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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 maximum value for the function g(x) = (-2x^2) -1?
1/2 times 7/3
12sqrt2
1
Two angles whose sum is 180.

2. What is the side length of an equilateral triangle with altitude 6?
71 - 73 - 79
4a^2(b)
18
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...

3. What is the absolute value function?
The sum of digits is divisible by 9.
G(x) = {x}
27^(-4)
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

4. What is the name for a grouping of the members within a set based on a shared characteristic?
Undefined - because we can'T divide by 0.
72
Factors are few - multiples are many.
A subset.

5. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
.0004809 X 10^11
10
2
2(pi)r^2 + 2(pi)rh

6. 0^0
16.6666%
The sum of its digits is divisible by 3.
75:11
Undefined

7. What are the roots of the quadrinomial x^2 + 2x + 1?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Divide by 100.
$3 -500 in the 9% and $2 -500 in the 7%.
The two xes after factoring.

8. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
(a - b)^2
2^9 / 2 = 256
18
Factors are few - multiples are many.

9. What is the surface area of a cylinder with radius 5 and height 8?
130pi
16.6666%
Its last two digits are divisible by 4.
41 - 43 - 47

10. 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)
71 - 73 - 79
Diameter(Pi)
F(x-c)

11. Number of degrees in a triangle
From northeast - counterclockwise. I - II - III - IV
180
A = pi(r^2)
83.333%

12. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
9 & 6/7
10! / (10-3)! = 720
Divide by 100.
2(pi)r^2 + 2(pi)rh

13. When does a function automatically have a restricted domain (2)?
52
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Sector area = (n/360) X (pi)r^2
413.03 / 10^4 (move the decimal point 4 places to the left)

14. Area of a triangle?
When the function is not defined for all real numbers -; only a subset of the real numbers.
(base*height) / 2
Relationship cannot be determined (what if x is negative?)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

15. Can the output value of a function have more than one input value?
2.592 kg
Yes. [i.e. f(x) = x^2 - 1
180 degrees
2sqrt6

16. Formula for the area of a circle?
11 - 13 - 17 - 19
20.5
A = pi(r^2)
Lies opposite the greater angle

17. Simplify 9^(1/2) X 4^3 X 2^(-6)?
An infinite set.
441000 = 1 10 10 10 21 * 21
3
13pi / 2

18. Circumference of a circle?
Diameter(Pi)
No - only like radicals can be added.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
(a - b)(a + b)

19. What is a parabola?
2sqrt6
Part = Percent X Whole
Ax^2 + bx + c where a -b and c are constants and a /=0
1

20. A number is divisible by 4 is...
Its last two digits are divisible by 4.
2.592 kg
12sqrt2
87.5%

21. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
A chord is a line segment joining two points on a circle.
12sqrt2
An arc is a portion of a circumference of a circle.

22. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
Triangles with same measure and same side lengths.
4.25 - 6 - 22
20.5
7 / 1000

23. a^2 - b^2 =
(a - b)(a + b)
1
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
III

24. Which quadrant is the upper right hand?
1
True
I
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

25. 1/8 in percent?
18
Its last two digits are divisible by 4.
All numbers multiples of 1.
12.5%

26. The larger the absolute value of the slope...
The steeper the slope.
413.03 / 10^4 (move the decimal point 4 places to the left)
The curve opens downward and the vertex is the maximum point on the graph.
Cd

27. (-1)^3 =
Area of the base X height = (pi)hr^2
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...
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)

28. What is the percent formula?
Part = Percent X Whole
An infinite set.
Triangles with same measure and same side lengths.
Its divisible by 2 and by 3.

29. What is the 'Restricted domain of a function'?
55%
1.7
Sector area = (n/360) X (pi)r^2
When the function is not defined for all real numbers -; only a subset of the real numbers.

30. (6sqrt3) x (2sqrt5) =
11 - 13 - 17 - 19
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
True
75:11

31. a^0 =
7 / 1000
6
1
.0004809 X 10^11

32. What is the ratio of the sides of an isosceles right triangle?
$3 -500 in the 9% and $2 -500 in the 7%.
F(x + c)
1:1:sqrt2
4096

33. a^2 + 2ab + b^2
Triangles with same measure and same side lengths.
(a + b)^2
The sum of digits is divisible by 9.
90 degrees

34. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
1:1:sqrt2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
From northeast - counterclockwise. I - II - III - IV
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

35. 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?
Cd
500
An expression with just one term (-6x - 2a^2)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

36. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
A grouping of the members within a set based on a shared characteristic.
10
0

37. 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?
A grouping of the members within a set based on a shared characteristic.
... the square of the ratios of the corresponding sides.
41 - 43 - 47
N! / (n-k)!

38. What is a chord of a circle?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A chord is a line segment joining two points on a circle.
The greatest value minus the smallest.
An expression with just one term (-6x - 2a^2)

39. x^(-y)=
x^(6-3) = x^3
A circle centered on the origin with radius 8.
72
1/(x^y)

40. 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
An arc is a portion of a circumference of a circle.
1.0843 X 10^11
Ax^2 + bx + c where a -b and c are constants and a /=0

41. How to determine percent decrease?
3sqrt4
(amount of decrease/original price) x 100%
An angle which is supplementary to an interior angle.
I

42. What is a piecewise equation?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
An expression with just one term (-6x - 2a^2)
48
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)

43. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
1/a^6
The set of input values for a function.
90
28. n = 8 - k = 2. n! / k!(n-k)!

44. Legs 6 - 8. Hypotenuse?
x(x - y + 1)
A set with no members - denoted by a circle with a diagonal through it.
10
7 / 1000

45. 2sqrt4 + sqrt4 =
8
Move the decimal point to the right x places
2^9 / 2 = 256
3sqrt4

46. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
The curve opens upward and the vertex is the minimal point on the graph.
F(x) - c
A reflection about the axis.
IV

47. Evaluate 4/11 + 11/12
1 & 37/132
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
4a^2(b)
1

48. What number between 70 & 75 - inclusive - has the greatest number of factors?
Divide by 100.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
3
72

49. 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?
Relationship cannot be determined (what if x is negative?)
75:11
Triangles with same measure and same side lengths.
10! / (10-3)! = 720

50. 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.
90 degrees
Diameter(Pi)
The third side is greater than the difference and less than the sum.
53 - 59