Mastering mathematical formulas is a prerequisite for achieving a top score on the GRE Quantitative Reasoning section, which evaluates arithmetic, algebra, geometry, and data analysis. While the GRE is primarily a test of quantitative reasoning rather than rote memorization, rapid recall of foundational formulas such as algebraic identities, area and volume equations, properties of circles, and coordinate geometry slopes is essential for efficient time management under strict 27-question modular limits. Knowing when and how to apply these mathematical principles prevents unnecessary calculation errors. Regular practice with targeted multiple-choice questions enables aspirants to bridge theoretical formula knowledge with practical problem-solving.
1. What is the formula for the area of a circle with radius r?
Correct Answer: b) pir^2
Explanation:
The area of a circle is calculated using the formula A = pir^2, where r is the radius.
2. What is the formula for the circumference of a circle with radius r?
Correct Answer: b) 2pir
Explanation:
The circumference of a circle is C = 2pir, or equivalently C = pi d where d is the diameter.
3. What is the Pythagorean theorem for a right-angled triangle with legs a and b and hypotenuse c?
Correct Answer: b) a^2 + b^2 = c^2
Explanation:
In any right-angled triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse: a^2 + b^2 = c^2.
4. What is the formula for the area of a triangle with base b and height h?
Correct Answer: b) (1/2)bh
Explanation:
The area of a triangle is one-half the product of its base and its corresponding height: Area = (1/2)bh.
5. What is the sum of the interior angles of a polygon with n sides?
Correct Answer: a) 180(n - 2) degrees
Explanation:
The sum of the interior angles of any n-sided convex polygon is given by the formula Sum = (n - 2) * 180 degrees.
6. What is the formula for the volume of a rectangular prism with length l, width w, and height h?
Correct Answer: b) lwh
Explanation:
The volume of a rectangular prism is the product of its length, width, and height: V = lwh.
7. What is the formula for the surface area of a rectangular prism with length l, width w, and height h?
Correct Answer: b) 2lw + 2lh + 2wh
Explanation:
The total surface area of a rectangular prism is the sum of the areas of its six rectangular faces: SA = 2lw + 2lh + 2wh.
8. What is the formula for the volume of a cylinder with radius r and height h?
Correct Answer: b) pir^2h
Explanation:
The volume of a cylinder is the area of the circular base multiplied by the height: V = pir^2h.
9. What is the formula for the volume of a sphere with radius r?
Correct Answer: b) (4/3)pir^3
Explanation:
The volume of a sphere is given by the formula V = (4/3)pir^3.
10. What is the formula for the surface area of a sphere with radius r?
Correct Answer: a) 4pir^2
Explanation:
The surface area of a sphere is calculated using the formula SA = 4pir^2.
11. What is the formula for the slope m of a line passing through points (x1, y1) and (x2, y2)?
Correct Answer: b) (y2 - y1) / (x2 - x1)
Explanation:
The slope of a line is defined as the change in y divided by the change in x: m = (y2 - y1) / (x2 - x1).
12. What is the slope-intercept form of a linear equation?
Correct Answer: b) y = mx + b
Explanation:
The slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept.
13. What is the quadratic formula used to solve ax^2 + bx + c = 0?
Correct Answer: a) x = (-b +- sqrt(b^2 - 4ac)) / 2a
Explanation:
The quadratic formula gives the roots of a quadratic equation: x = (-b +- sqrt(b^2 - 4ac)) / 2a.
14. What is the discriminant of a quadratic equation ax^2 + bx + c = 0?
Correct Answer: b) b^2 - 4ac
Explanation:
The discriminant is D = b^2 - 4ac, which determines the number and nature of the roots of a quadratic equation.
15. What does a negative discriminant (b^2 - 4ac < 0) indicate about a quadratic equation?
Correct Answer: c) Two complex (non-real) roots
Explanation:
A negative discriminant indicates that the quadratic equation has two distinct complex conjugate roots and no real x-intercepts.
