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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Simplify 9^(1/2) X 4^3 X 2^(-6)?
The union of A and B.
1
True
3

2. 10<all primes<20
y = 2x^2 - 3
11 - 13 - 17 - 19
7 / 1000
The two xes after factoring.

3. 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.
3 - -3
75:11
The overlapping sections.

4. How to find the area of a sector?
Sector area = (n/360) X (pi)r^2
Two angles whose sum is 90.
10! / 3!(10-3)! = 120
Angle/360 x (pi)r^2

5. Legs 5 - 12. Hypotenuse?
13
3
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(pi)r^2 + 2(pi)rh

6. Which is greater? 27^(-4) or 9^(-8)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
10! / 3!(10-3)! = 120
27^(-4)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

7. The objects in a set are called two names:
The curve opens upward and the vertex is the minimal point on the graph.
The union of A and B.
Members or elements
Two angles whose sum is 180.

8. How to find the diagonal of a rectangular solid?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
3sqrt4
2^9 / 2 = 256
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

9. Which quadrant is the upper left hand?
The third side is greater than the difference and less than the sum.
II
The two xes after factoring.
x= (1.2)(.8)lw

10. 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?
The shortest arc between points A and B on a circle'S diameter.
1.7
Infinite.
48

11. What is a parabola?
Ax^2 + bx + c where a -b and c are constants and a /=0
1
(a + b)^2
1

12. The larger the absolute value of the slope...
2sqrt6
(a + b)^2
1
The steeper the slope.

13. What is a tangent?
20.5
A tangent is a line that only touches one point on the circumference of a circle.
An arc is a portion of a circumference of a circle.
F(x) + c

14. What are the real numbers?
...multiply by 100.
83.333%
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)
12.5%

15. 6w^2 - w - 15 = 0
1:1:sqrt2
F(x + c)
3/2 - 5/3
A circle centered on the origin with radius 8.

16. What is the graph of f(x) shifted downward c units or spaces?
1/(x^y)
F(x) - c
67 - 71 - 73
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

17. Evaluate 4/11 + 11/12
... the square of the ratios of the corresponding sides.
1 & 37/132
55%
72

18. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A circle centered at -2 - -2 with radius 3.
180
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

19. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
18
0
Its negative reciprocal. (-b/a)
Indeterminable.

20. Simplify the expression [(b^2 - c^2) / (b - c)]
6 : 1 : 2
(amount of increase/original price) x 100%
(b + c)
An expression with just one term (-6x - 2a^2)

21. 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)
11 - 13 - 17 - 19
The set of elements which can be found in either A or B.
0

22. What is the ratio of the sides of an isosceles right triangle?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Cd
Undefined - because we can'T divide by 0.
1:1:sqrt2

23. Legs 6 - 8. Hypotenuse?
90
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
True
10

24. (x^2)^4
x^(2(4)) =x^8 = (x^4)^2
1
The direction of the inequality is reversed.
No - the input value has exactly one output.

25. x^4 + x^7 =
x^(4+7) = x^11
When the function is not defined for all real numbers -; only a subset of the real numbers.
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)
Lies opposite the greater angle

26. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
The direction of the inequality is reversed.
2(pi)r^2 + 2(pi)rh
3
72

27. Define an 'expression'.
37.5%
y = (x + 5)/2
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)
1

28. What is the maximum value for the function g(x) = (-2x^2) -1?
5
1
11 - 13 - 17 - 19
52

29. 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
5
Two angles whose sum is 180.
Even

30. Can you subtract 3sqrt4 from sqrt4?
(b + c)
The greatest value minus the smallest.
3
Yes - like radicals can be added/subtracted.

31. 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.
F(x + c)
16.6666%
10

32. What is the empty set?
1/a^6
41 - 43 - 47
N! / (n-k)!
A set with no members - denoted by a circle with a diagonal through it.

33. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Two equal sides and two equal angles.
28. n = 8 - k = 2. n! / k!(n-k)!
180 degrees
5

34. What is the measure of an exterior angle of a regular pentagon?
Indeterminable.
72
A 30-60-90 triangle.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

35. (-1)^3 =
1
The set of output values for a function.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
4725

36. What is the graph of f(x) shifted right c units or spaces?
F(x-c)
0
Yes - like radicals can be added/subtracted.
180 degrees

37. What is the name of set with a number of elements which cannot be counted?
An infinite set.
N! / (k!)(n-k)!
1
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

38. What is a central angle?
500
28. n = 8 - k = 2. n! / k!(n-k)!
A central angle is an angle formed by 2 radii.
Indeterminable.

39. a^2 + 2ab + b^2
An isosceles right triangle.
A circle centered at -2 - -2 with radius 3.
(a + b)^2
55%

40. Factor x^2 - xy + x.
The shortest arc between points A and B on a circle'S diameter.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Even
x(x - y + 1)

41. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
90 degrees
An isosceles right triangle.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
12! / 5!7! = 792

42. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
0
F(x + c)
1
G(x) = {x}

43. 30< all primes<40
C = (pi)d
31 - 37
Undefined
130pi

44. Length of an arc of a circle?
67 - 71 - 73
Infinite.
Angle/360 x 2(pi)r
F(x) - c

45. sqrt 2(sqrt 6)=
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
C = 2(pi)r
Sqrt 12
441000 = 1 10 10 10 21 * 21

46. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
52
70
5
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

47. How to determine percent increase?
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...
Triangles with same measure and same side lengths.
(amount of increase/original price) x 100%

48. What is the surface area of a cylinder with radius 5 and height 8?
C = 2(pi)r
3
130pi
61 - 67

49. What does the graph x^2 + y^2 = 64 look like?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
1/2 times 7/3
2 & 3/7
A circle centered on the origin with radius 8.

50. Can you simplify sqrt72?
90pi
6
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
180