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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.
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. Number of degrees in a triangle
An expression with just one term (-6x - 2a^2)
20.5
180
The overlapping sections.

2. a^2 - b^2 =
(a - b)(a + b)
Its last two digits are divisible by 4.
2
67 - 71 - 73

3. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
9 & 6/7
1
A reflection about the origin.
Relationship cannot be determined (what if x is negative?)

4. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Divide by 100.
The set of elements found in both A and B.
(a - b)^2

5. a^2 - b^2
Angle/360 x 2(pi)r
Two angles whose sum is 90.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
(a - b)(a + b)

6. Legs: 3 - 4. Hypotenuse?
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.
5
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1

7. 5x^2 - 35x -55 = 0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
70
IV
No - only like radicals can be added.

8. When the 'a' in the parabola is negative...
3
(b + c)
1
The curve opens downward and the vertex is the maximum point on the graph.

9. (-1)^3 =
A central angle is an angle formed by 2 radii.
1
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The curve opens upward and the vertex is the minimal point on the graph.

10. A number is divisible by 3 if ...
The sum of its digits is divisible by 3.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
The interesection of A and B.
Undefined - because we can'T divide by 0.

11. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
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
4725
0
A reflection about the axis.

12. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
87.5%
When the function is not defined for all real numbers -; only a subset of the real numbers.
Relationship cannot be determined (what if x is negative?)

13. Can you simplify sqrt72?
Move the decimal point to the right x places
A 30-60-90 triangle.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
N! / (n-k)!

14. Which is greater? 27^(-4) or 9^(-8)
Even
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)
27^(-4)
F(x) + c

15. Define a 'Term' -
441000 = 1 10 10 10 21 * 21
(amount of increase/original price) x 100%
The set of elements found in both A and 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)

16. The slope of a line perpendicular to (a/b)?
1:sqrt3:2
10
Its negative reciprocal. (-b/a)
(a - b)^2

17. What is the graph of f(x) shifted right c units or spaces?
F(x-c)
1.0843 X 10^11
1/2 times 7/3
(a - b)(a + b)

18. In a regular polygon with n sides - the formula for the sum of interior angles
Diameter(Pi)
Two angles whose sum is 90.
A circle centered on the origin with radius 8.
(n-2) x 180

19. 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
75:11
10! / 3!(10-3)! = 120
(a + b)^2

20. If an inequality is multiplied or divided by a negative number....
The direction of the inequality is reversed.
F(x) - c
1
(a - b)(a + b)

21. 40 < all primes<50
True
A reflection about the origin.
41 - 43 - 47
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...

22. What are the rational numbers?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Part = Percent X Whole
180 degrees
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

23. 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?
An isosceles right triangle.
500
No - only like radicals can be added.
The set of elements found in both A and B.

24. x^4 + x^7 =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
x^(4+7) = x^11
N! / (k!)(n-k)!
y = (x + 5)/2

25. 3/8 in percent?
37.5%
441000 = 1 10 10 10 21 * 21
(a - b)(a + b)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

26. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
(a - b)(a + b)
The sum of digits is divisible by 9.
A grouping of the members within a set based on a shared characteristic.
4:5

27. What is a set with no members called?
48
... the square of the ratios of the corresponding sides.
The empty set - denoted by a circle with a diagonal through it.
67 - 71 - 73

28. a^2 - 2ab + b^2
Ax^2 + bx + c where a -b and c are constants and a /=0
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
(a - b)^2
4:5

29. 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?
Its divisible by 2 and by 3.
2^9 / 2 = 256
(a - b)(a + b)
N! / (k!)(n-k)!

30. What are the smallest three prime numbers greater than 65?
The shortest arc between points A and B on a circle'S diameter.
When the function is not defined for all real numbers -; only a subset of the real numbers.
1/a^6
67 - 71 - 73

31. What does the graph x^2 + y^2 = 64 look like?
A circle centered on the origin with radius 8.
Area of the base X height = (pi)hr^2
The set of output values for a function.
71 - 73 - 79

32. The objects in a set are called two names:
Members or elements
53 - 59
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
180 degrees

33. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
2(pi)r^2 + 2(pi)rh
$3 -500 in the 9% and $2 -500 in the 7%.
90pi
13pi / 2

34. 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 second graph is less steep.
A circle centered at -2 - -2 with radius 3.
The steeper the slope.

35. Legs 5 - 12. Hypotenuse?
90pi
4:5
The second graph is less steep.
13

36. What number between 70 & 75 - inclusive - has the greatest number of factors?
75:11
72
Diameter(Pi)
y = 2x^2 - 3

37. Which is greater? 64^5 or 16^8
9 & 6/7
27^(-4)
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)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

38. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
Cd
12! / 5!7! = 792
y = (x + 5)/2

39. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
1
8
2sqrt6
The union of A and B.

40. To convert a decimal to a percent...
...multiply by 100.
Cd
Two angles whose sum is 180.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

41. What is the 'Solution' for a set of inequalities.
F(x) - c
The overlapping sections.
13
x^(4+7) = x^11

42. x^2 = 9. What is the value of x?
2 & 3/7
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)
Sqrt 12
3 - -3

43. What are the irrational numbers?

44. 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?
Its divisible by 2 and by 3.
... the square of the ratios of the corresponding sides.
87.5%
$3 -500 in the 9% and $2 -500 in the 7%.

45. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
3 - -3
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
0
$11 -448

46. What is the graph of f(x) shifted downward c units or spaces?
180 degrees
F(x) - c
18
1 & 37/132

47. What is the ratio of the sides of a 30-60-90 triangle?
A = I (1 + rt)
A reflection about the origin.
1:sqrt3:2
90

48. Legs 6 - 8. Hypotenuse?
Cd
10
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The union of A and B.

49. When does a function automatically have a restricted domain (2)?
1
Angle/360 x 2(pi)r
y = (x + 5)/2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

50. 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.
1:1:sqrt2
When the function is not defined for all real numbers -; only a subset of the real numbers.
The curve opens upward and the vertex is the minimal point on the graph.

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GRE Math: Common Errors

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