16. What is the formula for the distance d between two points (x1, y1) and (x2, y2) in the coordinate plane?
Correct Answer: b) sqrt((x2 - x1)^2 + (y2 - y1)^2)
Explanation:
The distance formula is derived from the Pythagorean theorem: d = sqrt((x2 - x1)^2 + (y2 - y1)^2).
17. What is the formula for the midpoint of a line segment joining (x1, y1) and (x2, y2)?
Correct Answer: a) ((x1 + x2)/2, (y1 + y2)/2)
Explanation:
The midpoint coordinates are found by averaging the x-coordinates and averaging the y-coordinates: ((x1 + x2)/2, (y1 + y2)/2).
18. What is the formula for simple interest?
Correct Answer: a) I = Prt
Explanation:
Simple interest is calculated as I = Prt, where P is principal, r is annual interest rate, and t is time in years.
19. What is the formula for compound interest where interest is compounded annually?
Correct Answer: b) A = P(1 + r)^t
Explanation:
Compound interest compounded annually is given by A = P(1 + r)^t, where A is the final amount and P is the principal.
20. What is the formula for compound interest compounded n times per year?
Correct Answer: a) A = P(1 + r/n)^(nt)
Explanation:
When compounded n times per year, the total amount is A = P(1 + r/n)^(nt).
21. What is the formula for percent change?
Correct Answer: a) ((New - Old) / Old) * 100
Explanation:
Percent change is calculated as the absolute difference (New - Old) divided by the original value (Old), multiplied by 100.
22. What is the formula for the average (arithmetic mean) of a set of n numbers?
Correct Answer: b) Sum of all numbers / n
Explanation:
The arithmetic mean is found by dividing the sum of all terms in the set by the total count of terms (n).
23. If the average of 5 numbers is 20, what is their sum?
Correct Answer: c) 100
Explanation:
Sum = Average * Count = 20 * 5 = 100.
24. What is the relationship between distance, speed, and time?
Correct Answer: a) Distance = Speed * Time
Explanation:
The fundamental motion formula is Distance = Speed * Time (often written as d = rt).
25. What is the formula for average speed over a total trip?
Correct Answer: b) Total Distance / Total Time
Explanation:
Average speed is always equal to the total distance traveled divided by the total time taken. (Note: it is NOT the simple average of speeds).
26. What is the formula for work when two workers A and B work together at rates a and b?
Correct Answer: a) Combined Rate = a + b
Explanation:
When working together, individual work rates add up: Combined Rate = RateA + RateB. Time taken is 1 / (RateA + RateB).
27. What is the formula for combinations (choosing r items from n items where order does not matter)?
Correct Answer: b) n! / (r!(n - r)!)
Explanation:
Combinations formula is C(n,r) = nCr = n! / (r!(n - r)!), where order does not matter.
28. What is the formula for permutations (arranging r items from n items where order matters)?
Correct Answer: a) n! / (n - r)!
Explanation:
Permutations formula is P(n,r) = nPr = n! / (n - r)!, where order matters.
29. What is the probability of an event E occurring, assuming all outcomes are equally likely?
Correct Answer: b) Number of favorable outcomes / Total possible outcomes
Explanation:
Probability P(E) = (Number of outcomes in E) / (Total number of possible outcomes in sample space).
30. What is the probability of either of two mutually exclusive events A and B occurring?
Correct Answer: b) P(A) + P(B)
Explanation:
For mutually exclusive events (cannot happen at the same time), P(A or B) = P(A) + P(B).
31. What is the general addition rule for the probability of either event A or event B occurring?
Correct Answer: b) P(A or B) = P(A) + P(B) - P(A and B)
Explanation:
The general addition rule accounts for overlap by subtracting the intersection: P(A or B) = P(A) + P(B) - P(A and B).
32. What is the probability of two independent events A and B both occurring?
Correct Answer: b) P(A) * P(B)
Explanation:
For independent events, the probability of both occurring is the product of their individual probabilities: P(A and B) = P(A) * P(B).
