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Test your basic knowledge |
GRE Math: Common Errors
Start Test
Study First
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 an arc of a circle?
3
An arc is a portion of a circumference of a circle.
4096
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
2. What is the percent formula?
2(pi)r^2 + 2(pi)rh
An arc is a portion of a circumference of a circle.
Part = Percent X Whole
4096
3. To multiply a number by 10^x
83.333%
1
Angle/360 x (pi)r^2
Move the decimal point to the right x places
4. If an inequality is multiplied or divided by a negative number....
0
(a - b)^2
N! / (k!)(n-k)!
The direction of the inequality is reversed.
5. Legs 5 - 12. Hypotenuse?
6
A tangent is a line that only touches one point on the circumference of a circle.
13
(a - b)(a + b)
6. What are the real numbers?
When the function is not defined for all real numbers -; only a subset of the real numbers.
Divide by 100.
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)
55%
7. A number is divisible by 9 if...
Ax^2 + bx + c where a -b and c are constants and a /=0
Sector area = (n/360) X (pi)r^2
The sum of digits is divisible by 9.
Area of the base X height = (pi)hr^2
8. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
Even
70
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
62.5%
9. 1/6 in percent?
16.6666%
No - only like radicals can be added.
10! / (10-3)! = 720
413.03 / 10^4 (move the decimal point 4 places to the left)
10. What is the graph of f(x) shifted left c units or spaces?
(b + c)
3/2 - 5/3
1
F(x + c)
11. a^2 - b^2
An angle which is supplementary to an interior angle.
(a - b)(a + b)
The set of output values for a function.
The set of elements which can be found in either A or B.
12. 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)
Lies opposite the greater angle
4.25 - 6 - 22
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1/a^6
13. Can you simplify sqrt72?
$3 -500 in the 9% and $2 -500 in the 7%.
Two angles whose sum is 90.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
16.6666%
14. (-1)^2 =
0
Pi is the ratio of a circle'S circumference to its diameter.
1
87.5%
15. To convert a decimal to a percent...
...multiply by 100.
83.333%
An isosceles right triangle.
4096
16. The perimeter of a square is 48 inches. The length of its diagonal is:
3
12sqrt2
A set with a number of elements which can be counted.
Area of the base X height = (pi)hr^2
17. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
.0004809 X 10^11
0
70
1
18. Evaluate (4^3)^2
1/a^6
4096
A tangent is a line that only touches one point on the circumference of a circle.
3sqrt4
19. What is the 'Restricted domain of a function'?
The direction of the inequality is reversed.
1
When the function is not defined for all real numbers -; only a subset of the real numbers.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
20. Pi is a ratio of what to what?
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183
21. What is the set of elements found in both A and B?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The sum of its digits is divisible by 3.
70
The interesection of A and B.
22. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
2
Its last two digits are divisible by 4.
4096
23. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
$11 -448
28. n = 8 - k = 2. n! / k!(n-k)!
A grouping of the members within a set based on a shared characteristic.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
24. What is the graph of f(x) shifted downward c units or spaces?
Its negative reciprocal. (-b/a)
4096
F(x) - c
x^(6-3) = x^3
25. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
A circle centered at -2 - -2 with radius 3.
53 - 59
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
26. What is the 'domain' of a function?
Relationship cannot be determined (what if x is negative?)
The set of input values for a function.
1:1:sqrt2
Yes - like radicals can be added/subtracted.
27. What are the smallest three prime numbers greater than 65?
The union of A and B.
1.0843 X 10^11
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
67 - 71 - 73
28. Convert 0.7% to a fraction.
413.03 / 10^4 (move the decimal point 4 places to the left)
No - the input value has exactly one output.
7 / 1000
1
29. 50 < all primes< 60
Two equal sides and two equal angles.
53 - 59
5
31 - 37
30. When the 'a' in the parabola is negative...
The curve opens downward and the vertex is the maximum point on the graph.
31 - 37
Angle/360 x (pi)r^2
180
31. 0^0
1
Angle/360 x 2(pi)r
Undefined
Divide by 100.
32. What percent of 40 is 22?
55%
Even
10! / (10-3)! = 720
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)
33. When does a function automatically have a restricted domain (2)?
y = (x + 5)/2
1:1:sqrt2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The two xes after factoring.
34. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
441000 = 1 10 10 10 21 * 21
3
Yes - like radicals can be added/subtracted.
2sqrt6
35. 1/2 divided by 3/7 is the same as
$3 -500 in the 9% and $2 -500 in the 7%.
.0004809 X 10^11
1/a^6
1/2 times 7/3
36. Can the input value of a function have more than one output value (i.e. x: y - y1)?
No - the input value has exactly one output.
10! / 3!(10-3)! = 120
The longest arc between points A and B on a circle'S diameter.
10
37. Evaluate 3& 2/7 / 1/3
9 & 6/7
Area of the base X height = (pi)hr^2
83.333%
2sqrt6
38. 3/8 in percent?
37.5%
$11 -448
2
Diameter(Pi)
39. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
6
1
71 - 73 - 79
40. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
The set of input values for a function.
Move the decimal point to the right x places
3
41. What is the graph of f(x) shifted upward c units or spaces?
Relationship cannot be determined (what if x is negative?)
x^(6-3) = x^3
4725
F(x) + c
42. What are complementary angles?
7 / 1000
Two angles whose sum is 90.
$11 -448
When the function is not defined for all real numbers -; only a subset of the real numbers.
43. Factor x^2 - xy + x.
x(x - y + 1)
Area of the base X height = (pi)hr^2
F(x) + c
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
44. What is the name of set with a number of elements which cannot be counted?
An infinite set.
11 - 13 - 17 - 19
The greatest value minus the smallest.
The union of A and B.
45. 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?
The longest arc between points A and B on a circle'S diameter.
$3 -500 in the 9% and $2 -500 in the 7%.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Indeterminable.
46. P and r are factors of 100. What is greater - pr or 100?
130pi
Indeterminable.
4:5
An isosceles right triangle.
47. (a^-1)/a^5
(a + b)^2
1/a^6
18
x^(4+7) = x^11
48. 30< all primes<40
31 - 37
1
20.5
70
49. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
The set of elements which can be found in either A or B.
An isosceles right triangle.
90pi
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...
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?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
9 : 25
Triangles with same measure and same side lengths.
1/a^6