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GRE Math: All In One

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Which is greater? 200x^295 or 10x^294?
A 30-60-90 triangle.
Negative
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
Relationship cannot be determined (what if x is negative?)

2. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
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
The sum of the digits is a multiple of 9.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
x²-y²

3. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
180
8
P=4s (s=side)
Even

4. If a lamp decreases to $80 - from $100 - what is the decrease in price?
P=2(l+w)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Relationship cannot be determined (what if x is negative?)
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

5. Area of a circle
A=pi*(r^2)
4.25 - 6 - 22
2²
23 - 29

6. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
28. n = 8 - k = 2. n! / k!(n-k)!
0
An isosceles right triangle.
Null

7. What is the side length of an equilateral triangle with altitude 6?
9 & 6/7
1/x
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...
Pi(diameter)

8. 3/8 in percent?
No - only like radicals can be added.
Ab=k (k is a constant)
1/x
37.5%

9. P and r are factors of 100. What is greater - pr or 100?
Ø
Indeterminable.
Factors are few - multiples are many.
A central angle is an angle formed by 2 radii.

10. a^2 - b^2
3/2 - 5/3
3
The point of intersection of the systems.
(a - b)(a + b)

11. a(b+c)
Ab+ac
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
.0004809 X 10^11
An angle which is supplementary to an interior angle.

12. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
x^(2(4)) =x^8 = (x^4)^2
A=pi*(r^2)
3
An arc is a portion of a circumference of a circle.

13. What is a central angle?
X
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
A central angle is an angle formed by 2 radii.
The set of elements which can be found in either A or B.

14. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A natural number greater than 1 that has no positive divisors other than 1 and itself
The longest arc between points A and B on a circle'S diameter.
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)
A reflection about the axis.

15. 30 60 90
18
2.592 kg
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
3x - 4x - 5x

16. Legs: 3 - 4. Hypotenuse?
F(x) - c
Ab-ac
5
Its divisible by 2 and by 3.

17. Consecutive integers
(b + c)
x - x+1 - x+2
2sqrt6
1/a^6

18. (x+y)²
360°
All numbers multiples of 1.
x²+2xy+y²
(distance)/(rate) d/r

19. formula for the volume of a cube
9 & 6/7
28. n = 8 - k = 2. n! / k!(n-k)!
V=side³
A<-b

20. How to recognize a # as a multiple of 4
An arc is a portion of a circumference of a circle.
90
1/x
The last 2 digits are a multiple of 4. (i.e 144 .... 44 is a multiple of 4 - so 144 must also be a multiple of 4.)

21. The Perimeter of a Square
P=4s (s=side)
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
A tangent is a line that only touches one point on the circumference of a circle.
Cd

22. If y is directly proportional to x - what does it equal?
4a^2(b)
Positive or Negative
x²-2xy+y²
y/x is a constant

23. Any Horizontal line slope
zero
(a - b)(a + b)
61 - 67
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)

24. Rate
D/t (distance)/(time)
Sum of digits is a multiple of 3 and the last digit is even.
13pi / 2
20.5

25. How to recognize if a # is a multiple of 12
The sum of the digits is a multiple of 9.
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3 - and 44 is a multiple of 4 - so 144 is a multiple of 12.)
48
11 - 13 - 17 - 19

26. Find distance when given time and rate
x^(4+7) = x^11
1.7
Even
D=rt so r= d/t and t=d/r

27. Positive integers that have exactly 2 positive divisors are
F(x) + c
18
Move the decimal point to the right x places
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)

28. Define a 'monomial'
Ø
An expression with just one term (-6x - 2a^2)
72
P=4s (s=side)

29. What are the roots of the quadrinomial x^2 + 2x + 1?
72
13pi / 2
1/a^6
The two xes after factoring.

30. Find the surface area of a cylinder with radius 3 and height 12.
Even
3
90pi
Its divisible by 2 and by 3.

31. First 10 prime #s
Two angles whose sum is 90.
F(x + c)
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
Relationship cannot be determined (what if x is negative?)

32. 30 60 90
5 - 12 - 13
$3 -500 in the 9% and $2 -500 in the 7%.
(a - b)(a + b)
P=4s (s=side)

33. What is the 'Range' of a series of numbers?
A multiple of every integer
23 - 29
N! / (k!)(n-k)!
The greatest value minus the smallest.

34. The sum of all angles around a point
0
360°
1
A²+b²=c²

35. Obtuse Angle
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Positive or Negative
angle that is greater than 90° but less than 180°
55%

36. Ø Is neither
360°
Positive or Negative
2
(2x7)³

37. If a product of two numbers is Ø - one number must be
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
An arc is a portion of a circumference of a circle.
The direction of the inequality is reversed.
Ø

38. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Diameter(Pi)
x²-2xy+y²
Cd
The set of elements which can be found in either A or B.

39. When dividing exponential #s with the same base - you do this to the exponents...
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
Subtract them. i.e (5^7)/(5^3)= 5^4
P(E) = number of favorable outcomes/total number of possible outcomes
An infinite set.

40. What is a subset?
A grouping of the members within a set based on a shared characteristic.
Two angles whose sum is 180.
Its last two digits are divisible by 4.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

41. 50 < all primes< 60
An isosceles right triangle.
P=4s (s=side)
53 - 59
Yes - like radicals can be added/subtracted.

42. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
(pi)r²
x²-y²
Ab-ac

43. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
18
C = 2(pi)r
An isosceles right triangle.

44. 4.809 X 10^7 =
1
.0004809 X 10^11
(n-2) x 180
6

45. Factor x^2 - xy + x.
2
2(pi)r
x(x - y + 1)
1:1:sqrt2

46. If E is certain
zero
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
P(E) = 1/1 = 1
9 : 25

47. What number between 70 & 75 - inclusive - has the greatest number of factors?
10! / 3!(10-3)! = 120
72
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)
N! / (n-k)!

48. a^2 - b^2 =
Pi is the ratio of a circle'S circumference to its diameter.
(a - b)(a + b)
Its last two digits are divisible by 4.
N! / (k!)(n-k)!

49. binomial product of (x-y)²
Pi is the ratio of a circle'S circumference to its diameter.
4725
(x+y)(x-y)
A=pi*(r^2)

50. 6w^2 - w - 15 = 0
3/2 - 5/3
Positive or Negative
(distance)/(rate) d/r
The triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.

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GRE Math: All In One

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