33. What is the expansion of (a + b)^2?
Correct Answer: b) a^2 + 2ab + b^2
Explanation:
The square of a binomial sum is (a + b)^2 = a^2 + 2ab + b^2.
34. What is the expansion of (a - b)^2?
Correct Answer: b) a^2 - 2ab + b^2
Explanation:
The square of a binomial difference is (a - b)^2 = a^2 - 2ab + b^2.
35. What is the factorization of the difference of squares, a^2 - b^2?
Correct Answer: c) (a - b)(a + b)
Explanation:
The difference of two squares factors as a^2 - b^2 = (a - b)(a + b).
36. What is the rule for multiplying exponents with the same base: x^a * x^b?
Correct Answer: b) x^(a + b)
Explanation:
When multiplying exponential expressions with the same base, keep the base and add the exponents: x^a * x^b = x^(a + b).
37. What is the rule for dividing exponents with the same base: x^a / x^b?
Correct Answer: a) x^(a - b)
Explanation:
When dividing exponential expressions with the same base, keep the base and subtract the exponent of the denominator from the numerator: x^a / x^b = x^(a - b).
38. What is the rule for a power raised to a power: (x^a)^b?
Correct Answer: b) x^(a * b)
Explanation:
When raising a power to a power, multiply the exponents: (x^a)^b = x^(a * b).
39. What is the value of any non-zero number raised to the power of 0 (x^0)?
Correct Answer: b) 1
Explanation:
Any non-zero real number raised to the zero power is equal to 1: x^0 = 1.
40. What does a negative exponent indicate: x^(-a)?
Correct Answer: b) 1 / x^a
Explanation:
A negative exponent represents the reciprocal of the base raised to the positive opposite power: x^(-a) = 1 / x^a.
41. What is the relationship between fractional exponents and radicals: x^(1/n)?
Correct Answer: b) nth root of x (sqrt[n]{x})
Explanation:
A fractional exponent 1/n corresponds to the nth root: x^(1/n) = sqrt[n]{x}.
42. What is the formula for the volume of a cone with radius r and height h?
Correct Answer: b) (1/3)pir^2h
Explanation:
The volume of a cone is one-third the volume of a cylinder with the same radius and height: V = (1/3)pir^2h.
43. What is the formula for the volume of a pyramid with base area B and height h?
Correct Answer: b) (1/3)Bh
Explanation:
The volume of any pyramid is one-third the product of its base area and height: V = (1/3)Bh.
44. What is the sum of the exterior angles of any convex polygon (one angle per vertex)?
Correct Answer: b) 360 degrees
Explanation:
The sum of the exterior angles of any convex polygon, taken one at each vertex, is always 360 degrees regardless of the number of sides.
45. What is the measure of each interior angle of a regular polygon with n sides?
Correct Answer: d) Both b and c
Explanation:
Each interior angle can be found by dividing the interior angle sum by n: 180(n - 2)/n, which simplifies to 180 - 360/n.
46. In a 45-45-90 right triangle, what is the ratio of the side lengths (leg : leg : hypotenuse)?
Correct Answer: a) 1 : 1 : sqrt(2)
Explanation:
In an isosceles right triangle (45-45-90), the legs are equal, and the hypotenuse is leg * sqrt(2).
47. In a 30-60-90 right triangle, what is the ratio of the side lengths (short leg : long leg : hypotenuse)?
Correct Answer: b) 1 : sqrt(3) : 2
Explanation:
In a 30-60-90 triangle, the side opposite the 30° angle is x, the side opposite 60° is x*sqrt(3), and the hypotenuse is 2x.
48. What is the formula for the area of a trapezoid with parallel bases b1 and b2 and height h?
Correct Answer: c) ((b1 + b2) / 2) * h
Explanation:
The area of a trapezoid is the average of the bases multiplied by the height: Area = ((b1 + b2)/2) * h.
49. What is the formula for the area of a rhombus or kite with diagonals d1 and d2?
Correct Answer: b) (1/2) * d1 * d2
Explanation:
The area of a rhombus or kite is equal to one-half the product of the lengths of its diagonals.
