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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. 25^(1/2) or sqrt. 25 =
5 OR -5
A tangent is a line that only touches one point on the circumference of a circle.
(amount of decrease/original price) x 100%
55%
2. Max and Min lengths for a side of a triangle?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Angle/360 x (pi)r^2
The third side is greater than the difference and less than the sum.
The greatest value minus the smallest.
3. 4.809 X 10^7 =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
C = (pi)d
.0004809 X 10^11
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
4. What are the rational numbers?
Two angles whose sum is 90.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
$3 -500 in the 9% and $2 -500 in the 7%.
The steeper the slope.
5. To multiply a number by 10^x
Move the decimal point to the right x places
The two xes after factoring.
From northeast - counterclockwise. I - II - III - IV
288 (8 9 4)
6. Formula of rectangle where l increases by 20% and w decreases by 20%
...multiply by 100.
x= (1.2)(.8)lw
13pi / 2
Move the decimal point to the right x places
7. Pi is a ratio of what to what?
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183
8. How to find the area of a sector?
2
Angle/360 x (pi)r^2
1 & 37/132
72
9. The ratio of the areas of two similar polygons is ...
The direction of the inequality is reversed.
x^(4+7) = x^11
... the square of the ratios of the corresponding sides.
(amount of decrease/original price) x 100%
10. How to find the diagonal of a rectangular solid?
(a + b)^2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
(n-2) x 180
11. When the 'a' in a parabola is positive....
III
The curve opens upward and the vertex is the minimal point on the graph.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Two equal sides and two equal angles.
12. Formula for the area of a sector of a circle?
A = I (1 + rt)
Area of the base X height = (pi)hr^2
4725
Sector area = (n/360) X (pi)r^2
13. What is a major arc?
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183
14. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
75:11
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.
Cd
4:5
15. 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?
I
The union of A and B.
$3 -500 in the 9% and $2 -500 in the 7%.
Yes. [i.e. f(x) = x^2 - 1
16. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
Indeterminable.
1
All numbers multiples of 1.
A tangent is a line that only touches one point on the circumference of a circle.
17. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
A central angle is an angle formed by 2 radii.
72
N! / (k!)(n-k)!
From northeast - counterclockwise. I - II - III - IV
18. 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
A circle centered on the origin with radius 8.
The objects within a set.
1
19. Factor x^2 - xy + x.
The curve opens upward and the vertex is the minimal point on the graph.
x(x - y + 1)
1 & 37/132
Factors are few - multiples are many.
20. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
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
90
Undefined - because we can'T divide by 0.
An isosceles right triangle.
21. What is the formula for compounded interest?
(b + c)
(a + b)^2
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.
4725
22. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
48
13pi / 2
1
23. Surface area for a cylinder?
2(pi)r^2 + 2(pi)rh
All numbers multiples of 1.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
True
24. The slope of a line perpendicular to (a/b)?
6 : 1 : 2
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
1
Its negative reciprocal. (-b/a)
25. a^2 + 2ab + b^2
4725
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
(a + b)^2
The objects within a set.
26. The perimeter of a square is 48 inches. The length of its diagonal is:
Indeterminable.
67 - 71 - 73
(amount of increase/original price) x 100%
12sqrt2
27. Is 0 even or odd?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
1.0843 X 10^11
Even
2sqrt6
28. The objects in a set are called two names:
1 & 37/132
No - the input value has exactly one output.
G(x) = {x}
Members or elements
29. 5/8 in percent?
Even
1/a^6
The third side is greater than the difference and less than the sum.
62.5%
30. What is the intersection of A and B?
Lies opposite the greater angle
The second graph is less steep.
The set of elements found in both A and B.
Sector area = (n/360) X (pi)r^2
31. Define a 'monomial'
288 (8 9 4)
Its divisible by 2 and by 3.
(p + q)/5
An expression with just one term (-6x - 2a^2)
32. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
Infinite.
0
2
The point of intersection of the systems.
33. (x^2)^4
Yes - like radicals can be added/subtracted.
x^(2(4)) =x^8 = (x^4)^2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
34. Which is greater? 200x^295 or 10x^294?
y = (x + 5)/2
The second graph is less steep.
An infinite set.
Relationship cannot be determined (what if x is negative?)
35. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
$11 -448
Divide by 100.
An infinite set.
36. What is the graph of f(x) shifted left c units or spaces?
F(x + c)
The sum of digits is divisible by 9.
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.
37. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
No - the input value has exactly one output.
Cd
1.0843 X 10^11
38. How many sides does a hexagon have?
6
3
1 & 37/132
1/a^6
39. What are the smallest three prime numbers greater than 65?
Divide by 100.
130pi
67 - 71 - 73
Part = Percent X Whole
40. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
The set of output values for a function.
13
y = (x + 5)/2
The set of input values for a function.
41. Convert 0.7% to a fraction.
1:sqrt3:2
12! / 5!7! = 792
(a - b)(a + b)
7 / 1000
42. What is a chord of a circle?
A set with no members - denoted by a circle with a diagonal through it.
(b + c)
A chord is a line segment joining two points on a circle.
6
43. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
The greatest value minus the smallest.
Area of the base X height = (pi)hr^2
A 30-60-90 triangle.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
44. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
All numbers multiples of 1.
3 - -3
7 / 1000
45. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
75:11
3sqrt4
70
From northeast - counterclockwise. I - II - III - IV
46. What is the 'Restricted domain of a function'?
2 & 3/7
When the function is not defined for all real numbers -; only a subset of the real numbers.
N! / (k!)(n-k)!
(amount of increase/original price) x 100%
47. (6sqrt3) x (2sqrt5) =
6
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
3
23 - 29
48. Describe the relationship between 3x^2 and 3(x - 1)^2
3/2 - 5/3
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The third side is greater than the difference and less than the sum.
1
49. Legs 5 - 12. Hypotenuse?
90 degrees
53 - 59
413.03 / 10^4 (move the decimal point 4 places to the left)
13
50. Find the surface area of a cylinder with radius 3 and height 12.
28. n = 8 - k = 2. n! / k!(n-k)!
180 degrees
13pi / 2
90pi