GRE math errors
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221 terms
Terms | Definitions |
|---|---|
 The number of degrees in the largest angle of a triangle inscribed in a circle, in which the diameter of the circle is one side of the triangle. | 90 degrees |
| (-1)^3 = | -1 |
| (-1)^2 = | 1 |
| 25^(1/2) or sqrt. 25 = | 5 OR -5 |
| Order of quadrants: | From northeast, counterclockwise. I, II, III, IV |
| Number of degrees in a triangle | 180 |
| Formula of rectangle where l increases by 20% and w decreases by 20% | x= (1.2)(.8)lw |
| In a triangle inscribed inside a circle, where the diameter is one side of the triangle, which angle is largest? | The angle intersecting the circumference is always the largest angle, and is always 90 degrees. |
| sqrt 2(sqrt 6)= | sqrt 12 |
| 2sqrt4 + sqrt4 = | 3sqrt4 |
| In a regular polygon with n sides , the formula for the sum of interior angles | (n-2) x 180 |
| x^(-y)= | 1/(x^y) |
| What are the real numbers? | All the numbers on the number line (negative, rational, irrational, decimal, integer). All the numbers on the GRE are real. (-2, 1, .25, 1/2, pi) |
| What are the rational numbers? | All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2, 1, .25, 1/2) |
| What are the irrational numbers? | All real numbers which can't be expressed as a ratio of two integers, positive and negative (pi, -sqrt3) |
| What are the integers? | All numbers multiples of 1. |
| 1/2 divided by 3/7 is the same as | 1/2 times 7/3 |
| A number is divisible by 3 if ... | the sum of its digits is divisible by 3. |
| A number is divisible by 4 is... | its last two digits are divisible by 4. |
| A number is divisible by 6 if... | its divisible by 2 and by 3. |
| A number is divisible by 9 if... | the sum of digits is divisible by 9. |
| 10<all primes<20 | 11, 13, 17, 19 |
| 20<all primes<30 | 23, 29 |
| 30< all primes<40 | 31, 37 |
| 40 < all primes<50 | 41, 43, 47 |
| 50 < all primes< 60 | 53, 59 |
| 60 < all primes <70 | 61, 67 |
| 70 < all primes< 80 | 71, 73, 79 |
| To convert a decimal to a percent... | ...multiply by 100. |
| To convert a percent to a fraction.... | divide by 100. |
| 1/8 in percent? | 12.5% |
| 1/6 in percent? | 16.6666% |
| 3/8 in percent? | 37.5% |
| 5/8 in percent? | 62.5% |
| 7/8 in percent? | 87.5% |
| 5/6 in percent? | 83.333% |
| x^4 + x^7 = | x^(4+7) = x^11 |
| x^6 / x^3 | x^(6-3) = x^3 |
| (x^2)^4 | x^(2(4)) =x^8 = (x^4)^2 |
| a^0 = | 1 |
| 0^0 | undefined |
| Can you add sqrt 3 and sqrt 5? | No, only like radicals can be added. |
| Can you subtract 3sqrt4 from sqrt4? | Yes, like radicals can be added/subtracted. |
| (6sqrt3) x (2sqrt5) = | (6 x 2)(sqrt3 x sqrt5) = 12sqrt15 |
| (12sqrt15) / (2sqrt5) = | (12/2) x (sqrt15 / sqrt5) = 6sqrt3 |
| Can you simplify sqrt72? | Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2. |
| 10^6 has how many zeroes? | 6 |
| To multiply a number by 10^x | move the decimal point to the right x places |
| 413.03 x 10^(-4) = | 413.03 / 10^4 (move the decimal point 4 places to the left) |
| What does scientific notation mean? | Expressing a number as the product of a decimal between 1 and 10, and a power of 10. |
| Define a "term", | A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x, 4x^2 and 2a/c) |
| Define an "expression". | An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy, 4ab, -5cd, x^2 + x - 1) |
| Define a "monomial" | An expression with just one term (-6x, 2a^2) |
| a^2 - b^2 = | (a - b)(a + b) |
| a^2 + 2ab + b^2 | (a + b)^2 |
| Solve the quadratic equation ax^2 + bx + c= 0 | x = [(-b)+/- (sqrt b^2 - 4ac)]/2a |
| If an inequality is multiplied or divided by a negative number.... | the direction of the inequality is reversed. |
| What is the "domain" of a function? | The set of input values for a function. |
| What is the "range" of a function? | The set of output values for a function. |
| What is the "restricted domain of a function"? | When the function is not defined for all real numbers,; only a subset of the real numbers. |
| What is the absolute value function? | g(x) = {x} |
| What is the formula for computing simple interest? | A = I (1 + rt) |
| What is the formula for compounded interest? | A= I (1 + (r/c))^tC, where I is the investment, C is the number of times compounded annually, and t is the number of years. |
| What is the order of operations? | PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction) |
| What is the sum of the angles of a triangle? | 180 degrees |
| What is the percent formula? | Part = Percent X Whole |
