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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 'Range' of a function?
N! / (k!)(n-k)!
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
The set of output values for a function.
II

2. 5x^2 - 35x -55 = 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
1:sqrt3:2

3. a^2 - 2ab + b^2
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
16.6666%
(a - b)^2
28. n = 8 - k = 2. n! / k!(n-k)!

4. 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?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
y = 2x^2 - 3
70
1:1:sqrt2

5. What are complementary angles?
Diameter(Pi)
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
Two angles whose sum is 90.
y = (x + 5)/2

6. Pi is a ratio of what to what?

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7. In a regular polygon with n sides - the formula for the sum of interior angles
2sqrt6
(a + b)^2
(n-2) x 180
31 - 37

8. A number is divisible by 6 if...
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...
y = (x + 5)/2
(a + b)^2
Its divisible by 2 and by 3.

9. 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?
N! / (k!)(n-k)!
10! / (10-3)! = 720
(a + b)^2
(amount of increase/original price) x 100%

10. Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
5 OR -5
(a - b)(a + b)
The point of intersection of the systems.

11. Volume for a cylinder?
3
3
Area of the base X height = (pi)hr^2
1/a^6

12. Is 0 even or odd?
Even
441000 = 1 10 10 10 21 * 21
67 - 71 - 73
G(x) = {x}

13. (-1)^2 =
71 - 73 - 79
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
72
1

14. Which is greater? 200x^295 or 10x^294?
... the square of the ratios of the corresponding sides.
2
Relationship cannot be determined (what if x is negative?)
A chord is a line segment joining two points on a circle.

15. What is the ratio of the sides of an isosceles right triangle?
11 - 13 - 17 - 19
1:1:sqrt2
IV
1

16. 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! / (10-3)! = 720
2 & 3/7
Angle/360 x (pi)r^2
12! / 5!7! = 792

17. Define an 'expression'.
(base*height) / 2
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)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
An infinite set.

18. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
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...
The steeper the slope.
An expression with just one term (-6x - 2a^2)

19. What is the name for a grouping of the members within a set based on a shared characteristic?
1/(x^y)
1
A subset.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

20. What is the graph of f(x) shifted downward c units or spaces?
y = (x + 5)/2
3
F(x) - c
G(x) = {x}

21. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
y = 2x^2 - 3
3
Members or elements
28. n = 8 - k = 2. n! / k!(n-k)!

22. How many multiples does a given number have?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Infinite.
(a - b)^2
2(pi)r^2 + 2(pi)rh

23. What is an exterior angle?
An infinite set.
441000 = 1 10 10 10 21 * 21
3
An angle which is supplementary to an interior angle.

24. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
y = (x + 5)/2
1:sqrt3:2
x^(2(4)) =x^8 = (x^4)^2
From northeast - counterclockwise. I - II - III - IV

25. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
28. n = 8 - k = 2. n! / k!(n-k)!
288 (8 9 4)
The sum of its digits is divisible by 3.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

26. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
4096
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
From northeast - counterclockwise. I - II - III - IV
48

27. What are the real numbers?
x^(2(4)) =x^8 = (x^4)^2
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)
1
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

28. What is the formula for compounded interest?
The greatest value minus the smallest.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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.

29. Which is greater? 64^5 or 16^8
The interesection of A and B.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
The set of output values for a function.
1

30. Describe the relationship between the graphs of x^2 and (1/2)x^2
A = pi(r^2)
The second graph is less steep.
G(x) = {x}
62.5%

31. How to determine percent increase?
6
11 - 13 - 17 - 19
(amount of increase/original price) x 100%
Its negative reciprocal. (-b/a)

32. Which quandrant is the lower right hand?
27^(-4)
IV
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.
12! / 5!7! = 792

33. Formula of rectangle where l increases by 20% and w decreases by 20%
x^(4+7) = x^11
23 - 29
x= (1.2)(.8)lw
A circle centered on the origin with radius 8.

34. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Move the decimal point to the right x places
90
180

35. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
G(x) = {x}
4:5
The set of elements found in both A and B.
Factors are few - multiples are many.

36. 0^0
Undefined
Yes - like radicals can be added/subtracted.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The set of elements which can be found in either A or B.

37. The larger the absolute value of the slope...
3
The steeper the slope.
5 OR -5
The second graph is less steep.

38. 70 < all primes< 80
IV
Move the decimal point to the right x places
71 - 73 - 79
F(x) + c

39. What is the 'domain' of a function?
10
Part = Percent X Whole
The set of input values for a function.
6

40. What is an arc of a circle?
An arc is a portion of a circumference of a circle.
A set with a number of elements which can be counted.
288 (8 9 4)
13

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
A reflection about the origin.
A 30-60-90 triangle.
18
52

42. What is a subset?
x^(2(4)) =x^8 = (x^4)^2
71 - 73 - 79
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A grouping of the members within a set based on a shared characteristic.

43. If a=-1 and b=3 - what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
20.5
The longest arc between points A and B on a circle'S diameter.
x^(6-3) = x^3
The objects within a set.

44. a^0 =
27^(-4)
Its divisible by 2 and by 3.
4096
1

45. Formula to find a circle'S circumference from its diameter?
C = (pi)d
4.25 - 6 - 22
y = (x + 5)/2
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

46. 413.03 x 10^(-4) =
0
A tangent is a line that only touches one point on the circumference of a circle.
1/(x^y)
413.03 / 10^4 (move the decimal point 4 places to the left)

47. Legs 6 - 8. Hypotenuse?
G(x) = {x}
10
F(x + c)
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

48. What is the percent formula?
2sqrt6
Part = Percent X Whole
(a - b)^2
52

49. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
1/(x^y)
5
67 - 71 - 73

50. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
87.5%
II
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)