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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 does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A reflection about the origin.
N! / (n-k)!
Move the decimal point to the right x places
A circle centered at -2 - -2 with radius 3.
2. 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?
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
75:11
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
3. x^6 / x^3
IV
Diameter(Pi)
x^(6-3) = x^3
72
4. P and r are factors of 100. What is greater - pr or 100?
A grouping of the members within a set based on a shared characteristic.
Indeterminable.
F(x + c)
0
5. To convert a percent to a fraction....
9 : 25
Divide by 100.
Two angles whose sum is 180.
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...
6. To multiply a number by 10^x
90
Two angles whose sum is 90.
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)
Move the decimal point to the right x places
7. Formula to calculate arc length?
From northeast - counterclockwise. I - II - III - IV
Arc length = (n/360) x pi(2r) where n is the number of degrees.
C = 2(pi)r
F(x) + c
8. What are the smallest three prime numbers greater than 65?
A circle centered at -2 - -2 with radius 3.
67 - 71 - 73
A reflection about the axis.
Ax^2 + bx + c where a -b and c are constants and a /=0
9. What is the graph of f(x) shifted left c units or spaces?
III
The second graph is less steep.
F(x + c)
5
10. 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)
(a - b)(a + b)
0
23 - 29
11. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
500
2sqrt6
4:5
4a^2(b)
12. Evaluate 4/11 + 11/12
1 & 37/132
The curve opens downward and the vertex is the maximum point on the graph.
Two equal sides and two equal angles.
A 30-60-90 triangle.
13. How to find the area of a sector?
1.7
N! / (n-k)!
All numbers multiples of 1.
Angle/360 x (pi)r^2
14. a^2 - b^2
True
(a - b)(a + b)
A grouping of the members within a set based on a shared characteristic.
Yes. [i.e. f(x) = x^2 - 1
15. What is the 'Range' of a function?
4a^2(b)
Sqrt 12
The set of output values for a function.
...multiply by 100.
16. Is 0 even or odd?
90
5 OR -5
True
Even
17. How to determine percent increase?
3
(amount of increase/original price) x 100%
IV
3 - -3
18. What is the set of elements which can be found in either A or B?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Undefined - because we can'T divide by 0.
7 / 1000
The union of A and B.
19. What are the irrational numbers?
20. What is the formula for compounded interest?
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.
9 & 6/7
28. n = 8 - k = 2. n! / k!(n-k)!
(amount of increase/original price) x 100%
21. Pi is a ratio of what to what?
22. What is the side length of an equilateral triangle with altitude 6?
Yes - like radicals can be added/subtracted.
3
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
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...
23. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
(n-2) x 180
The curve opens downward and the vertex is the maximum point on the graph.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
24. 5/6 in percent?
83.333%
The set of output values for a function.
4725
13
25. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
(b + c)
6
$3 -500 in the 9% and $2 -500 in the 7%.
70
26. If the two sides of a triangle are unequal then the longer side...
Lies opposite the greater angle
180
y = 2x^2 - 3
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
27. Number of degrees in a triangle
A 30-60-90 triangle.
10! / 3!(10-3)! = 120
180
The point of intersection of the systems.
28. 413.03 x 10^(-4) =
A circle centered on the origin with radius 8.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
413.03 / 10^4 (move the decimal point 4 places to the left)
A circle centered at -2 - -2 with radius 3.
29. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
6 : 1 : 2
Yes - like radicals can be added/subtracted.
30. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
An infinite set.
2^9 / 2 = 256
N! / (n-k)!
31. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
441000 = 1 10 10 10 21 * 21
Cd
The overlapping sections.
87.5%
32. What is a finite set?
52
83.333%
The longest arc between points A and B on a circle'S diameter.
A set with a number of elements which can be counted.
33. 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
2 & 3/7
18
No - only like radicals can be added.
The point of intersection of the systems.
34. What are 'Supplementary angles?'
III
A reflection about the origin.
A circle centered at -2 - -2 with radius 3.
Two angles whose sum is 180.
35. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
No - the input value has exactly one output.
Part = Percent X Whole
2 & 3/7
36. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
The point of intersection of the systems.
4:5
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
.0004809 X 10^11
37. How many multiples does a given number have?
The sum of digits is divisible by 9.
N! / (k!)(n-k)!
1
Infinite.
38. How to determine percent decrease?
(amount of decrease/original price) x 100%
41 - 43 - 47
An expression with just one term (-6x - 2a^2)
Triangles with same measure and same side lengths.
39. Define an 'expression'.
Sector area = (n/360) X (pi)r^2
31 - 37
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
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)
40. 1/8 in percent?
12.5%
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Move the decimal point to the right x places
1 & 37/132
41. What is the set of elements found in both A and B?
1
70
The interesection of A and B.
A chord is a line segment joining two points on a circle.
42. Which quadrant is the upper left hand?
2^9 / 2 = 256
A 30-60-90 triangle.
II
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
43. 0^0
Indeterminable.
Undefined
2
An isosceles right triangle.
44. x^2 = 9. What is the value of x?
x^(6-3) = x^3
Sqrt 12
C = 2(pi)r
3 - -3
45. Write 10 -843 X 10^7 in scientific notation
A tangent is a line that only touches one point on the circumference of a circle.
1.0843 X 10^11
20.5
13
46. Simplify the expression (p^2 - q^2)/ -5(q - p)
G(x) = {x}
C = 2(pi)r
3/2 - 5/3
(p + q)/5
47. a^2 - b^2 =
12! / 5!7! = 792
(a - b)(a + b)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
A grouping of the members within a set based on a shared characteristic.
48. When does a function automatically have a restricted domain (2)?
The point of intersection of the systems.
16.6666%
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
49. Can you simplify sqrt72?
4a^2(b)
0
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
50. Reduce: 4.8 : 0.8 : 1.6
III
10! / (10-3)! = 720
C = (pi)d
6 : 1 : 2