| Surface area for a cylinder? | 2(pi)r^2 + 2(pi)rh |
| Volume for a cylinder? | Area of the base X height = (pi)hr^2 |
| How to find the area of a sector? | Angle/360 x (pi)r^2 |
| Length of an arc of a circle? | Angle/360 x 2(pi)r |
| Max and Min lengths for a side of a triangle? | The third side is greater than the difference and less than the sum. |
| Factor a^2 + 2ab + b^2 | (a + b)^2 |
| a^2 - 2ab + b^2 | (a - b)^2 |
| a^2 - b^2 | (a - b)(a + b) |
| What is the "range" of a series of numbers? | The greatest value minus the smallest. |
| How to determine percent increase? | (amount of increase/original price) x 100% |
| How to determine percent decrease? | (amount of decrease/original price) x 100% |
| Area of a triangle? | (base*height) / 2 |
| What is an isoceles triangle? | Two equal sides and two equal angles. |
| How to find the diagonal of a rectangular solid? | Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge). |
| Circumference of a circle? | Diameter(Pi) |
| How to find the circumference of a circle which circumscribes a square? | Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter). |
| Can the input value of a function have more than one output value (i.e. x: y, y1)? | No, the input value has exactly one output. |
| Can the output value of a function have more than one input value? | Yes. [i.e. f(x) = x^2 - 1 |
| When does a function automatically have a restricted domain (2)? | When we need to avoid having a zero in the denominator or avoid taking the square root of a number. |
| The larger the absolute value of the slope... | the steeper the slope. |
| What is the slope of a horizontal line? | 0 |
| What is the slope of a vertical line? | Undefined, because we can't divide by 0. |
| The slope of a line perpendicular to (a/b)? | Its negative reciprocal. (-b/a) |
| Which quadrant is the upper right hand? | I |
| Which quandrant is the lower right hand? | IV |
| Which quadrant is the upper left hand? | II |
| Which quadrant is the lower left hand? | III |
| What is a parabola? | ax^2 + bx + c where a,b and c are constants and a /=0 |
| When the "a" in a parabola is positive.... | the curve opens upward and the vertex is the minimal point on the graph. |
| When the "a" in the parabola is negative... | the curve opens downward and the vertex is the maximum point on the graph. |
| What does the graph x^2 + y^2 = 64 look like? | A circle centered on the origin with radius 8. |
| What does the graph (x+2)^2 + (y+2)^2 = 9 look like? | A circle centered at -2, -2 with radius 3. |
| What is a piecewise equation? | It is a function defined by more than one equation, where each equation applies to a different part of the domain of the function. |
| What are "supplementary angles?" | Two angles whose sum is 180. |
| If the two sides of a triangle are unequal then the longer side... | lies opposite the greater angle |
| What is a chord of a circle? | A chord is a line segment joining two points on a circle. |
| What is a central angle? | A central angle is an angle formed by 2 radii. |
| What is a tangent? | A tangent is a line that only touches one point on the circumference of a circle. |
| Pi is a ratio of what to what? | Pi is the ratio of a circle's circumference to its diameter. |
| Formula to find a circle's circumference from its diameter? | C = (pi)d |
| Formula to find a circle's circumference from its radius? | C = 2(pi)r |
| What is an arc of a circle? | An arc is a portion of a circumference of a circle. |
| What is a minor arc? | The shortest arc between points A and B on a circle's diameter. |
| What is a major arc? | The longest arc between points A and B on a circle's diameter. |
| Formula to calculate arc length? | Arc length = (n/360) x pi(2r) where n is the number of degrees. |
| Formula for the area of a circle? | A = pi(r^2) |
| Formula for the area of a sector of a circle? | Sector area = (n/360) X (pi)r^2 |
| What is the "solution" for a system of linear equations? | The point of intersection of the systems. |
| What is the "solution" for a set of inequalities. | The overlapping sections. |
| What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)? | A reflection about the origin. |
| What is the graph of f(x) shifted upward c units or spaces? | f(x) + c |
| What is the graph of f(x) shifted downward c units or spaces? | f(x) - c |
| What is the graph of f(x) shifted left c units or spaces? | f(x + c) |
| What is the graph of f(x) shifted right c units or spaces? | f(x-c) |
