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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. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
8
10! / (10-3)! = 720
Its last two digits are divisible by 4.
1:1:sqrt2

2. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
F(x) - c
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)
Yes. [i.e. f(x) = x^2 - 1

3. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
True
The empty set - denoted by a circle with a diagonal through it.
62.5%
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

4. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
Yes - like radicals can be added/subtracted.
No - the input value has exactly one output.
31 - 37

5. Simplify 9^(1/2) X 4^3 X 2^(-6)?
53 - 59
A circle centered on the origin with radius 8.
3
C = (pi)d

6. When the 'a' in a parabola is positive....
The overlapping sections.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The curve opens upward and the vertex is the minimal point on the graph.
10

7. What are 'Supplementary angles?'
1/2 times 7/3
61 - 67
3sqrt4
Two angles whose sum is 180.

8. To multiply a number by 10^x
Move the decimal point to the right x places
413.03 / 10^4 (move the decimal point 4 places to the left)
A circle centered on the origin with radius 8.
9 & 6/7

9. Max and Min lengths for a side of a triangle?
2
The third side is greater than the difference and less than the sum.
(b + c)
Move the decimal point to the right x places

10. Evaluate 4/11 + 11/12
5 OR -5
1 & 37/132
28. n = 8 - k = 2. n! / k!(n-k)!
II

11. What is a major arc?

12. How to find the circumference of a circle which circumscribes a square?
20.5
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
.0004809 X 10^11
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

13. What is the set of elements found in both A and B?
The interesection of A and B.
The steeper the slope.
5
(a - b)(a + b)

14. 10<all primes<20
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
11 - 13 - 17 - 19
5
The curve opens upward and the vertex is the minimal point on the graph.

15. What are the rational numbers?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
8
Angle/360 x (pi)r^2
The sum of its digits is divisible by 3.

16. a^2 - b^2 =
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(a - b)(a + b)
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
C = (pi)d

17. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
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)
Its last two digits are divisible by 4.
Divide by 100.
1

18. Can you simplify sqrt72?
500
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
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 + b)^2

19. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
No - only like radicals can be added.
The two xes after factoring.
A set with a number of elements which can be counted.

20. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
10! / 3!(10-3)! = 120
x= (1.2)(.8)lw
Its negative reciprocal. (-b/a)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

21. What is the set of elements which can be found in either A or B?
Even
The union of A and B.
413.03 / 10^4 (move the decimal point 4 places to the left)
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.

22. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
Part = Percent X Whole
Two angles whose sum is 90.
5 OR -5

23. What is the side length of an equilateral triangle with altitude 6?
The set of input values for a function.
II
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
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...

24. Solve the quadratic equation ax^2 + bx + c= 0
x= (1.2)(.8)lw
From northeast - counterclockwise. I - II - III - IV
Two equal sides and two equal angles.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

25. 3/8 in percent?
37.5%
10! / (10-3)! = 720
The point of intersection of the systems.
6 : 1 : 2

26. 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?
75:11
1:sqrt3:2
70
(n-2) x 180

27. The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
An expression with just one term (-6x - 2a^2)
5 OR -5

28. Can you add sqrt 3 and sqrt 5?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
When the function is not defined for all real numbers -; only a subset of the real numbers.
No - only like radicals can be added.
Two angles whose sum is 90.

29. Formula to find a circle'S circumference from its radius?
67 - 71 - 73
(amount of decrease/original price) x 100%
4.25 - 6 - 22
C = 2(pi)r

30. What is an isoceles triangle?
5 OR -5
Divide by 100.
C = 2(pi)r
Two equal sides and two equal angles.

31. a^2 - b^2
N! / (k!)(n-k)!
The two xes after factoring.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(a - b)(a + b)

32. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
Two equal sides and two equal angles.
180
90

33. 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?
A grouping of the members within a set based on a shared characteristic.
48
3 - -3
x(x - y + 1)

34. What is the ratio of the sides of a 30-60-90 triangle?
III
x^(4+7) = x^11
1:sqrt3:2
(base*height) / 2

35. Factor a^2 + 2ab + b^2
1
The sum of digits is divisible by 9.
An arc is a portion of a circumference of a circle.
(a + b)^2

36. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
The sum of its digits is divisible by 3.
3
C = 2(pi)r
N! / (k!)(n-k)!

37. What are the integers?
All numbers multiples of 1.
The empty set - denoted by a circle with a diagonal through it.
x^(6-3) = x^3
The longest arc between points A and B on a circle'S diameter.

38. What is a tangent?
(amount of increase/original price) x 100%
413.03 / 10^4 (move the decimal point 4 places to the left)
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 tangent is a line that only touches one point on the circumference of a circle.

39. 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?
10
10! / (10-3)! = 720
The two xes after factoring.
83.333%

40. 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?
A chord is a line segment joining two points on a circle.
N! / (k!)(n-k)!
6
180 degrees

41. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
1/2 times 7/3
500
18
From northeast - counterclockwise. I - II - III - IV

42. 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?
An arc is a portion of a circumference of a circle.
9 : 25
90 degrees
11 - 13 - 17 - 19

43. x^6 / x^3
Indeterminable.
2(pi)r^2 + 2(pi)rh
Two angles whose sum is 180.
x^(6-3) = x^3

44. What is the percent formula?
(amount of decrease/original price) x 100%
3sqrt4
1/a^6
Part = Percent X Whole

45. 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)
10! / (10-3)! = 720
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
III

46. Is 0 even or odd?
9 : 25
Undefined - because we can'T divide by 0.
The overlapping sections.
Even

47. Whats the difference between factors and multiples?
Factors are few - multiples are many.
Ax^2 + bx + c where a -b and c are constants and a /=0
Two angles whose sum is 90.
The sum of its digits is divisible by 3.

48. Reduce: 4.8 : 0.8 : 1.6
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
2(pi)r^2 + 2(pi)rh
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...
6 : 1 : 2

49. a^2 + 2ab + b^2
Yes. [i.e. f(x) = x^2 - 1
(a + b)^2
1/a^6
No - only like radicals can be added.

50. How to determine percent increase?
70
(amount of increase/original price) x 100%
1
9 : 25