50. What is the formula for the length of an arc of a circle with radius r and central angle theta (in degrees)?
Correct Answer: a) (theta / 360) * 2pir
Explanation:
Arc length is the fraction of the circle's circumference determined by the central angle: (theta / 360) * 2pir.
51. What is the formula for the area of a sector of a circle with radius r and central angle theta (in degrees)?
Correct Answer: b) (theta / 360) * pir^2
Explanation:
Sector area is the fraction of the circle's total area determined by the central angle: (theta / 360) * pir^2.
52. What is the fundamental counting principle?
Correct Answer: b) If an event can occur in m ways and a second independent event can occur in n ways, the two events can occur in m * n ways.
Explanation:
The fundamental counting principle states that if there are m ways to do one thing and n ways to do another, there are m * n ways to do both.
53. What is the formula for the nth term of an arithmetic sequence with first term a1 and common difference d?
Correct Answer: a) an = a1 + (n - 1)d
Explanation:
The nth term of an arithmetic progression is given by an = a1 + (n - 1)d.
54. What is the formula for the sum of the first n terms of an arithmetic sequence?
Correct Answer: a) Sn = (n/2) * (2a1 + (n - 1)d)
Explanation:
The sum of an arithmetic series can be expressed as Sn = (n/2)(a1 + an) or Sn = (n/2)(2a1 + (n - 1)d).
55. What is the formula for the nth term of a geometric sequence with first term a1 and common ratio r?
Correct Answer: b) an = a1 * r^(n - 1)
Explanation:
The nth term of a geometric sequence is an = a1 * r^(n - 1).
56. What is the formula for the sum of the first n terms of a geometric sequence when r != 1?
Correct Answer: a) Sn = a1 * (1 - r^n) / (1 - r)
Explanation:
The sum of a finite geometric series is Sn = a1 * (1 - r^n) / (1 - r).
57. What is the formula for the sum of an infinite geometric series when |r| < 1?
Correct Answer: a) S = a1 / (1 - r)
Explanation:
The sum of an infinite converging geometric series is S = a1 / (1 - r), provided that -1 < r < 1.
58. How do you calculate the median of a set containing an odd number of sorted elements?
Correct Answer: b) The exact middle number in the sorted list
Explanation:
When a dataset has an odd number of elements and is sorted in order, the median is the single middle value.
59. How do you calculate the median of a set containing an even number of sorted elements?
Correct Answer: c) The arithmetic mean of the two middle numbers
Explanation:
When there is an even number of elements, the median is calculated by taking the average of the two central numbers in the sorted set.
60. What is the range of a numerical dataset?
Correct Answer: a) The difference between the maximum and minimum values
Explanation:
Range = Maximum value - Minimum value.
61. What does standard deviation measure in a dataset?
Correct Answer: b) The spread or dispersion of data points around the mean
Explanation:
Standard deviation quantifies how much members of a group differ or spread out from the arithmetic mean of the group.
62. If every number in a dataset is increased by a constant k, what happens to the standard deviation?
Correct Answer: c) It remains unchanged
Explanation:
Adding or subtracting a constant to all values shifts the entire distribution without altering its spread, so the standard deviation stays the same.
63. If every number in a dataset is multiplied by a positive constant c, what happens to the standard deviation?
Correct Answer: b) It is multiplied by c
Explanation:
Multiplying all data points by a positive constant c scales the spread, so the standard deviation is also multiplied by c.
64. What is the formula for calculating speed when given distance and time?
Correct Answer: b) Speed = Distance / Time
Explanation:
Speed is defined as distance traveled per unit of time: Speed = Distance / Time.
65. What is the formula for calculating time when given distance and speed?
Correct Answer: c) Time = Distance / Speed
Explanation:
Rearranging the motion formula gives Time = Distance / Speed.
66. If a car travels at 60 mph for 2.5 hours, how far does it travel?
Correct Answer: b) 150 miles
Explanation:
Distance = Speed * Time = 60 * 2.5 = 150 miles.