| What are complementary angles? | Two angles whose sum is 90. |
| What are congruent triangles? | Triangles with same measure and same side lengths. |
| Legs: 3, 4. Hypotenuse? | 5 |
| Legs 6, 8. Hypotenuse? | 10 |
| Legs 5, 12. Hypotenuse? | 13 |
| Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14 | 2 & 3/7 |
| 8.84 / 5.2 | 1.7 |
| Evaluate 4/11 + 11/12 | 1 & 37/132 |
| Evaluate 3& 2/7 / 1/3 | 9 & 6/7 |
| 200 <_ x <_ 300. How many values of x are divisible by 5 & 8? | 3 |
| What number between 70 & 75, inclusive, has the greatest number of factors? | 72 |
| What are the smallest three prime numbers greater than 65? | 67, 71, 73 |
| Which is greater? 64^5 or 16^8 | 16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16 |
| Evaluate (4^3)^2 | 4096 |
| Write 10,843 X 10^7 in scientific notation | 1.0843 X 10^11 |
| True or false? 4.809 X 10^7 = .0004809 X 10^11 | True |
| If a=-1 and b=3, what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))? | 20.5 |
| T or F? Given d,e &f =/ 0, [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]? | True |
| Simplify 4sqrt21 X 5sqrt2 / 10sqrt7 | 2sqrt6 |
| Simplify 9^(1/2) X 4^3 X 2^(-6)? | 3 |
| 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same, what is the average of muffins per bakery sold among the remaining? | 500 |
| Reduce: 4.8 : 0.8 : 1.6 | 6 : 1 : 2 |
| Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages? | 9 : 25 |
| What percent of 40 is 22? | 55% |
| Convert 0.7% to a fraction. | 7 / 1000 |
| Hector invested $6000. Part was invested in account with 9% simple annual interest, and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments, how much did he invest in each account? | $3,500 in the 9% and $2,500 in the 7%. |
| Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week, how many did each work? | 48 |
| The perimeter of a square is 48 inches. The length of its diagonal is: | 12sqrt2 |
| If Madagascar's exports totaled 1.3 billion in 2009, and 4% came from China, what was the value in millions of the country's exports to China? | 52 |
| Whats the difference between factors and multiples? | Factors are few, multiples are many. |
| How many multiples does a given number have? | Infinite. |
| P and r are factors of 100. What is greater, pr or 100? | Indeterminable. |
| If r, t, s & u are distinct, consecutive prime numbers, less than 31, which of the following could be an average of them (4, 4.25, 6, 9, 24, 22, 24) | 4.25, 6, 22 |
| Is 0 even or odd? | Even |
| How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)] | 0 |
| What are the roots of the quadrinomial x^2 + 2x + 1? | The two xes after factoring. |
| Factor x^2 - xy + x. | x(x - y + 1) |
| Simplify the expression [(b^2 - c^2) / (b - c)] | (b + c) |
| Simplify (a^2 + b)^2 - (a^2 - b)^2 | 4a^2(b) |
| What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd? | cd |
| Simplify the expression (p^2 - q^2)/ -5(q - p) | (p + q)/5 |
| What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)? | 2 |
| (a^-1)/a^5 | 1/a^6 |
| x^2 = 9. What is the value of x? | 3, -3 |
| 6w^2 - w - 15 = 0 | -3/2 , 5/3 |
| 5x^2 - 35x -55 = 0 | [(7+ sqrt93) /2], [(7 - sqrt93) / 2] |
| If 10800 is invested at a simple interest rate of 4%, what is the value of the investment after 18 months? | $11,448 |
| If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months? | 4725 |
| What is the maximum value for the function g(x) = (-2x^2) -1? | -1 |
| For what values should the domain be restricted for the function f(x) = sqrt(x + 8) | -8 |
| What transformation occurs if point C is reflected over the x-axis and then the y-axis? | A reflection about the axis. |
| The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y? | 90 |
| For similar triangles, the ratio of their corresponding sides is 2:3. What is the ratio of their areas? | 4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides. |
| What is the ratio of the sides of an isosceles right triangle? | 1:1:sqrt2 |
| 1:1:sqrt2 is the ratio of the sides of what kind of triangle? | An isosceles right triangle. |
| What is the ratio of the sides of a 30-60-90 triangle? | 1:sqrt3:2 |
| 1:sqrt3:2 is the ratio of the sides of what kind of triangle? | A 30-60-90 triangle. |
| What is the side length of an equilateral triangle with altitude 6? | 4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3... |
| In a triangle where the two legs are 4 and 3, what is the value of a line directly intersecting the middle coming from the meeting point of the two legs? | 2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6 |
