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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. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
x(x - y + 1)
2sqrt6
x= (1.2)(.8)lw
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
2. a^2 + 2ab + b^2
(a + b)^2
500
180 degrees
Its last two digits are divisible by 4.
3. 5/6 in percent?
The curve opens upward and the vertex is the minimal point on the graph.
8
83.333%
The set of elements which can be found in either A or B.
4. x^6 / x^3
Its divisible by 2 and by 3.
x^(6-3) = x^3
An infinite set.
x(x - y + 1)
5. What is a parabola?
A circle centered at -2 - -2 with radius 3.
II
Divide by 100.
Ax^2 + bx + c where a -b and c are constants and a /=0
6. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
The curve opens downward and the vertex is the maximum point on the graph.
The interesection of A and B.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
8
7. 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?
Its last two digits are divisible by 4.
2.592 kg
A chord is a line segment joining two points on a circle.
The steeper the slope.
8. 30< all primes<40
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
31 - 37
A reflection about the origin.
No - only like radicals can be added.
9. What is an isoceles triangle?
6
180
An infinite set.
Two equal sides and two equal angles.
10. What is the measure of an exterior angle of a regular pentagon?
The sum of digits is divisible by 9.
288 (8 9 4)
3
72
11. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
Triangles with same measure and same side lengths.
x^(6-3) = x^3
13pi / 2
An arc is a portion of a circumference of a circle.
12. Define a 'Term' -
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)
An arc is a portion of a circumference of a circle.
1
16.6666%
13. 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?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
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
The union of A and B.
6
14. What are complementary angles?
The overlapping sections.
Two angles whose sum is 90.
A circle centered on the origin with radius 8.
The set of elements which can be found in either A or B.
15. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
The union of A and B.
70
1/2 times 7/3
16. What is the name of set with a number of elements which cannot be counted?
7 / 1000
(b + c)
An infinite set.
III
17. What is the slope of a horizontal line?
C = 2(pi)r
0
(amount of decrease/original price) x 100%
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
18. What is the set of elements which can be found in either A or B?
A set with a number of elements which can be counted.
Triangles with same measure and same side lengths.
Part = Percent X Whole
The union of A and B.
19. What is the 'Range' of a series of numbers?
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
The point of intersection of the systems.
An arc is a portion of a circumference of a circle.
The greatest value minus the smallest.
20. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
The shortest arc between points A and B on a circle'S diameter.
5 OR -5
x^(4+7) = x^11
21. x^(-y)=
A chord is a line segment joining two points on a circle.
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)
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1/(x^y)
22. (-1)^2 =
1
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The longest arc between points A and B on a circle'S diameter.
288 (8 9 4)
23. 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?
16.6666%
N! / (n-k)!
When the function is not defined for all real numbers -; only a subset of the real numbers.
A set with no members - denoted by a circle with a diagonal through it.
24. What is a piecewise 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.
Two angles whose sum is 90.
The objects within a set.
10
25. What is the slope of a vertical line?
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26. What number between 70 & 75 - inclusive - has the greatest number of factors?
(a + b)^2
12! / 5!7! = 792
70
72
27. What are the smallest three prime numbers greater than 65?
F(x) + c
67 - 71 - 73
A set with no members - denoted by a circle with a diagonal through it.
55%
28. Formula to find a circle'S circumference from its diameter?
Yes. [i.e. f(x) = x^2 - 1
90
The empty set - denoted by a circle with a diagonal through it.
C = (pi)d
29. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
16.6666%
A 30-60-90 triangle.
4:5
Two angles whose sum is 90.
30. What is the surface area of a cylinder with radius 5 and height 8?
75:11
130pi
...multiply by 100.
4.25 - 6 - 22
31. a^2 - 2ab + b^2
A reflection about the origin.
1.0843 X 10^11
x^(2(4)) =x^8 = (x^4)^2
(a - b)^2
32. Area of a triangle?
(base*height) / 2
(n-2) x 180
Indeterminable.
The third side is greater than the difference and less than the sum.
33. Which quadrant is the upper right hand?
The steeper the slope.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A set with a number of elements which can be counted.
I
34. a^0 =
2 & 3/7
3
1
The greatest value minus the smallest.
35. What is the intersection of A and B?
67 - 71 - 73
The steeper the slope.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The set of elements found in both A and B.
36. 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
13pi / 2
G(x) = {x}
Angle/360 x (pi)r^2
37. What is an exterior angle?
An angle which is supplementary to an interior angle.
II
x^(2(4)) =x^8 = (x^4)^2
y = (x + 5)/2
38. What is the 'Solution' for a set of inequalities.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Two angles whose sum is 90.
1
The overlapping sections.
39. Formula for the area of a sector of a circle?
(a - b)(a + b)
13pi / 2
Sector area = (n/360) X (pi)r^2
52
40. How to find the area of a sector?
3 - -3
The set of input values for a function.
$3 -500 in the 9% and $2 -500 in the 7%.
Angle/360 x (pi)r^2
41. What is a major arc?
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42. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
A set with a number of elements which can be counted.
C = 2(pi)r
1
The interesection of A and B.
43. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
I
.0004809 X 10^11
44. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
Area of the base X height = (pi)hr^2
Undefined
A set with no members - denoted by a circle with a diagonal through it.
45. Order of quadrants:
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
53 - 59
From northeast - counterclockwise. I - II - III - IV
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)
46. How to determine percent decrease?
Yes. [i.e. f(x) = x^2 - 1
III
Two equal sides and two equal angles.
(amount of decrease/original price) x 100%
47. 1/2 divided by 3/7 is the same as
No - the input value has exactly one output.
1/2 times 7/3
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A tangent is a line that only touches one point on the circumference of a circle.
48. To multiply a number by 10^x
90 degrees
Move the decimal point to the right x places
The set of elements which can be found in either A or B.
87.5%
49. Which is greater? 64^5 or 16^8
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Diameter(Pi)
288 (8 9 4)
x^(4+7) = x^11
50. x^4 + x^7 =
The two xes after factoring.
x^(4+7) = x^11
67 - 71 - 73
The shortest arc between points A and B on a circle'S diameter.