67. What is the formula for finding the original price given a sale price and discount percentage p?
Correct Answer: b) Original = Sale Price / (1 - p/100)
Explanation:
Since Sale Price = Original * (1 - Discount%), solving for Original yields Original = Sale Price / (1 - p/100).
68. What is the formula for profit?
Correct Answer: b) Profit = Revenue - Cost
Explanation:
Profit is the financial gain calculated as total revenue minus total cost.
69. What is the formula for profit margin (percentage)?
Correct Answer: b) (Profit / Revenue) * 100
Explanation:
Profit margin is expressed as a percentage of total revenue: (Profit / Revenue) * 100.
70. What is the formula for the sum of interior angles of a triangle?
Correct Answer: b) 180 degrees
Explanation:
The sum of the three interior angles of any triangle is always 180 degrees.
71. What is the exterior angle theorem for triangles?
Correct Answer: a) An exterior angle equals the sum of the two remote interior angles.
Explanation:
The measure of an exterior angle of a triangle is equal to the sum of the measures of its two non-adjacent interior angles.
72. In any triangle, what is the relationship between side lengths and angle measures?
Correct Answer: b) The longest side is opposite the largest angle.
Explanation:
In a triangle, the longest side is always opposite the largest interior angle, and the shortest side is opposite the smallest angle.
73. What is the triangle inequality theorem?
Correct Answer: b) The sum of the lengths of any two sides must be strictly greater than the length of the third side.
Explanation:
For any triangle with sides a, b, and c, a + b > c, a + c > b, and b + c > a must hold true.
74. If a triangle has side lengths 5 and 8, what is the range of possible lengths for the third side x?
Correct Answer: a) 3 < x < 13
Explanation:
By the triangle inequality theorem, the third side must be greater than the absolute difference (8 - 5 = 3) and less than the sum (8 + 5 = 13).
75. What is the formula for the area of a square with side length s?
Correct Answer: b) s^2
Explanation:
The area of a square is the square of its side length: A = s^2.
76. What is the formula for the perimeter of a rectangle with length l and width w?
Correct Answer: b) 2l + 2w
Explanation:
Perimeter is the total distance around the outside of a shape: P = 2l + 2w.
77. What is the length of the diagonal d of a square with side length s?
Correct Answer: b) s * sqrt(2)
Explanation:
Using the Pythagorean theorem on a square's sides (s^2 + s^2 = d^2), the diagonal is d = s * sqrt(2).
78. What is the length of the main space diagonal d of a rectangular box with dimensions l, w, and h?
Correct Answer: b) sqrt(l^2 + w^2 + h^2)
Explanation:
The three-dimensional space diagonal of a rectangular prism is given by d = sqrt(l^2 + w^2 + h^2).
79. What is the formula for the sum of the first n positive integers (1 + 2 + 3 + ... + n)?
Correct Answer: b) n(n + 1) / 2
Explanation:
The sum of the first n positive integers is given by Gauss's formula: S = n(n + 1) / 2.
80. What is the formula for the sum of the first n consecutive even positive integers (2 + 4 + 6 + ... + 2n)?
Correct Answer: a) n(n + 1)
Explanation:
The sum of the first n even positive integers is n(n + 1).
81. What is the formula for the sum of the first n consecutive odd positive integers (1 + 3 + 5 + ... + (2n - 1))?
Correct Answer: b) n^2
Explanation:
The sum of the first n odd positive integers is always equal to n^2.
82. What is the formula for converting Celsius (C) to Fahrenheit (F)?
Correct Answer: a) F = (9/5)C + 32
Explanation:
The temperature conversion formula from Celsius to Fahrenheit is F = (9/5)C + 32.
83. What is the formula for converting Fahrenheit (F) to Celsius (C)?
Correct Answer: b) C = (5/9)(F - 32)
Explanation:
Rearranging the temperature formula yields C = (5/9)(F - 32).
