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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. a^0 =
$11 -448
(a + b)^2
1
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...

2. How to determine percent increase?
(amount of increase/original price) x 100%
A central angle is an angle formed by 2 radii.
(p + q)/5
3

3. 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)
0
83.333%
6 : 1 : 2

4. 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
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
(b + c)
A circle centered at -2 - -2 with radius 3.

5. 5/6 in percent?
83.333%
1
A chord is a line segment joining two points on a circle.
71 - 73 - 79

6. What is the graph of f(x) shifted upward c units or spaces?
Yes - like radicals can be added/subtracted.
Two equal sides and two equal angles.
F(x) + c
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)

7. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
Divide by 100.
(amount of increase/original price) x 100%
Relationship cannot be determined (what if x is negative?)

8. What are the integers?
An isosceles right triangle.
31 - 37
All numbers multiples of 1.
Infinite.

9. sqrt 2(sqrt 6)=
A set with a number of elements which can be counted.
F(x + c)
Sqrt 12
27^(-4)

10. What is the ratio of the sides of an isosceles right triangle?
The third side is greater than the difference and less than the sum.
N! / (n-k)!
27^(-4)
1:1:sqrt2

11. What are the roots of the quadrinomial x^2 + 2x + 1?
10! / (10-3)! = 720
The two xes after factoring.
When the function is not defined for all real numbers -; only a subset of the real numbers.
Two angles whose sum is 180.

12. What is an exterior angle?
An angle which is supplementary to an interior angle.
F(x) + c
The shortest arc between points A and B on a circle'S diameter.
F(x) - c

13. How many sides does a hexagon have?
... the square of the ratios of the corresponding sides.
180 degrees
6
Cd

14. 2sqrt4 + sqrt4 =
3sqrt4
The empty set - denoted by a circle with a diagonal through it.
Part = Percent X Whole
(a - b)^2

15. 5x^2 - 35x -55 = 0
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
441000 = 1 10 10 10 21 * 21
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1.0843 X 10^11

16. a^2 - b^2 =
(a - b)(a + b)
A reflection about the axis.
16.6666%
11 - 13 - 17 - 19

17. What is a major arc?

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18. What is the measure of an exterior angle of a regular pentagon?
II
72
Angle/360 x (pi)r^2
The longest arc between points A and B on a circle'S diameter.

19. What is the area of a regular hexagon with side 6?
18
The second graph is less steep.
70
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

20. Reduce: 4.8 : 0.8 : 1.6
31 - 37
1
2
6 : 1 : 2

21. Can you subtract 3sqrt4 from sqrt4?
(a + b)^2
Area of the base X height = (pi)hr^2
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Yes - like radicals can be added/subtracted.

22. 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?
4:5
N! / (n-k)!
12! / 5!7! = 792
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

23. Circumference of a circle?
A 30-60-90 triangle.
N! / (k!)(n-k)!
Diameter(Pi)
C = 2(pi)r

24. Legs 6 - 8. Hypotenuse?
A subset.
1
y = (x + 5)/2
10

25. Which quandrant is the lower right hand?
F(x + c)
IV
1.0843 X 10^11
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

26. What is the empty set?
An angle which is supplementary to an interior angle.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A set with no members - denoted by a circle with a diagonal through it.
The second graph is less steep.

27. Simplify 9^(1/2) X 4^3 X 2^(-6)?
70
10! / 3!(10-3)! = 120
3
Infinite.

28. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
70
1
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

29. Define a 'Term' -
(a - b)(a + b)
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)
1 & 37/132
The sum of digits is divisible by 9.

30. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
C = (pi)d
90
The sum of its digits is divisible by 3.
13pi / 2

31. Can the output value of a function have more than one input value?
(p + q)/5
A reflection about the origin.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Yes. [i.e. f(x) = x^2 - 1

32. What is the maximum value for the function g(x) = (-2x^2) -1?
1
A set with no members - denoted by a circle with a diagonal through it.
52
Move the decimal point to the right x places

33. Formula for the area of a circle?
Sqrt 12
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
A = pi(r^2)
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)

34. If the two sides of a triangle are unequal then the longer side...
Lies opposite the greater angle
1
6 : 1 : 2
(a + b)^2

35. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
(n-2) x 180
(a + b)^2
II
1

36. What is the 'Solution' for a system of linear equations?
A set with a number of elements which can be counted.
1/2 times 7/3
Infinite.
The point of intersection of the systems.

37. What are congruent triangles?
1/a^6
Triangles with same measure and same side lengths.
1 & 37/132
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

38. x^(-y)=
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Area of the base X height = (pi)hr^2
1/(x^y)
Ax^2 + bx + c where a -b and c are constants and a /=0

39. a^2 - 2ab + b^2
(a - b)^2
500
The curve opens downward and the vertex is the maximum point on the graph.
A chord is a line segment joining two points on a circle.

40. What is a set with no members called?
Sqrt 12
The set of elements which can be found in either A or B.
C = (pi)d
The empty set - denoted by a circle with a diagonal through it.

41. 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
12.5%
II
180

42. Length of an arc of a circle?
I
2(pi)r^2 + 2(pi)rh
90 degrees
Angle/360 x 2(pi)r

43. 7/8 in percent?
(a + b)^2
A circle centered on the origin with radius 8.
y = 2x^2 - 3
87.5%

44. Can you simplify sqrt72?
III
Even
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
C = (pi)d

45. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
Ax^2 + bx + c where a -b and c are constants and a /=0
(b + c)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

46. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
1/a^6
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A = I (1 + rt)
28. n = 8 - k = 2. n! / k!(n-k)!

47. What is the intersection of A and B?
0
Triangles with same measure and same side lengths.
The set of elements found in both A and B.
72

48. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
$11 -448
A central angle is an angle formed by 2 radii.
Two angles whose sum is 90.

49. 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?
A circle centered at -2 - -2 with radius 3.
3
2.592 kg
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

50. (6sqrt3) x (2sqrt5) =
27^(-4)
(base*height) / 2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
180 degrees

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GRE Math: Common Errors

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