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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. What is the side length of an equilateral triangle with altitude 6?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
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...
A reflection about the origin.
12sqrt2

2. What are the integers?
Yes - like radicals can be added/subtracted.
All numbers multiples of 1.
x^(6-3) = x^3
9 : 25

3. 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
180
4a^2(b)
...multiply by 100.

4. What is a chord of a circle?
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)
4096
A chord is a line segment joining two points on a circle.
12sqrt2

5. Can you subtract 3sqrt4 from sqrt4?
x^(2(4)) =x^8 = (x^4)^2
87.5%
Yes - like radicals can be added/subtracted.
11 - 13 - 17 - 19

6. What are the smallest three prime numbers greater than 65?
(b + c)
62.5%
67 - 71 - 73
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

7. What is the 'Solution' for a system of linear equations?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
53 - 59
The point of intersection of the systems.

8. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
No - the input value has exactly one output.
The overlapping sections.
2 & 3/7
6 : 1 : 2

9. What is the intersection of A and B?
The set of elements found in both A and B.
... the square of the ratios of the corresponding sides.
288 (8 9 4)
Yes. [i.e. f(x) = x^2 - 1

10. What is a major arc?

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11. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
An angle which is supplementary to an interior angle.
0
67 - 71 - 73

12. To multiply a number by 10^x
Move the decimal point to the right x places
Diameter(Pi)
12sqrt2
8

13. Volume for a cylinder?
Area of the base X height = (pi)hr^2
Infinite.
Even
A tangent is a line that only touches one point on the circumference of a circle.

14. What is the percent formula?
48
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A 30-60-90 triangle.
Part = Percent X Whole

15. How many sides does a hexagon have?
A central angle is an angle formed by 2 radii.
6
1
10

16. Find the surface area of a cylinder with radius 3 and height 12.
90pi
0
Indeterminable.
The union of A and B.

17. What is the empty set?
x^(6-3) = x^3
A set with no members - denoted by a circle with a diagonal through it.
3 - -3
C = 2(pi)r

18. Which is greater? 27^(-4) or 9^(-8)
11 - 13 - 17 - 19
27^(-4)
3
A subset.

19. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
The union of A and B.
Infinite.
The point of intersection of the systems.

20. 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?
F(x) + c
180
II
75:11

21. a^0 =
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)
Two angles whose sum is 180.
The sum of its digits is divisible by 3.
1

22. Simplify the expression (p^2 - q^2)/ -5(q - p)
From northeast - counterclockwise. I - II - III - IV
(p + q)/5
F(x) + c
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

23. Which is greater? 200x^295 or 10x^294?
x^(2(4)) =x^8 = (x^4)^2
2(pi)r^2 + 2(pi)rh
True
Relationship cannot be determined (what if x is negative?)

24. What are complementary angles?
Two angles whose sum is 90.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
23 - 29
Divide by 100.

25. a^2 - b^2 =
(amount of decrease/original price) x 100%
(a - b)(a + b)
An infinite set.
55%

26. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
Sector area = (n/360) X (pi)r^2
F(x + c)
Area of the base X height = (pi)hr^2
70

27. Evaluate (4^3)^2
Two angles whose sum is 180.
4096
C = (pi)d
Angle/360 x 2(pi)r

28. How many 3-digit positive integers are even and do not contain the digit 4?
(p + q)/5
Pi is the ratio of a circle'S circumference to its diameter.
1
288 (8 9 4)

29. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
IV
$11 -448
A = I (1 + rt)
F(x + c)

30. What is the graph of f(x) shifted left c units or spaces?
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...
.0004809 X 10^11
0
F(x + c)

31. What is the name of set with a number of elements which cannot be counted?
y = 2x^2 - 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)
An infinite set.
.0004809 X 10^11

32. When the 'a' in the parabola is negative...
The curve opens downward and the vertex is the maximum point on the graph.
7 / 1000
F(x) - c
F(x + c)

33. A number is divisible by 3 if ...
The sum of its digits is divisible by 3.
Lies opposite the greater angle
Yes. [i.e. f(x) = x^2 - 1
x^(6-3) = x^3

34. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
1/a^6
1/2 times 7/3

35. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A = I (1 + rt)
A set with a number of elements which can be counted.
A reflection about the origin.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

36. When does a function automatically have a restricted domain (2)?
180 degrees
72
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)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

37. Can the output value of a function have more than one input value?
2
Yes. [i.e. f(x) = x^2 - 1
8
The second graph is less steep.

38. What is the surface area of a cylinder with radius 5 and height 8?
11 - 13 - 17 - 19
(n-2) x 180
130pi
(a - b)(a + b)

39. What is an isoceles triangle?
$11 -448
Two equal sides and two equal angles.
1
Angle/360 x 2(pi)r

40. Evaluate 4/11 + 11/12
1 & 37/132
A chord is a line segment joining two points on a circle.
10! / 3!(10-3)! = 120
The objects within a set.

41. x^(-y)=
Its last two digits are divisible by 4.
9 & 6/7
1/(x^y)
The longest arc between points A and B on a circle'S diameter.

42. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
(a - b)^2
G(x) = {x}
Part = Percent X Whole
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

43. What is the order of operations?
3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
.0004809 X 10^11
4725

44. 8.84 / 5.2
The two xes after factoring.
1.7
9 & 6/7
The set of elements which can be found in either A or B.

45. Which quandrant is the lower right hand?
Cd
7 / 1000
IV
Divide by 100.

46. Formula of rectangle where l increases by 20% and w decreases by 20%
N! / (n-k)!
x= (1.2)(.8)lw
6
x^(6-3) = x^3

47. 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?
Sector area = (n/360) X (pi)r^2
The longest arc between points A and B on a circle'S diameter.
N! / (n-k)!
A circle centered on the origin with radius 8.

48. Write 10 -843 X 10^7 in scientific notation
A circle centered at -2 - -2 with radius 3.
(amount of increase/original price) x 100%
Diameter(Pi)
1.0843 X 10^11

49. Describe the relationship between 3x^2 and 3(x - 1)^2
The interesection of A and B.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Area of the base X height = (pi)hr^2
4a^2(b)

50. The perimeter of a square is 48 inches. The length of its diagonal is:
37.5%
All numbers multiples of 1.
12sqrt2
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.