84. What is the equation of a circle with center (h, k) and radius r in the coordinate plane?
Correct Answer: b) (x - h)^2 + (y - k)^2 = r^2
Explanation:
The standard equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
85. What is the slope of any line perpendicular to a line with slope m (where m != 0)?
Correct Answer: c) -1 / m
Explanation:
Perpendicular lines have slopes that are negative reciprocals of each other: m2 = -1 / m1.
86. What is the relationship between the slopes of two parallel lines in the coordinate plane?
Correct Answer: b) Their slopes are equal.
Explanation:
Parallel lines never intersect and therefore have identical slopes: m1 = m2.
87. What is the formula for the exterior angle of a triangle?
Correct Answer: d) Both b and c
Explanation:
An exterior angle equals the sum of the two remote interior angles, and because it forms a linear pair with the adjacent interior angle, it also equals 180 minus that adjacent angle.
88. What is the formula for the nth term of a sequence where each term is the square of its position n?
Correct Answer: b) an = n^2
Explanation:
The standard square number sequence is generated by an = n^2.
89. What is the formula for the total number of diagonals in a convex polygon with n sides?
Correct Answer: a) n(n - 3) / 2
Explanation:
The total number of diagonals connecting non-adjacent vertices in an n-sided polygon is n(n - 3) / 2.
90. What is the formula for direct proportionality between variables x and y?
Correct Answer: a) y = kx
Explanation:
Direct proportion means y varies directly with x, expressed as y = kx or y/x = k, where k is a non-zero constant.
91. What is the formula for inverse proportionality between variables x and y?
Correct Answer: b) y = k / x
Explanation:
Inverse proportion means y varies inversely with x, expressed as y = k / x or xy = k.
92. What is the formula for the area of an equilateral triangle with side length s?
Correct Answer: b) (s^2 * sqrt(3)) / 4
Explanation:
The area of an equilateral triangle is derived using its height (s * sqrt(3) / 2), resulting in Area = (s^2 * sqrt(3)) / 4.
93. What is the height h of an equilateral triangle with side length s?
Correct Answer: b) s * sqrt(3) / 2
Explanation:
Dropping an altitude splits the equilateral triangle into two 30-60-90 right triangles, giving height h = s * sqrt(3) / 2.
94. What is the formula for compound growth or decay over time t with growth rate r?
Correct Answer: a) P(t) = P0 * (1 + r)^t
Explanation:
Exponential growth/decay follows P(t) = P0 * (1 + r)^t, where r is positive for growth and negative for decay.
95. What is the formula for the sum of angles around a single point in a plane?
Correct Answer: c) 360 degrees
Explanation:
The sum of all adjacent angles meeting at a single point around a full circle is 360 degrees.
96. What is the relationship between inscribed angles and central angles that intercept the same arc in a circle?
Correct Answer: b) The inscribed angle is half the measure of the central angle.
Explanation:
An inscribed angle is always half the measure of the central angle that subtends the exact same arc.
97. What is the measure of an angle inscribed in a semicircle?
Correct Answer: b) 90 degrees
Explanation:
Thales's theorem states that any angle inscribed in a semicircle is a right angle (90 degrees), since the corresponding central angle is 180 degrees.
98. What is the formula for the combined rate when two machines or workers complete a task together in times t1 and t2?
Correct Answer: a) T_combined = (t1 * t2) / (t1 + t2)
Explanation:
Combining individual times t1 and t2 yields the joint time formula: T_combined = (t1 * t2) / (t1 + t2).
99. What is the formula for mixture problems involving concentrations c1 and c2 mixed in volumes v1 and v2?
Correct Answer: a) Final Concentration = (c1*v1 + c2*v2) / (v1 + v2)
Explanation:
The weighted average concentration of a mixture is total solute divided by total volume: (c1*v1 + c2*v2) / (v1 + v2).
100. What is the formula for the volume of a sphere expressed in terms of its diameter d?
Correct Answer: a) (1/6) * pi * d^3
Explanation:
Since radius r = d / 2, substituting into V = (4/3)pir^3 gives V = (4/3)pi(d/2)^3 = (4/3)pi(d^3 / 8) = (1/6)pi*d^3.
