Test your basic knowledge |

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. When the 'a' in a parabola is positive....
13
1
The curve opens upward and the vertex is the minimal point on the graph.
Infinite.

2. Number of degrees in a triangle
4096
18
An infinite set.
180

3. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
23 - 29
87.5%
A 30-60-90 triangle.

4. 7/8 in percent?
...multiply by 100.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
87.5%
180 degrees

5. Describe the relationship between the graphs of x^2 and (1/2)x^2
x= (1.2)(.8)lw
62.5%
The second graph is less steep.
...multiply by 100.

6. Write 10 -843 X 10^7 in scientific notation
72
1.0843 X 10^11
A = pi(r^2)
The longest arc between points A and B on a circle'S diameter.

7. 20<all primes<30
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Yes. [i.e. f(x) = x^2 - 1
23 - 29
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)

8. What is the empty set?
A chord is a line segment joining two points on a circle.
1/a^6
A set with no members - denoted by a circle with a diagonal through it.
The shortest arc between points A and B on a circle'S diameter.

9. Legs 6 - 8. Hypotenuse?
10! / (10-3)! = 720
10
Sector area = (n/360) X (pi)r^2
.0004809 X 10^11

10. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
(b + c)
No - only like radicals can be added.
4.25 - 6 - 22

11. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Diameter(Pi)
The third side is greater than the difference and less than the sum.
The set of elements which can be found in either A or B.
2^9 / 2 = 256

12. 10^6 has how many zeroes?
An angle which is supplementary to an interior angle.
The shortest arc between points A and B on a circle'S diameter.
Even
6

13. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
$3 -500 in the 9% and $2 -500 in the 7%.
75:11
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
x^(6-3) = x^3

14. (6sqrt3) x (2sqrt5) =
2 & 3/7
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Its divisible by 2 and by 3.
Yes - like radicals can be added/subtracted.

15. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
A set with a number of elements which can be counted.
Part = Percent X Whole
3
The union of A and B.

16. What is the side length of an equilateral triangle with altitude 6?
The empty set - denoted by a circle with a diagonal through it.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
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...
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

17. Evaluate 3& 2/7 / 1/3
3
9 & 6/7
The overlapping sections.
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

18. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
180
13pi / 2
52
Yes. [i.e. f(x) = x^2 - 1

19. 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?
9 : 25
(a - b)(a + b)
An arc is a portion of a circumference of a circle.
N! / (n-k)!

20. Formula to find a circle'S circumference from its radius?
C = 2(pi)r
True
70
$3 -500 in the 9% and $2 -500 in the 7%.

21. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
Diameter(Pi)
(base*height) / 2
8
2 & 3/7

22. To convert a percent to a fraction....
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)
4096
Divide by 100.
N! / (k!)(n-k)!

23. 25^(1/2) or sqrt. 25 =
5 OR -5
75:11
F(x) + c
4a^2(b)

24. 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)
4.25 - 6 - 22
y = 2x^2 - 3
N! / (k!)(n-k)!
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

25. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
2.592 kg
y = 2x^2 - 3
3sqrt4

26. Evaluate 4/11 + 11/12
1 & 37/132
12! / 5!7! = 792
The sum of its digits is divisible by 3.
(b + c)

27. P and r are factors of 100. What is greater - pr or 100?
4a^2(b)
90 degrees
Indeterminable.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

28. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
The set of input values for a function.
$11 -448
From northeast - counterclockwise. I - II - III - IV
72

29. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
5 OR -5
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
7 / 1000
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

30. If an inequality is multiplied or divided by a negative number....
x(x - y + 1)
The direction of the inequality is reversed.
37.5%
4.25 - 6 - 22

31. 6w^2 - w - 15 = 0
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
16.6666%
1 & 37/132
3/2 - 5/3

32. 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))?
3sqrt4
20.5
The third side is greater than the difference and less than the sum.
Undefined

33. 40 < all primes<50
13
12sqrt2
F(x) - c
41 - 43 - 47

34. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
Its last two digits are divisible by 4.
A reflection about the origin.
9 & 6/7

35. 3/8 in percent?
III
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The second graph is less steep.
37.5%

36. What are the integers?
All numbers multiples of 1.
8
441000 = 1 10 10 10 21 * 21
$3 -500 in the 9% and $2 -500 in the 7%.

37. Circumference of a circle?
288 (8 9 4)
Diameter(Pi)
A 30-60-90 triangle.
When the function is not defined for all real numbers -; only a subset of the real numbers.

38. Can you subtract 3sqrt4 from sqrt4?
2 & 3/7
The set of elements found in both A and B.
7 / 1000
Yes - like radicals can be added/subtracted.

39. What is the name for 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)
1 & 37/132
A subset.
10! / (10-3)! = 720

40. 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
18
No - the input value has exactly one output.
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...

41. What does scientific notation mean?
500
4:5
3
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

42. x^4 + x^7 =
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)
x^(4+7) = x^11
6
Diameter(Pi)

43. Is 0 even or odd?
Even
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Its divisible by 2 and by 3.
83.333%

44. Which quandrant is the lower right hand?
1/a^6
IV
6
Area of the base X height = (pi)hr^2

45. To multiply a number by 10^x
A circle centered on the origin with radius 8.
6
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
Move the decimal point to the right x places

46. (-1)^3 =
From northeast - counterclockwise. I - II - III - IV
10! / (10-3)! = 720
1
No - only like radicals can be added.

47. Can the output value of a function have more than one input value?
20.5
1
A grouping of the members within a set based on a shared characteristic.
Yes. [i.e. f(x) = x^2 - 1

48. Formula for the area of a sector of a circle?
The shortest arc between points A and B on a circle'S diameter.
III
(b + c)
Sector area = (n/360) X (pi)r^2

49. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
The empty set - denoted by a circle with a diagonal through it.
5 OR -5
A circle centered on the origin with radius 8.

50. (a^-1)/a^5
75:11
When the function is not defined for all real numbers -; only a subset of the real numbers.
A 30-60-90 triangle.
1/a^6