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GRE Math: All In One

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. (x+y)²
Null
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x²+2xy+y²
180°

2. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
A percent is a fraction whose denominator is 100.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

3. 3 is the opposite of
B?b?b (where b is used as a factor n times)
180°
3
1:1:sqrt2

4. If a product of two numbers is Ø - one number must be
27
3
Ø
Lies opposite the greater angle

5. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
4a^2(b)
The sum of the digits is a multiple of 9.
$3 -500 in the 9% and $2 -500 in the 7%.

6. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
4:5
A natural number greater than 1 that has no positive divisors other than 1 and itself
V=Lwh

7. (6sqrt3) x (2sqrt5) =
180
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
2(pi)r
A central angle is an angle formed by 2 radii.

8. To multiply a number by 10^x
Move the decimal point to the right x places
4:5
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
A natural number greater than 1 that has no positive divisors other than 1 and itself

9. Ø is
An angle which is supplementary to an interior angle.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Even
V=l×w×h

10. x^4 + x^7 =
x^(4+7) = x^11
Undefined
41 - 43 - 47
$3 -500 in the 9% and $2 -500 in the 7%.

11. What is the set of elements found in both A and B?
Be Zero!
The interesection of A and B.
Sector area = (n/360) X (pi)r^2
Triangles with same measure and same side lengths.

12. 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?
75:11
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
90pi
x^(2(4)) =x^8 = (x^4)^2

13. x^6 / x^3
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
x^(6-3) = x^3
D=rt so r= d/t and t=d/r
The overlapping sections.

14. 5/6 in percent?
83.333%
Positive or Negative
10! / (10-3)! = 720
67 - 71 - 73

15. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
52
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
4.25 - 6 - 22
Ø

16. the slope of a line in y=mx+b
M
4a^2(b)
53 - 59
10! / (10-3)! = 720

17. -3²
9
A reflection about the origin.
4:5
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60

18. 7/8 in percent?
87.5%
1 - P(E)
31 - 37
The sum of the digits is a multiple of 3 (i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)

19. 5x^2 - 35x -55 = 0
Do not have slopes!
F(x + c)
Undefined
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

20. 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
y/x is a constant
90°
A=(base)(height)

21. (2²)³
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
P=2(l+w)
ODD number
26

22. Write 10 -843 X 10^7 in scientific notation
1/2 times 7/3
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
1.0843 X 10^11
The point of intersection of the systems.

23. A quadrilateral where two diagonals bisect each other
P(E) = 1/1 = 1
Lies opposite the greater angle
Parallelogram
M

24. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
x²+2xy+y²
Move the decimal point to the right x places
0

25. To increase a number by x%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Ø
441000 = 1 10 10 10 21 * 21
180°

26. Area of a circle
angle that is greater than 90° but less than 180°
Yes - like radicals can be added/subtracted.
(a - b)(a + b)
(pi)r²

27. To decrease a number by x%
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.
6
55%
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50

28. Pi is a ratio of what to what?

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29. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
360/n
48
Two equal sides and two equal angles.
y2-y1/x2-x1

30. (x^2)^4
The two xes after factoring.
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...
x^(2(4)) =x^8 = (x^4)^2
90pi

31. 10^6 has how many zeroes?
x²+2xy+y²
3
The objects within a set.
6

32. Product of any number and Ø is
Ø
An infinite set.
y/x is a constant
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)

33. In a Regular Polygon - the measure of each exterior angle
360/n
An angle which is supplementary to an interior angle.
N! / (n-k)!
9

34. -3³
x²-y²
27
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)
D/t (distance)/(time)

35. When dividing exponential #s with the same base - you do this to the exponents...
87.5%
180°
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Subtract them. i.e (5^7)/(5^3)= 5^4

36. What are complementary angles?
Two angles whose sum is 90.
360/n
Parallelogram
The sum of digits is divisible by 9.

37. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
360°
12! / 5!7! = 792
1/a^6
Ø

38. 30 60 90
3x - 4x - 5x
27^(-4)
Its last two digits are divisible by 4.
1/x

39. The product of any number x and its reciprocal
1
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1.0843 X 10^11
A set with a number of elements which can be counted.

40. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
7 / 1000
1.0843 X 10^11
4.25 - 6 - 22
3

41. 25^(1/2) or sqrt. 25 =
5 OR -5
(a - b)(a + b)
28
Ab+ac

42. The ratio of the areas of two similar polygons is ...
360°
... the square of the ratios of the corresponding sides.
1
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50

43. Positive integers that have exactly 2 positive divisors are
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
A = length x width
$11 -448
Sum of digits is a multiple of 3 and the last digit is even.

44. Legs: 3 - 4. Hypotenuse?
x - x(SR3) - 2x
5
A = pi(r^2)
3 - 4 - 5

45. How many sides does a hexagon have?
Ø
6
Even
N! / (n-k)!

46. 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?
20.5
N! / (k!)(n-k)!
x²-y²
10

47. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
A subset.
13pi / 2
x²-2xy+y²
3/2 - 5/3

48. Is 0 even or odd?
Even
5
V=side³
72

49. formula for distance problems
Distance=rate×time or d=rt
180°
A<-b
V=side³

50. What is an isoceles triangle?
Two equal sides and two equal angles.
(amount of decrease/original price) x 100%
x(x - y + 1)
(rate)(time) d=rt