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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. What is the name of set with a number of elements which cannot be counted?
90 degrees
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
A grouping of the members within a set based on a shared characteristic.
An infinite set.

2. Area of a triangle?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
0
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
(base*height) / 2

3. Formula to find a circle'S circumference from its radius?
48
71 - 73 - 79
0
C = 2(pi)r

4. What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
The empty set - denoted by a circle with a diagonal through it.
Angle/360 x 2(pi)r
The set of output values for a function.

5. What is the area of a regular hexagon with side 6?
The objects within a set.
N! / (n-k)!
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
90pi

6. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
130pi
A circle centered on the origin with radius 8.
83.333%

7. What is the 'domain' of a function?
87.5%
62.5%
The set of input values for a function.
Diameter(Pi)

8. 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?
1/a^6
N! / (k!)(n-k)!
A reflection about the axis.
Factors are few - multiples are many.

9. Which quadrant is the upper left hand?
2sqrt6
II
(base*height) / 2
23 - 29

10. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
8
The shortest arc between points A and B on a circle'S diameter.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x^(2(4)) =x^8 = (x^4)^2

11. In a regular polygon with n sides - the formula for the sum of interior angles
(n-2) x 180
413.03 / 10^4 (move the decimal point 4 places to the left)
N! / (n-k)!
1/2 times 7/3

12. 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?
The curve opens downward and the vertex is the maximum point on the graph.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
1
10! / (10-3)! = 720

13. Solve the quadratic equation ax^2 + bx + c= 0
3
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(amount of decrease/original price) x 100%
I

14. How many multiples does a given number have?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
18
Infinite.

15. 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.
62.5%
Pi is the ratio of a circle'S circumference to its diameter.
28. n = 8 - k = 2. n! / k!(n-k)!

16. Which quandrant is the lower right hand?
Yes - like radicals can be added/subtracted.
(a + b)^2
IV
... the square of the ratios of the corresponding sides.

17. What are the rational numbers?
9 & 6/7
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
67 - 71 - 73
An infinite set.

18. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
x^(2(4)) =x^8 = (x^4)^2
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

19. 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
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Cd
70

20. Can you simplify sqrt72?
The shortest arc between points A and B on a circle'S diameter.
83.333%
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
1/(x^y)

21. Which quadrant is the upper right hand?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
130pi
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
I

22. Evaluate 4/11 + 11/12
1 & 37/132
37.5%
441000 = 1 10 10 10 21 * 21
$3 -500 in the 9% and $2 -500 in the 7%.

23. 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.
500
90 degrees
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
27^(-4)

24. What is the side length of an equilateral triangle with altitude 6?
180 degrees
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...
Undefined
The sum of its digits is divisible by 3.

25. If the two sides of a triangle are unequal then the longer side...
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
An angle which is supplementary to an interior angle.
Lies opposite the greater angle
3

26. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
The greatest value minus the smallest.
0

27. 0^0
Undefined
(p + q)/5
1/2 times 7/3
5 OR -5

28. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
2(pi)r^2 + 2(pi)rh
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
75:11
The interesection of A and B.

29. What is a chord of a circle?
1:1:sqrt2
A chord is a line segment joining two points on a circle.
(a - b)^2
Angle/360 x 2(pi)r

30. The slope of a line perpendicular to (a/b)?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Members or elements
Its negative reciprocal. (-b/a)
12sqrt2

31. (12sqrt15) / (2sqrt5) =
The union of A and B.
10! / (10-3)! = 720
13pi / 2
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

32. 5/8 in percent?
Sqrt 12
Sector area = (n/360) X (pi)r^2
The direction of the inequality is reversed.
62.5%

33. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
y = (x + 5)/2
$11 -448
(a - b)(a + b)

34. Convert 0.7% to a fraction.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
0
7 / 1000
1

35. a^2 - b^2
(a - b)(a + b)
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Move the decimal point to the right x places
A grouping of the members within a set based on a shared characteristic.

36. Formula to find a circle'S circumference from its diameter?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
C = (pi)d
The shortest arc between points A and B on a circle'S diameter.
12.5%

37. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
20.5
A reflection about the origin.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Cd

38. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
1/a^6
1/(x^y)
$11 -448

39. What is a major arc?

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40. Number of degrees in a triangle
500
Sector area = (n/360) X (pi)r^2
75:11
180

41. What number between 70 & 75 - inclusive - has the greatest number of factors?
An infinite set.
6
72
The third side is greater than the difference and less than the sum.

42. (6sqrt3) x (2sqrt5) =
3 - -3
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Sqrt 12
Diameter(Pi)

43. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
4:5
48
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.

44. 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
180
A reflection about the origin.
31 - 37

45. What is the graph of f(x) shifted downward c units or spaces?
An arc is a portion of a circumference of a circle.
Angle/360 x 2(pi)r
75:11
F(x) - c

46. Legs: 3 - 4. Hypotenuse?
Area of the base X height = (pi)hr^2
5
No - only like radicals can be added.
Factors are few - multiples are many.

47. Define an 'expression'.
The sum of its digits is divisible by 3.
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)
The longest arc between points A and B on a circle'S diameter.
x^(4+7) = x^11

48. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
61 - 67
1
12! / 5!7! = 792
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.

49. What is the 'Range' of a function?
The set of output values for a function.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
0
...multiply by 100.

50. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
18
A reflection about the origin.
48

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GRE Math: Common Errors

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