving this equation for n gives the correct answer of 12.

    Incorrect Answer: A. -12. “Subtracted from twice n” does not indicate that the final answer should be negative.

    Incorrect Answer: B. -2. The equation was incorrectly set up as: (n + 5) – 2n = 7. “The sum of n and 5 is subtracted from twice n” indicates that it should be (n + 5) that is subtracted.

    Incorrect Answer: C. 0. Explanation. The equation was incorrectly set up as 2 – (n + 5) = 7. “Twice n” does not indicate the number 2.

    Incorrect Answer: D. 2. The classic algebra mistake can be seen here where a student forgets to distribute the negative sign to both the “n” and the “5”. 2n – (n + 5) = 7 is incorrectly simplified to: 2n – n + 5 = 7 instead of the correct 2n – n – 5 = 7.

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  • 21. 
    Directions: For this section, solve each problem and choose the best answer from among the choices given. - ProProfs

    Directions: For this section, solve each problem and choose the best answer from among the choices given.

  • 22. 
    - ProProfs

  • 23. 
    - ProProfs

  • 24. 
    - ProProfs

  • 25. 
    - ProProfs

  • 26. 
    - ProProfs

  • 27. 
    - ProProfs

  • 28. 

    Directions: for the following questions, please answer the question with a number, decimal or fraction.  Do not spell out a numeric answer.  Example: 12 is an acceptable answer.  "Twelve" is not an acceptable answer.  Some problems have more than one correct answer. Please use only one answer for each question.  No student response questions have negative answers.

  • 29. 
    - ProProfs

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    - ProProfs

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