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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 are complementary angles?
Two angles whose sum is 90.
Cd
$3 -500 in the 9% and $2 -500 in the 7%.
27^(-4)
2. 413.03 x 10^(-4) =
An isosceles right triangle.
62.5%
413.03 / 10^4 (move the decimal point 4 places to the left)
2(pi)r^2 + 2(pi)rh
3. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
An infinite set.
13
y = (x + 5)/2
70
4. Simplify the expression [(b^2 - c^2) / (b - c)]
72
(b + c)
N! / (n-k)!
Two angles whose sum is 90.
5. What is the name of set with a number of elements which cannot be counted?
1.0843 X 10^11
An infinite set.
61 - 67
1 & 37/132
6. 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?
Two angles whose sum is 180.
N! / (n-k)!
(amount of increase/original price) x 100%
180
7. What is the empty set?
180
A set with no members - denoted by a circle with a diagonal through it.
A 30-60-90 triangle.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
8. Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
Ax^2 + bx + c where a -b and c are constants and a /=0
The third side is greater than the difference and less than the sum.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
9. What is the sum of the angles of a triangle?
180 degrees
No - only like radicals can be added.
The overlapping sections.
The sum of digits is divisible by 9.
10. When the 'a' in a parabola is positive....
The curve opens upward and the vertex is the minimal point on the graph.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
No - the input value has exactly one output.
The direction of the inequality is reversed.
11. What is the 'Solution' for a set of inequalities.
The overlapping sections.
F(x + c)
Cd
Yes. [i.e. f(x) = x^2 - 1
12. (12sqrt15) / (2sqrt5) =
500
11 - 13 - 17 - 19
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
An arc is a portion of a circumference of a circle.
13. Simplify the expression (p^2 - q^2)/ -5(q - p)
1/(x^y)
(p + q)/5
12sqrt2
5
14. 60 < all primes <70
x^(4+7) = x^11
61 - 67
(amount of increase/original price) x 100%
70
15. Formula for the area of a circle?
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)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A = pi(r^2)
(a + b)^2
16. 10^6 has how many zeroes?
Indeterminable.
An infinite set.
A tangent is a line that only touches one point on the circumference of a circle.
6
17. To convert a percent to a fraction....
Divide by 100.
12sqrt2
The sum of digits is divisible by 9.
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)
18. 10<all primes<20
11 - 13 - 17 - 19
N! / (k!)(n-k)!
1/2 times 7/3
130pi
19. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
The direction of the inequality is reversed.
180
28. n = 8 - k = 2. n! / k!(n-k)!
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. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
The third side is greater than the difference and less than the sum.
An arc is a portion of a circumference of a circle.
x(x - y + 1)
21. What are the real numbers?
The interesection of A and B.
70
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)
48
22. What is the surface area of a cylinder with radius 5 and height 8?
130pi
The sum of digits is divisible by 9.
4:5
No - only like radicals can be added.
23. What is an isoceles triangle?
The longest arc between points A and B on a circle'S diameter.
Sqrt 12
Two equal sides and two equal angles.
Angle/360 x 2(pi)r
24. What does the graph x^2 + y^2 = 64 look like?
A circle centered at -2 - -2 with radius 3.
72
41 - 43 - 47
A circle centered on the origin with radius 8.
25. x^2 = 9. What is the value of x?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
75:11
3 - -3
0
26. What is the ratio of the sides of a 30-60-90 triangle?
An angle which is supplementary to an interior angle.
1:sqrt3:2
28. n = 8 - k = 2. n! / k!(n-k)!
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
27. x^4 + x^7 =
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The interesection of A and B.
0
x^(4+7) = x^11
28. How to find the diagonal of a rectangular solid?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
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...
Infinite.
1/2 times 7/3
29. What is the 'union' of A and B?
... the square of the ratios of the corresponding sides.
The set of elements which can be found in either A or B.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Triangles with same measure and same side lengths.
30. 1/6 in percent?
Infinite.
1
4096
16.6666%
31. Formula to find a circle'S circumference from its diameter?
C = (pi)d
N! / (n-k)!
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
x^(4+7) = x^11
32. 4.809 X 10^7 =
28. n = 8 - k = 2. n! / k!(n-k)!
Diameter(Pi)
.0004809 X 10^11
67 - 71 - 73
33. What is a piecewise equation?
1/2 times 7/3
(a + b)^2
Undefined - because we can'T divide by 0.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
34. 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?
1
Triangles with same measure and same side lengths.
2.592 kg
IV
35. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
(a + b)^2
10
x^(4+7) = x^11
36. Surface area for a cylinder?
x^(2(4)) =x^8 = (x^4)^2
Two equal sides and two equal angles.
2(pi)r^2 + 2(pi)rh
Move the decimal point to the right x places
37. What is the graph of f(x) shifted upward c units or spaces?
1
x^(2(4)) =x^8 = (x^4)^2
F(x) + c
Undefined
38. Which is greater? 200x^295 or 10x^294?
(a - b)(a + b)
Relationship cannot be determined (what if x is negative?)
The empty set - denoted by a circle with a diagonal through it.
F(x) - c
39. What is a parabola?
(p + q)/5
16.6666%
Ax^2 + bx + c where a -b and c are constants and a /=0
2.592 kg
40. Legs 6 - 8. Hypotenuse?
Ax^2 + bx + c where a -b and c are constants and a /=0
C = 2(pi)r
10
9 : 25
41. Length of an arc of a circle?
Angle/360 x 2(pi)r
16.6666%
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The overlapping sections.
42. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
A set with a number of elements which can be counted.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A circle centered on the origin with radius 8.
An arc is a portion of a circumference of a circle.
43. Whats the difference between factors and multiples?
True
Factors are few - multiples are many.
Infinite.
1.0843 X 10^11
44. a^2 + 2ab + b^2
9 & 6/7
N! / (n-k)!
(a + b)^2
...multiply by 100.
45. Order of quadrants:
72
From northeast - counterclockwise. I - II - III - IV
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
46. What is a tangent?
1:sqrt3:2
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
(a - b)^2
A tangent is a line that only touches one point on the circumference of a circle.
47. 5x^2 - 35x -55 = 0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
II
The direction of the inequality is reversed.
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)
48. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
1:1:sqrt2
A circle centered at -2 - -2 with radius 3.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Two equal sides and two equal angles.
49. Describe the relationship between 3x^2 and 3(x - 1)^2
31 - 37
6
13
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
50. Which quadrant is the upper right hand?
53 - 59
Undefined - because we can'T divide by 0.
A set with no members - denoted by a circle with a diagonal through it.
I