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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. Can you add sqrt 3 and sqrt 5?
III
3/2 - 5/3
500
No - only like radicals can be added.

2. 4.809 X 10^7 =
The set of elements which can be found in either A or B.
.0004809 X 10^11
...multiply by 100.
4725

3. What is a finite set?
75:11
The set of input values for a function.
2 & 3/7
A set with a number of elements which can be counted.

4. (-1)^2 =
1
Members or elements
Yes - like radicals can be added/subtracted.
(p + q)/5

5. Length of an arc of a circle?
2(pi)r^2 + 2(pi)rh
Angle/360 x 2(pi)r
The longest arc between points A and B on a circle'S diameter.
$11 -448

6. To convert a percent to a fraction....
72
Divide by 100.
x^(6-3) = x^3
1

7. Which quadrant is the upper left hand?
I
The longest arc between points A and B on a circle'S diameter.
II
No - only like radicals can be added.

8. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
2.592 kg
23 - 29
4:5
(a + b)^2

9. Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
75:11
y = (x + 5)/2
5

10. 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?
The objects within a set.
10! / 3!(10-3)! = 120
Arc length = (n/360) x pi(2r) where n is the number of degrees.
5

11. What is the name for a grouping of the members within a set based on a shared characteristic?
4096
1
A subset.
A circle centered at -2 - -2 with radius 3.

12. Reduce: 4.8 : 0.8 : 1.6
Its negative reciprocal. (-b/a)
6
6 : 1 : 2
II

13. (a^-1)/a^5
The set of elements found in both A and B.
1/a^6
A set with a number of elements which can be counted.
Its last two digits are divisible by 4.

14. How many 3-digit positive integers are even and do not contain the digit 4?
A central angle is an angle formed by 2 radii.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
288 (8 9 4)

15. What is the order of operations?
5 OR -5
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
53 - 59
1

16. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
F(x-c)
Area of the base X height = (pi)hr^2
Undefined - because we can'T divide by 0.

17. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
180 degrees
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
4:5

18. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
The objects within a set.
4725
N! / (k!)(n-k)!
28. n = 8 - k = 2. n! / k!(n-k)!

19. 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))?
Two angles whose sum is 180.
130pi
x^(2(4)) =x^8 = (x^4)^2
20.5

20. What is the set of elements which can be found in either A or B?
The third side is greater than the difference and less than the sum.
Two angles whose sum is 180.
Undefined
The union of A and B.

21. What is the formula for computing simple interest?
62.5%
A = I (1 + rt)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
70

22. The perimeter of a square is 48 inches. The length of its diagonal is:
A = I (1 + rt)
Move the decimal point to the right x places
12sqrt2
27^(-4)

23. What is the slope of a horizontal line?
52
0
3sqrt4
The empty set - denoted by a circle with a diagonal through it.

24. 3/8 in percent?
37.5%
2 & 3/7
N! / (n-k)!
The direction of the inequality is reversed.

25. Legs 5 - 12. Hypotenuse?
288 (8 9 4)
1
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
13

26. What is the 'domain' of a function?
The greatest value minus the smallest.
1
Move the decimal point to the right x places
The set of input values for a function.

27. 0^0
Cd
Undefined
(a - b)(a + b)
...multiply by 100.

28. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
3sqrt4
Its last two digits are divisible by 4.
(n-2) x 180
8

29. Max and Min lengths for a side of a triangle?
Infinite.
Lies opposite the greater angle
4:5
The third side is greater than the difference and less than the sum.

30. Convert 0.7% to a fraction.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
7 / 1000
6
Ax^2 + bx + c where a -b and c are constants and a /=0

31. 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?
2sqrt6
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
Relationship cannot be determined (what if x is negative?)
G(x) = {x}

32. Number of degrees in a triangle
The third side is greater than the difference and less than the sum.
55%
2(pi)r^2 + 2(pi)rh
180

33. 7/8 in percent?
(amount of increase/original price) x 100%
6
13pi / 2
87.5%

34. What are complementary angles?
62.5%
The set of output values for a function.
Two angles whose sum is 90.
A grouping of the members within a set based on a shared characteristic.

35. 1/8 in percent?
Pi is the ratio of a circle'S circumference to its diameter.
Angle/360 x 2(pi)r
12.5%
83.333%

36. What are the smallest three prime numbers greater than 65?
Angle/360 x 2(pi)r
I
11 - 13 - 17 - 19
67 - 71 - 73

37. What is the slope of a vertical line?

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38. Which quandrant is the lower right hand?
3
Cd
IV
True

39. What is a central angle?
A central angle is an angle formed by 2 radii.
(a + b)^2
y = 2x^2 - 3
6 : 1 : 2

40. 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?
y = 2x^2 - 3
Factors are few - multiples are many.
The greatest value minus the smallest.
...multiply by 100.

41. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
6
180
3sqrt4

42. What is a subset?
18
A grouping of the members within a set based on a shared characteristic.
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)
2sqrt6

43. Which is greater? 27^(-4) or 9^(-8)
90pi
x(x - y + 1)
27^(-4)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

44. (-1)^3 =
Pi is the ratio of a circle'S circumference to its diameter.
(amount of increase/original price) x 100%
1
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

45. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
1
10
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...

46. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
(base*height) / 2
Divide by 100.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

47. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
16.6666%
The empty set - denoted by a circle with a diagonal through it.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Divide by 100.

48. What is an arc of a circle?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
F(x) - c
1
An arc is a portion of a circumference of a circle.

49. x^6 / x^3
4:5
x^(6-3) = x^3
A central angle is an angle formed by 2 radii.
The steeper the slope.

50. 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
Two angles whose sum is 180.
(a - b)^2
9 & 6/7