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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 absolute value function?
12! / 5!7! = 792
G(x) = {x}
2(pi)r^2 + 2(pi)rh
0

2. Number of degrees in a triangle
180
Diameter(Pi)
A 30-60-90 triangle.
C = (pi)d

3. What is a tangent?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
5 OR -5
A tangent is a line that only touches one point on the circumference of a circle.
90pi

4. a^2 - b^2
(amount of increase/original price) x 100%
288 (8 9 4)
(a - b)(a + b)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

5. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
A subset.
83.333%
$3 -500 in the 9% and $2 -500 in the 7%.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

6. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
3/2 - 5/3
4725
90
1 & 37/132

7. What are the integers?
(a - b)(a + b)
All numbers multiples of 1.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

8. What is the graph of f(x) shifted downward c units or spaces?
13
An arc is a portion of a circumference of a circle.
F(x) - c
x^(6-3) = x^3

9. What is the 'Range' of a series of numbers?
Its last two digits are divisible by 4.
1
The greatest value minus the smallest.
2

10. Legs: 3 - 4. Hypotenuse?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
5
x(x - y + 1)
Angle/360 x (pi)r^2

11. 5/6 in percent?
9 : 25
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.
83.333%

12. How to find the area of a sector?
Angle/360 x (pi)r^2
62.5%
1
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

13. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
3
6
10! / 3!(10-3)! = 120

14. Can the output value of a function have more than one input value?
(a - b)^2
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Yes. [i.e. f(x) = x^2 - 1
70

15. What is the 'Restricted domain of a function'?
1.0843 X 10^11
When the function is not defined for all real numbers -; only a subset of the real numbers.
y = 2x^2 - 3
4.25 - 6 - 22

16. Define a 'monomial'
Its last two digits are divisible by 4.
12! / 5!7! = 792
72
An expression with just one term (-6x - 2a^2)

17. (-1)^3 =
1
The steeper the slope.
Ax^2 + bx + c where a -b and c are constants and 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)

18. (x^2)^4
G(x) = {x}
x^(2(4)) =x^8 = (x^4)^2
Divide by 100.
All numbers multiples of 1.

19. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
3
C = (pi)d
1
... the square of the ratios of the corresponding sides.

20. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
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)
2 & 3/7
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
x^(4+7) = x^11

21. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
x^(4+7) = x^11
4:5
4725
10! / 3!(10-3)! = 120

22. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
0
61 - 67
A circle centered on the origin with radius 8.
28. n = 8 - k = 2. n! / k!(n-k)!

23. Can you subtract 3sqrt4 from sqrt4?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Yes - like radicals can be added/subtracted.
71 - 73 - 79
6

24. How to determine percent increase?
Its divisible by 2 and by 3.
x^(6-3) = x^3
A circle centered on the origin with radius 8.
(amount of increase/original price) x 100%

25. What is a minor arc?

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26. 5/8 in percent?
62.5%
... the square of the ratios of the corresponding sides.
.0004809 X 10^11
y = 2x^2 - 3

27. Reduce: 4.8 : 0.8 : 1.6
The greatest value minus the smallest.
6 : 1 : 2
Sqrt 12
From northeast - counterclockwise. I - II - III - IV

28. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
1/a^6
Its last two digits are divisible by 4.
N! / (n-k)!
True

29. Define an 'expression'.
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.
...multiply by 100.
C = 2(pi)r

30. What is a major arc?

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31. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
Part = Percent X Whole
7 / 1000
55%
8

32. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A circle centered at -2 - -2 with radius 3.
12! / 5!7! = 792
Even
8

33. What is the graph of f(x) shifted upward c units or spaces?
No - only like radicals can be added.
F(x) + c
IV
N! / (k!)(n-k)!

34. 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
Part = Percent X Whole
11 - 13 - 17 - 19
1

35. Evaluate (4^3)^2
55%
4096
1
10

36. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
9 : 25
5 OR -5
$3 -500 in the 9% and $2 -500 in the 7%.
55%

37. Legs 6 - 8. Hypotenuse?
0
The objects within a set.
Relationship cannot be determined (what if x is negative?)
10

38. Simplify the expression [(b^2 - c^2) / (b - c)]
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
53 - 59
(b + c)
A reflection about the axis.

39. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
The two xes after factoring.
55%
2^9 / 2 = 256
71 - 73 - 79

40. What is the ratio of the sides of a 30-60-90 triangle?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
1:sqrt3:2
28. n = 8 - k = 2. n! / k!(n-k)!
Sqrt 12

41. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
Its negative reciprocal. (-b/a)
x^(6-3) = x^3
0
6

42. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
1
3
2sqrt6
A chord is a line segment joining two points on a circle.

43. The number of degrees in the largest angle of a triangle inscribed in a circle - in which the diameter of the circle is one side of the triangle.
.0004809 X 10^11
0
90 degrees
(amount of decrease/original price) x 100%

44. A number is divisible by 6 if...
(b + c)
Its divisible by 2 and by 3.
10! / 3!(10-3)! = 120
Its last two digits are divisible by 4.

45. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
The empty set - denoted by a circle with a diagonal through it.
0
The third side is greater than the difference and less than the sum.

46. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
Two equal sides and two equal angles.
1.7
A circle centered on the origin with radius 8.
y = 2x^2 - 3

47. Write 10 -843 X 10^7 in scientific notation
53 - 59
III
1.0843 X 10^11
2sqrt6

48. What is the name of set with a number of elements which cannot be counted?
10! / 3!(10-3)! = 120
Area of the base X height = (pi)hr^2
An infinite set.
Sector area = (n/360) X (pi)r^2

49. x^2 = 9. What is the value of x?
23 - 29
The objects within a set.
3 - -3
130pi

50. Circumference of a circle?
Yes. [i.e. f(x) = x^2 - 1
Infinite.
288 (8 9 4)
Diameter(Pi)