101. What is the formula for the surface area of a cube with edge length e?
Correct Answer: b) 6e^2
Explanation:
A cube has 6 identical square faces, each with area e^2, giving a total surface area of 6e^2.
102. What is the formula for the volume of a cube with edge length e?
Correct Answer: b) e^3
Explanation:
The volume of a cube is calculated by cubing its edge length: V = e^3.
103. What is the formula for the length of the space diagonal of a cube with edge length e?
Correct Answer: b) e * sqrt(3)
Explanation:
Using the 3D diagonal formula with l = w = h = e gives d = sqrt(e^2 + e^2 + e^2) = e * sqrt(3).
104. What is the probability of an event NOT occurring (complementary probability) if the probability of it occurring is P(E)?
Correct Answer: b) 1 - P(E)
Explanation:
The sum of the probability of an event happening and not happening is 1, so P(not E) = 1 - P(E).
105. What is the formula for conditional probability of event A given event B: P(A | B)?
Correct Answer: a) P(A and B) / P(B)
Explanation:
Conditional probability is defined as the probability of both events occurring divided by the probability of the conditioning event: P(A | B) = P(A and B) / P(B).
106. What is the expansion of (a + b)^3?
Correct Answer: b) a^3 + 3a^2b + 3ab^2 + b^3
Explanation:
The binomial cube expansion is (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.
107. What is the factorization of the sum of cubes, a^3 + b^3?
Correct Answer: a) (a + b)(a^2 - ab + b^2)
Explanation:
The sum of cubes factors as a^3 + b^3 = (a + b)(a^2 - ab + b^2).
108. What is the factorization of the difference of cubes, a^3 - b^3?
Correct Answer: b) (a - b)(a^2 + ab + b^2)
Explanation:
The difference of cubes factors as a^3 - b^3 = (a - b)(a^2 + ab + b^2).
109. What is the formula for the lateral surface area of a cylinder with radius r and height h?
Correct Answer: b) 2pirh
Explanation:
The lateral surface area of a cylinder (excluding the two circular bases) is the circumference of the base times the height: 2pirh.
110. What is the formula for the total surface area of a cylinder with radius r and height h?
Correct Answer: b) 2pir^2 + 2pirh
Explanation:
Total surface area includes the lateral area plus the two circular ends: SA = 2pir^2 + 2pirh.
111. What is the formula for the lateral surface area of a right circular cone with radius r and slant height l?
Correct Answer: b) pirl
Explanation:
The lateral surface area of a cone is given by the formula LSA = pirl, where l is the slant height.
112. What is the formula for the total surface area of a right circular cone with radius r and slant height l?
Correct Answer: b) pir^2 + pirl
Explanation:
Total surface area of a cone is the sum of the circular base area (pir^2) and the lateral area (pirl): SA = pir(r + l).
113. What is the relationship between radius r, height h, and slant height l in a right circular cone?
Correct Answer: a) r^2 + h^2 = l^2
Explanation:
The radius, height, and slant height form a right triangle inside the cone, satisfying the Pythagorean theorem: r^2 + h^2 = l^2.
114. What is the formula for the sum of interior angles in an n-sided polygon divided by n?
Correct Answer: a) Measure of each interior angle of a regular n-gon
Explanation:
Dividing the total sum of interior angles, 180(n - 2), by the number of vertices n gives the measure of each interior angle in a regular polygon.
115. What is the formula for weighted average when quantities w1 and w2 have values x1 and x2?
Correct Answer: b) (w1*x1 + w2*x2) / (w1 + w2)
Explanation:
The weighted average formula is the sum of (weight * value) for all components divided by the sum of all weights.
116. What is the formula for determining markup percentage based on cost?
Correct Answer: a) (Markup Amount / Cost) * 100
Explanation:
Markup percentage is calculated relative to the original cost: (Markup Amount / Cost) * 100.
