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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. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
Pi is the ratio of a circle'S circumference to its diameter.
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.
A tangent is a line that only touches one point on the circumference of a circle.

2. 3/8 in percent?
37.5%
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
N! / (n-k)!
10! / 3!(10-3)! = 120

3. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
1:1:sqrt2
90
A grouping of the members within a set based on a shared characteristic.
Angle/360 x (pi)r^2

4. What are the real numbers?
13
87.5%
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.
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)

5. 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.
x^(6-3) = x^3
The curve opens upward and the vertex is the minimal point on the graph.
The shortest arc between points A and B on a circle'S diameter.

6. Formula of rectangle where l increases by 20% and w decreases by 20%
x= (1.2)(.8)lw
(base*height) / 2
$3 -500 in the 9% and $2 -500 in the 7%.
5

7. A number is divisible by 6 if...
Its divisible by 2 and by 3.
90
3
Diameter(Pi)

8. 5/8 in percent?
62.5%
The empty set - denoted by a circle with a diagonal through it.
When the function is not defined for all real numbers -; only a subset of the real numbers.
5

9. What is the 'Range' of a function?
9 : 25
87.5%
12.5%
The set of output values for a function.

10. 20<all primes<30
23 - 29
The set of elements found in both A and B.
4.25 - 6 - 22
Undefined - because we can'T divide by 0.

11. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Part = Percent X Whole
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
72

12. What is the surface area of a cylinder with radius 5 and height 8?
Two angles whose sum is 180.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
130pi
Area of the base X height = (pi)hr^2

13. 60 < all primes <70
61 - 67
x= (1.2)(.8)lw
Yes. [i.e. f(x) = x^2 - 1
20.5

14. What is the 'Range' of a series of numbers?
31 - 37
The greatest value minus the smallest.
75:11
5 OR -5

15. (a^-1)/a^5
(a + b)^2
1/a^6
18
Undefined

16. (12sqrt15) / (2sqrt5) =
A 30-60-90 triangle.
Sqrt 12
2^9 / 2 = 256
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

17. If the two sides of a triangle are unequal then the longer side...
Lies opposite the greater angle
90pi
1.0843 X 10^11
23 - 29

18. 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
The empty set - denoted by a circle with a diagonal through it.
500
90 degrees

19. How to find the diagonal of a rectangular solid?
23 - 29
The two xes after factoring.
N! / (n-k)!
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

20. 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?
A reflection about the origin.
No - the input value has exactly one output.
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
...multiply by 100.

21. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
1
2^9 / 2 = 256
y = (x + 5)/2
Move the decimal point to the right x places

22. What are the smallest three prime numbers greater than 65?
The sum of digits is divisible by 9.
The set of elements which can be found in either A or B.
67 - 71 - 73
1 & 37/132

23. x^(-y)=
A 30-60-90 triangle.
A grouping of the members within a set based on a shared characteristic.
1/(x^y)
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

24. Factor x^2 - xy + x.
C = (pi)d
x(x - y + 1)
The overlapping sections.
(p + q)/5

25. 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?
4a^2(b)
75:11
The objects within a set.
F(x-c)

26. Length of an arc of a circle?
Angle/360 x 2(pi)r
The set of elements which can be found in either A or B.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
87.5%

27. (-1)^3 =
23 - 29
413.03 / 10^4 (move the decimal point 4 places to the left)
1
31 - 37

28. What is a parabola?
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)
Ax^2 + bx + c where a -b and c are constants and a /=0
A chord is a line segment joining two points on a circle.
No - only like radicals can be added.

29. What are the roots of the quadrinomial x^2 + 2x + 1?
All numbers multiples of 1.
Infinite.
The sum of digits is divisible by 9.
The two xes after factoring.

30. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
Cd
20.5
23 - 29
2 & 3/7

31. 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?
(base*height) / 2
...multiply by 100.
3
500

32. Which is greater? 200x^295 or 10x^294?
(p + q)/5
Relationship cannot be determined (what if x is negative?)
.0004809 X 10^11
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

33. The ratio of the areas of two similar polygons is ...
The union of A and B.
12sqrt2
... the square of the ratios of the corresponding sides.
C = 2(pi)r

34. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
The objects within a set.
III
5 OR -5

35. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
3sqrt4
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)

36. What is a finite set?
A set with a number of elements which can be counted.
...multiply by 100.
48
90

37. 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?
Area of the base X height = (pi)hr^2
$3 -500 in the 9% and $2 -500 in the 7%.
C = 2(pi)r
The empty set - denoted by a circle with a diagonal through it.

38. 7/8 in percent?
87.5%
An expression with just one term (-6x - 2a^2)
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
(a - b)(a + b)

39. Simplify the expression [(b^2 - c^2) / (b - c)]
x^(6-3) = x^3
(b + c)
72
A set with a number of elements which can be counted.

40. 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.
52
$11 -448
(a + b)^2

41. Can the output value of a function have more than one input value?
Yes. [i.e. f(x) = x^2 - 1
70
Relationship cannot be determined (what if x is negative?)
0

42. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
4725
130pi

43. Define a 'Term' -
The curve opens upward and the vertex is the minimal point on the graph.
1.0843 X 10^11
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)
The overlapping sections.

44. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
F(x) + c
90 degrees
Even

45. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Yes - like radicals can be added/subtracted.
27^(-4)
A 30-60-90 triangle.

46. The objects in a set are called two names:
Two angles whose sum is 90.
Area of the base X height = (pi)hr^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...
Members or elements

47. Circumference of a circle?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
5 OR -5
Diameter(Pi)
A circle centered at -2 - -2 with radius 3.

48. 6w^2 - w - 15 = 0
All numbers multiples of 1.
3/2 - 5/3
Two angles whose sum is 90.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

49. Reduce: 4.8 : 0.8 : 1.6
x^(4+7) = x^11
6 : 1 : 2
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
When the function is not defined for all real numbers -; only a subset of the real numbers.

50. The perimeter of a square is 48 inches. The length of its diagonal is:
41 - 43 - 47
Two equal sides and two equal angles.
Infinite.
12sqrt2