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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. 1/2 divided by 3/7 is the same as
0
(amount of decrease/original price) x 100%
1/(x^y)
1/2 times 7/3
2. How to determine percent decrease?
1
The set of output values for a function.
1/(x^y)
(amount of decrease/original price) x 100%
3. Pi is a ratio of what to what?
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183
4. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
2(pi)r^2 + 2(pi)rh
6 : 1 : 2
C = (pi)d
4:5
5. What is the slope of a horizontal line?
0
413.03 / 10^4 (move the decimal point 4 places to the left)
The shortest arc between points A and B on a circle'S diameter.
The two xes after factoring.
6. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
Diameter(Pi)
2 & 3/7
Factors are few - multiples are many.
1/2 times 7/3
7. 1/6 in percent?
A tangent is a line that only touches one point on the circumference of a circle.
The union of A and B.
16.6666%
70
8. Simplify the expression (p^2 - q^2)/ -5(q - p)
Two angles whose sum is 90.
(p + q)/5
1/2 times 7/3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
9. 4.809 X 10^7 =
2 & 3/7
.0004809 X 10^11
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
1.0843 X 10^11
10. How many 3-digit positive integers are even and do not contain the digit 4?
180
288 (8 9 4)
(a - b)^2
1:1:sqrt2
11. Define a 'Term' -
1/a^6
A set with a number of elements which can be counted.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
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. 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))?
20.5
70
0
F(x + c)
13. 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).
Divide by 100.
9 & 6/7
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
14. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
x= (1.2)(.8)lw
4.25 - 6 - 22
90
15. a^2 - 2ab + b^2
2
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)
2^9 / 2 = 256
(a - b)^2
16. 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?
52
Ax^2 + bx + c where a -b and c are constants and a /=0
N! / (k!)(n-k)!
Its divisible by 2 and by 3.
17. 40 < all primes<50
41 - 43 - 47
Two angles whose sum is 180.
6 : 1 : 2
27^(-4)
18. What is the ratio of the sides of an isosceles right triangle?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
1:1:sqrt2
Area of the base X height = (pi)hr^2
19. To convert a percent to a fraction....
Part = Percent X Whole
130pi
Divide by 100.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
20. What is the empty set?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The curve opens upward and the vertex is the minimal point on the graph.
F(x + c)
A set with no members - denoted by a circle with a diagonal through it.
21. Circumference of a circle?
Diameter(Pi)
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Lies opposite the greater angle
A subset.
22. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
x^(2(4)) =x^8 = (x^4)^2
A circle centered on the origin with radius 8.
(amount of decrease/original price) x 100%
23. Which quandrant is the lower right hand?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
9 : 25
.0004809 X 10^11
IV
24. What is a parabola?
The steeper the slope.
55%
An expression with just one term (-6x - 2a^2)
Ax^2 + bx + c where a -b and c are constants and a /=0
25. What is the 'Restricted domain of a function'?
(base*height) / 2
Cd
5
When the function is not defined for all real numbers -; only a subset of the real numbers.
26. Factor x^2 - xy + x.
87.5%
90 degrees
x(x - y + 1)
The two xes after factoring.
27. The perimeter of a square is 48 inches. The length of its diagonal is:
The objects within a set.
12sqrt2
Area of the base X height = (pi)hr^2
No - the input value has exactly one output.
28. What is a piecewise equation?
(a + b)^2
Even
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Relationship cannot be determined (what if x is negative?)
29. (6sqrt3) x (2sqrt5) =
27^(-4)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
When the function is not defined for all real numbers -; only a subset of the real numbers.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
30. What is the percent formula?
Part = Percent X Whole
(n-2) x 180
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Undefined
31. 5/8 in percent?
55%
62.5%
III
1.7
32. 5/6 in percent?
83.333%
x^(6-3) = x^3
Angle/360 x (pi)r^2
71 - 73 - 79
33. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
6
Two equal sides and two equal angles.
Its negative reciprocal. (-b/a)
2
34. What is the set of elements found in both A and B?
The interesection of A and B.
0
The shortest arc between points A and B on a circle'S diameter.
Factors are few - multiples are many.
35. 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?
All numbers multiples of 1.
An isosceles right triangle.
N! / (n-k)!
11 - 13 - 17 - 19
36. Legs 5 - 12. Hypotenuse?
13
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)
The union of A and B.
10
37. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
7 / 1000
4096
16.6666%
True
38. What is the graph of f(x) shifted right c units or spaces?
F(x-c)
.0004809 X 10^11
413.03 / 10^4 (move the decimal point 4 places to the left)
Arc length = (n/360) x pi(2r) where n is the number of degrees.
39. Which quadrant is the upper right hand?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
1
The sum of digits is divisible by 9.
I
40. What is the ratio of the sides of a 30-60-90 triangle?
Angle/360 x (pi)r^2
From northeast - counterclockwise. I - II - III - IV
1
1:sqrt3:2
41. (x^2)^4
10! / (10-3)! = 720
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
x^(2(4)) =x^8 = (x^4)^2
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
42. To convert a decimal to a percent...
70
The set of elements which can be found in either A or B.
...multiply by 100.
10! / 3!(10-3)! = 120
43. The larger the absolute value of the slope...
A = I (1 + rt)
The steeper the slope.
5
A = pi(r^2)
44. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
72
8
Diameter(Pi)
F(x) - c
45. 30< all primes<40
23 - 29
The set of elements which can be found in either A or B.
1
31 - 37
46. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
4096
The set of elements which can be found in either A or B.
The overlapping sections.
47. What is a tangent?
A reflection about the origin.
A tangent is a line that only touches one point on the circumference of a circle.
x(x - y + 1)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
48. Convert 0.7% to a fraction.
1
7 / 1000
All numbers multiples of 1.
The set of elements which can be found in either A or B.
49. a^2 - b^2
72
A set with a number of elements which can be counted.
(a - b)(a + b)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
50. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
70
75:11
Its divisible by 2 and by 3.