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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. 3/8 in percent?
37.5%
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Triangles with same measure and same side lengths.
72
2. How to determine percent decrease?
1:1:sqrt2
...multiply by 100.
(amount of decrease/original price) x 100%
Divide by 100.
3. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
1:1:sqrt2
F(x) + c
The set of input values for a function.
4. Formula for the area of a sector of a circle?
y = (x + 5)/2
4725
Sector area = (n/360) X (pi)r^2
18
5. 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?
...multiply by 100.
413.03 / 10^4 (move the decimal point 4 places to the left)
75:11
1:1:sqrt2
6. Formula to find a circle'S circumference from its diameter?
C = (pi)d
The steeper the slope.
1
Sector area = (n/360) X (pi)r^2
7. What is the order of operations?
3 - -3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
6 : 1 : 2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
8. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
2sqrt6
An expression with just one term (-6x - 2a^2)
Undefined - because we can'T divide by 0.
70
9. (-1)^2 =
72
4.25 - 6 - 22
1
Diameter(Pi)
10. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
The set of elements found in both A and B.
The longest arc between points A and B on a circle'S diameter.
71 - 73 - 79
11. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
9 & 6/7
6
13pi / 2
12. Pi is a ratio of what to what?
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183
13. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Pi is the ratio of a circle'S circumference to its diameter.
3 - -3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
14. What is a subset?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
A grouping of the members within a set based on a shared characteristic.
An infinite set.
A set with no members - denoted by a circle with a diagonal through it.
15. 25^(1/2) or sqrt. 25 =
1:1:sqrt2
5 OR -5
The set of output values for a function.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
16. What are the roots of the quadrinomial x^2 + 2x + 1?
Divide by 100.
.0004809 X 10^11
12sqrt2
The two xes after factoring.
17. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
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)
The sum of its digits is divisible by 3.
3
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
18. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
The objects within a set.
28. n = 8 - k = 2. n! / k!(n-k)!
The shortest arc between points A and B on a circle'S diameter.
A circle centered at -2 - -2 with radius 3.
19. What is the side length of an equilateral triangle with altitude 6?
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...
(a - b)(a + b)
53 - 59
20. What are complementary angles?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A 30-60-90 triangle.
Two angles whose sum is 90.
A circle centered on the origin with radius 8.
21. 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
12sqrt2
The objects within a set.
(a + b)^2
22. 50 < all primes< 60
The curve opens upward and the vertex is the minimal point on the graph.
53 - 59
6 : 1 : 2
The longest arc between points A and B on a circle'S diameter.
23. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
2(pi)r^2 + 2(pi)rh
(a - b)(a + b)
IV
24. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
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)
Diameter(Pi)
2sqrt6
25. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
1
The interesection of A and B.
10! / 3!(10-3)! = 120
Diameter(Pi)
26. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
N! / (n-k)!
441000 = 1 10 10 10 21 * 21
1
Lies opposite the greater angle
27. Simplify 9^(1/2) X 4^3 X 2^(-6)?
20.5
F(x) + c
3
13pi / 2
28. To convert a decimal to a percent...
The objects within a set.
...multiply by 100.
y = 2x^2 - 3
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
29. 7/8 in percent?
87.5%
53 - 59
31 - 37
41 - 43 - 47
30. What does the graph x^2 + y^2 = 64 look like?
x^(6-3) = x^3
28. n = 8 - k = 2. n! / k!(n-k)!
1
A circle centered on the origin with radius 8.
31. To convert a percent to a fraction....
No - only like radicals can be added.
Undefined - because we can'T divide by 0.
4725
Divide by 100.
32. What is the maximum value for the function g(x) = (-2x^2) -1?
y = (x + 5)/2
1
A chord is a line segment joining two points on a circle.
The second graph is less steep.
33. What is the name of set with a number of elements which cannot be counted?
20.5
Two angles whose sum is 180.
An infinite set.
x^(6-3) = x^3
34. 70 < all primes< 80
F(x) - c
1/2 times 7/3
71 - 73 - 79
The union of A and B.
35. Which quandrant is the lower right hand?
12sqrt2
IV
...multiply by 100.
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...
36. Factor a^2 + 2ab + b^2
(a - b)^2
(a + b)^2
III
2(pi)r^2 + 2(pi)rh
37. Formula to calculate arc length?
(a - b)(a + b)
The third side is greater than the difference and less than the sum.
41 - 43 - 47
Arc length = (n/360) x pi(2r) where n is the number of degrees.
38. 5x^2 - 35x -55 = 0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1
6 : 1 : 2
90pi
39. What is the 'Solution' for a system of linear equations?
A circle centered on the origin with radius 8.
The sum of digits is divisible by 9.
x= (1.2)(.8)lw
The point of intersection of the systems.
40. Factor x^2 - xy + x.
The longest arc between points A and B on a circle'S diameter.
The set of elements which can be found in either A or B.
x(x - y + 1)
1/a^6
41. Order of quadrants:
From northeast - counterclockwise. I - II - III - IV
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
6
42. If an inequality is multiplied or divided by a negative number....
The direction of the inequality is reversed.
48
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
1/(x^y)
43. 1/6 in percent?
62.5%
A set with a number of elements which can be counted.
90 degrees
16.6666%
44. Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
Relationship cannot be determined (what if x is negative?)
(n-2) x 180
1
45. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
55%
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A set with no members - denoted by a circle with a diagonal through it.
A circle centered at -2 - -2 with radius 3.
46. What is the graph of f(x) shifted right c units or spaces?
90pi
72
F(x-c)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
47. Can the input value of a function have more than one output value (i.e. x: y - y1)?
4:5
No - the input value has exactly one output.
A = I (1 + rt)
90pi
48. a^2 - 2ab + b^2
(a - b)^2
13pi / 2
90pi
Its last two digits are divisible by 4.
49. a^2 - b^2 =
(a - b)(a + b)
10! / 3!(10-3)! = 120
The sum of its digits is divisible by 3.
No - only like radicals can be added.
50. What is a finite set?
A set with a number of elements which can be counted.
y = (x + 5)/2
F(x-c)
Undefined