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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. To convert a percent to a fraction....
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)
(a + b)^2
A chord is a line segment joining two points on a circle.
Divide by 100.
2. The objects in a set are called two names:
An infinite set.
90pi
Members or elements
The union of A and B.
3. What is the measure of an exterior angle of a regular pentagon?
7 / 1000
27^(-4)
Yes. [i.e. f(x) = x^2 - 1
72
4. Max and Min lengths for a side of a triangle?
1/2 times 7/3
The third side is greater than the difference and less than the sum.
.0004809 X 10^11
12.5%
5. Can you add sqrt 3 and sqrt 5?
1
No - only like radicals can be added.
Lies opposite the greater angle
F(x) + c
6. a^2 - b^2
4a^2(b)
2sqrt6
(a - b)(a + b)
The set of output values for a function.
7. Describe the relationship between 3x^2 and 3(x - 1)^2
(n-2) x 180
The union of A and B.
Infinite.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
8. P and r are factors of 100. What is greater - pr or 100?
83.333%
Indeterminable.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
9. 1/6 in percent?
16.6666%
1/(x^y)
Its divisible by 2 and by 3.
2
10. What is the 'union' of A and B?
10
The set of elements which can be found in either A or B.
Yes - like radicals can be added/subtracted.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
11. What is the 'Range' of a series of numbers?
IV
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
III
The greatest value minus the smallest.
12. What is the set of elements which can be found in either A or B?
.0004809 X 10^11
Its negative reciprocal. (-b/a)
11 - 13 - 17 - 19
The union of A and B.
13. 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?
All numbers multiples of 1.
A = pi(r^2)
IV
52
14. 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?
N! / (n-k)!
9 : 25
12! / 5!7! = 792
The set of input values for a function.
15. Formula for the area of a circle?
A = pi(r^2)
7 / 1000
6
The steeper the slope.
16. What is an exterior angle?
An angle which is supplementary to an interior angle.
The set of output values for a function.
The set of input values for a function.
3
17. What is the formula for compounded interest?
... the square of the ratios of the corresponding sides.
A= I (1 + (r/c))^tC - where I is the investment - C is the number of times compounded annually - and t is the number of years.
The overlapping sections.
A set with no members - denoted by a circle with a diagonal through it.
18. x^(-y)=
5 OR -5
F(x-c)
1/(x^y)
Part = Percent X Whole
19. What is a piecewise equation?
4:5
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
3
27^(-4)
20. If the two sides of a triangle are unequal then the longer side...
Lies opposite the greater angle
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)
Its divisible by 2 and by 3.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
21. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Sqrt 12
A circle centered at -2 - -2 with radius 3.
8
22. What is the surface area of a cylinder with radius 5 and height 8?
67 - 71 - 73
130pi
(p + q)/5
1
23. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
55%
3 - -3
(a + b)^2
24. 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.
Undefined
(a + b)^2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
25. Write 10 -843 X 10^7 in scientific notation
1
Yes - like radicals can be added/subtracted.
48
1.0843 X 10^11
26. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
441000 = 1 10 10 10 21 * 21
0
413.03 / 10^4 (move the decimal point 4 places to the left)
62.5%
27. Factor x^2 - xy + x.
x(x - y + 1)
G(x) = {x}
4.25 - 6 - 22
C = 2(pi)r
28. 0^0
Undefined
An expression with just one term (-6x - 2a^2)
75:11
The curve opens downward and the vertex is the maximum point on the graph.
29. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Triangles with same measure and same side lengths.
28. n = 8 - k = 2. n! / k!(n-k)!
G(x) = {x}
1/(x^y)
30. What is the intersection of A and B?
Sqrt 12
The set of elements found in both A and B.
4725
An isosceles right triangle.
31. Circumference of a circle?
The two xes after factoring.
Diameter(Pi)
12! / 5!7! = 792
Triangles with same measure and same side lengths.
32. Simplify (a^2 + b)^2 - (a^2 - b)^2
413.03 / 10^4 (move the decimal point 4 places to the left)
1
4a^2(b)
90 degrees
33. 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 curve opens downward and the vertex is the maximum point on the graph.
$3 -500 in the 9% and $2 -500 in the 7%.
Infinite.
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)
34. How to determine percent increase?
2(pi)r^2 + 2(pi)rh
The point of intersection of the systems.
$3 -500 in the 9% and $2 -500 in the 7%.
(amount of increase/original price) x 100%
35. 60 < all primes <70
Lies opposite the greater angle
61 - 67
18
16.6666%
36. To multiply a number by 10^x
Move the decimal point to the right x places
An arc is a portion of a circumference of a circle.
x^(2(4)) =x^8 = (x^4)^2
2sqrt6
37. Factor a^2 + 2ab + b^2
12.5%
All numbers multiples of 1.
(a + b)^2
1/2 times 7/3
38. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
1 & 37/132
2 & 3/7
4725
1
39. When does a function automatically have a restricted domain (2)?
Triangles with same measure and same side lengths.
180 degrees
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The greatest value minus the smallest.
40. What is the name of set with a number of elements which cannot be counted?
Two equal sides and two equal angles.
72
II
An infinite set.
41. 50 < all primes< 60
53 - 59
7 / 1000
A circle centered at -2 - -2 with radius 3.
x^(2(4)) =x^8 = (x^4)^2
42. Define a 'monomial'
The second graph is less steep.
41 - 43 - 47
An expression with just one term (-6x - 2a^2)
2 & 3/7
43. Pi is a ratio of what to what?
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183
44. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Diameter(Pi)
IV
A grouping of the members within a set based on a shared characteristic.
45. What is the area of a regular hexagon with side 6?
Ax^2 + bx + c where a -b and c are constants and a /=0
Undefined
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
2^9 / 2 = 256
46. Which quadrant is the lower left hand?
(base*height) / 2
C = (pi)d
III
75:11
47. 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?
All numbers multiples of 1.
0
10! / 3!(10-3)! = 120
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
48. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
37.5%
Indeterminable.
An arc is a portion of a circumference of a circle.
8
49. What is the maximum value for the function g(x) = (-2x^2) -1?
A central angle is an angle formed by 2 radii.
48
1
The set of input values for a function.
50. 413.03 x 10^(-4) =
1
87.5%
x(x - y + 1)
413.03 / 10^4 (move the decimal point 4 places to the left)