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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. The Denominator can never
The sum of digits is divisible by 9.
27
Be Zero!
2

2. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
2.592 kg
V=side³
x(x - y + 1)
Cd

3. (x^2)^4
C = 2(pi)r
x^(2(4)) =x^8 = (x^4)^2
P(E) = 1/1 = 1
V=Lwh

4. The objects in a set are called two names:
x^(6-3) = x^3
Members or elements
72
9 : 25

5. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
A set with a number of elements which can be counted.
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.
A natural number greater than 1 that has no positive divisors other than 1 and itself
10

6. Ø divided by 7
A percent is a fraction whose denominator is 100.
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Ø
N! / (n-k)!

7. Probability of an Event
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Ab-ac
180 degrees
P(E) = number of favorable outcomes/total number of possible outcomes

8. Volume of a rectangular solid
360°
(length)(width)(height)
(base*height) / 2
75:11

9. 3 is the opposite of
3
Reciprocal
Undefined
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)

10. (a^-1)/a^5
1/a^6
A multiple of every integer
An is positive
x²-2xy+y²

11. Time
16.6666%
The empty set - denoted by a circle with a diagonal through it.
Be Zero!
(distance)/(rate) d/r

12. Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The interesection of A and B.
5 - 12 - 13
A percent is a fraction whose denominator is 100.

13. A number is divisible by 4 is...
180
Distance=rate×time or d=rt
Its last two digits are divisible by 4.
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.)

14. Important properties of a 30-60-90 triangle?
The triangle is a right triangle. The hypotenuse is twice the length of the shorter leg. The ratio of the length of the three sides is x:xv3:2x
P(E) = 1/1 = 1
Negative
(length)(width)(height)

15. bn
Ab-ac
x²-2xy+y²
= (actual decrease/Original amount) x 100%
B?b?b (where b is used as a factor n times)

16. Evaluate 4/11 + 11/12
Undefined - because we can'T divide by 0.
1 & 37/132
x²-2xy+y²
Ø

17. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
72
Diameter(Pi)
(n-2) x 180

18. How to recognize a # as a multiple of 9
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x²+2xy+y²
The sum of the digits is a multiple of 9.
The longest arc between points A and B on a circle'S diameter.

19. Area of a circle
441000 = 1 10 10 10 21 * 21
A+c<b+c
180°
A=pi*(r^2)

20. When multiplying exponential #s with the same base - you do this to the exponents...
Add them. i.e. (5^7) * (5^3) = 5^10
Ø
The union of A and B.
V=l×w×h

21. What are the integers?
87.5%
$3 -500 in the 9% and $2 -500 in the 7%.
(length)(width)(height)
All numbers multiples of 1.

22. What is an exterior angle?
13pi / 2
A reflection about the axis.
An angle which is supplementary to an interior angle.
P(E) = number of favorable outcomes/total number of possible outcomes

23. What is the 'Range' of a function?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The set of output values for a function.
X
x^(2(4)) =x^8 = (x^4)^2

24. Can you simplify sqrt72?
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
3
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

25. 30 60 90
87.5%
(n-2) x 180
9
5 - 12 - 13

26. Evaluate (4^3)^2
D=rt so r= d/t and t=d/r
18
A=pi*(r^2)
4096

27. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
72
0
The empty set - denoted by a circle with a diagonal through it.
A percent is a fraction whose denominator is 100.

28. Define a 'monomial'
(length)(width)(height)
An expression with just one term (-6x - 2a^2)
(2x7)³
2²

29. How to recognize a multiple of 6
Sum of digits is a multiple of 3 and the last digit is even.
x - x(SR3) - 2x
F(x) - c
M= (Y1-Y2)/(X1-X2)

30. a^2 - b^2 =
(a - b)(a + b)
52
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...
The set of elements which can be found in either A or B.

31. If the two sides of a triangle are unequal then the longer side.................
72
70
Lies opposite the greater angle
An isosceles right triangle.

32. 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?
0
1
3 - -3
y = 2x^2 - 3

33. 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))?
The objects within a set.
90pi
20.5
y = 2x^2 - 3

34. How to recognize a # as a multiple of 4
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.)
500
(a - b)(a + b)
(a + b)^2

35. If a<b - then
1.7
A+c<b+c
The greatest value minus the smallest.
A set with a number of elements which can be counted.

36. Area of a triangle?
(base*height) / 2
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
2
The sum of the digits is a multiple of 9.

37. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
1
The second graph is less steep.
Two equal sides and two equal angles.
3 - -3

38. To increase a number by x%
D/t (distance)/(time)
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
NOT A PRIME
Cd

39. A number is divisible by 3 if ...
Negative
(a - b)^2
The two xes after factoring.
The sum of its digits is divisible by 3.

40. Ø is a multiple of
(x+y)(x+y)
Two (Ø×2=Ø)
A-b is positive
C=2 x pi x r OR pi x D

41. x^6 / x^3
x^(6-3) = x^3
75:11
10! / (10-3)! = 720
12! / 5!7! = 792

42. 1n
3 - 4 - 5
Even
Subtract them. i.e (5^7)/(5^3)= 5^4
1

43. The reciprocal of any non-zero number is
Members or elements
3/2 - 5/3
1/x
90pi

44. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
6
A subset.
1:sqrt3:2

45. Rate
An is positive
A=pi*(r^2)
Be Zero!
D/t (distance)/(time)

46. 0^0
Can be negative - zero - or positive
Undefined
Ab-ac
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.

47. Simplify 9^(1/2) X 4^3 X 2^(-6)?
A tangent is a line that only touches one point on the circumference of a circle.
$11 -448
3
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

48. Which is greater? 27^(-4) or 9^(-8)
Ab-ac
3x - 4x - 5x
27^(-4)
Ø=P(E)=1

49. Ø is
An isosceles right triangle.
A multiple of every integer
The direction of the inequality is reversed.
A+c<b+c

50. Ø Is neither
(p + q)/5
The point of intersection of the systems.
Positive or Negative
A²+b²=c²

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GRE Math: All In One

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