| Describe the relationship between 3x^2 and 3(x - 1)^2 | The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right. |
| Describe the relationship between the graphs of x^2 and (1/2)x^2 | The second graph is less steep. |
| Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)? | y = (x + 5)/2 |
| Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation? | y = 2x^2 - 3 |
| How many sides does a hexagon have? | 6 |
| What is an exterior angle? | An angle which is supplementary to an interior angle. |
| What is the measure of an exterior angle of a regular pentagon? | 72 |
| The ratio of the areas of two similar polygons is ... | ... the square of the ratios of the corresponding sides. |
| In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides? | 4:5 |
| What is the area of a regular hexagon with side 6? | 54sqrt3. (divide the hexagon into 6 congruent equilateral triangles. |
| A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle? | 13pi / 2 |
| A cylinder has a surface area of 22pi. If the cylinder has a height of 10, what is the radius? | 1 |
| What is the third quartile of the following data set: 44, 58, 63, 63, 68, 70, 82 | 70 |
| If the 80th percentile of the measurements is 72degrees, about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth | 18 |
| The objects in a set are called two names: | members or elements |
| What are the members or elements of a set? | The objects within a set. |
| What is a finite set? | A set with a number of elements which can be counted. |
| What is the name of set with a number of elements which cannot be counted? | An infinite set. |
| What is a subset? | a grouping of the members within a set based on a shared characteristic. |
| What is the name for a grouping of the members within a set based on a shared characteristic? | A subset. |
| What is the empty set? | A set with no members, denoted by a circle with a diagonal through it. |
| What is a set with no members called? | the empty set, denoted by a circle with a diagonal through it. |
| What is the "union" of A and B? | The set of elements which can be found in either A or B. |
| What is the set of elements which can be found in either A or B? | The union of A and B. |
| What is the intersection of A and B? | The set of elements found in both A and B. |
| What is the set of elements found in both A and B? | The interesection of A and B. |
| If you have a set of n objects, but you only want to order k of them, what formula do you use to determine the number of permutations? | n! / (n-k)! |
| Suppose you have a set of n objects, and you want to select k of them, but the order doesn't matter. What formula do you use to determine the number of combinations of n objects taken k at a time? | n! / (k!)(n-k)! |
| How many 3-digit positive integers are even and do not contain the digit 4? | 288 (8 9 4) |
| From a box of 12 candles, you are to remove 5. How many different sets of 5 candles could you remove? | 12! / 5!7! = 792 |
| There are 10 finalists for the school spelling bee. A first, second, and third place trophy will be awarded. In how many ways can the judges award the 3 prizes? | 10! / (10-3)! = 720 |
| There are 10 finalists for the school spelling bee. A first, second, and third place trophy will be awarded. How many different people can get the three prizes? | 10! / 3!(10-3)! = 120 |
| A company places a 6-symbol code on each product. The code consists of the letter T, followed by 3 numerical digits, and then 2 consonants (Y is a conson). How many codes are possible? | 441000 = 1 10 10 10 21 * 21 |
| Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads? | 2^9 / 2 = 256 |
| Find the surface area of a cylinder with radius 3 and height 12. | 90pi |
| What is the surface area of a cylinder with radius 5 and height 8? | 130pi |
| A cylinder has surface area 22pi. If the cylinder has a height of 10, what is its radius? | 1 |
| What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2, 4, and 6? | 75:11 |
| A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12, 18, and 30. What is the weight of the second brick? | 2.592 kg |
| If 8 schools are in a conference, how many games are played if each team plays each other exactly once? | 28. n = 8, k = 2. n! / k!(n-k)! |
| Which is greater? 27^(-4) or 9^(-8) | 27^(-4) |
| Which is greater? 200x^295 or 10x^294? | Relationship cannot be determined (what if x is negative?) |
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