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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. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
Straight Angle
180
A chord is a line segment joining two points on a circle.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

2. In a Regular Polygon - the measure of each exterior angle
Straight Angle
360/n
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...
.0004809 X 10^11

3. 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))?
EVEN
20.5
D/t (distance)/(time)
0

4. The larger the absolute value of the slope...
Positive
48
The steeper the slope.
18

5. The negative exponent x?n is equivalent to what?
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
... the square of the ratios of the corresponding sides.
3
An arc is a portion of a circumference of a circle.

6. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
C=2 x pi x r OR pi x D
Add them. i.e. (5^7) * (5^3) = 5^10
Relationship cannot be determined (what if x is negative?)

7. What is the name for a grouping of the members within a set based on a shared characteristic?
An isosceles right triangle.
4:5
180
A subset.

8. 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?
The union of A and B.
23 - 29
8
N! / (k!)(n-k)!

9. Slope of any line that goes down as you move from left to right is
Negative
The longest arc between points A and B on a circle'S diameter.
y = (x + 5)/2
Can be negative - zero - or positive

10. What is the slope of a horizontal line?
4725
0
28. n = 8 - k = 2. n! / k!(n-k)!
A=pi*(r^2)

11. The sum of all angles around a point
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
360°
Undefined - because we can'T divide by 0.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

12. What are the roots of the quadrinomial x^2 + 2x + 1?
0
A reflection about the origin.
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)
The two xes after factoring.

13. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
90
180
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
A reflection about the axis.

14. 30 60 90
3x - 4x - 5x
A=½bh
75:11
Infinite.

15. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
The shortest arc between points A and B on a circle'S diameter.
(pi)r²
2sqrt6

16. a^2 + 2ab + b^2
180°
(a + b)^2
The direction of the inequality is reversed.
1 - P(E)

17. If a is negative and n is even then an is (positive or negative?)
An is positive
Reciprocal
The overlapping sections.
The longest arc between points A and B on a circle'S diameter.

18. a(b-c)
9 & 6/7
4.25 - 6 - 22
Ab-ac
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

19. a^2 - b^2 =
P=4s (s=side)
180 degrees
0
(a - b)(a + b)

20. 7/8 in percent?
130pi
4:5
87.5%
Ø=P(E)=1

21. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
No - only like radicals can be added.
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 triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.
ODD number

22. What are the rational numbers?
4096
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
28
1

23. How to recognize a # as a multiple of 4
No - only like radicals can be added.
1/a^6
2(pi)r
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.)

24. Find the surface area of a cylinder with radius 3 and height 12.
90pi
x - x+1 - x+2
1/a^6
1

25. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
The set of output values for a function.
28
A subset.

26. The objects in a set are called two names:
x^(2(4)) =x^8 = (x^4)^2
Members or elements
x²-2xy+y²
1:1:sqrt2

27. What is the sum of the angles of a triangle?
180 degrees
A= (1/2) b*h
10
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.)

28. (12sqrt15) / (2sqrt5) =
Ab+ac
The sum of its digits is divisible by 3.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A<-b

29. Describe the relationship between the graphs of x^2 and (1/2)x^2
... the square of the ratios of the corresponding sides.
The second graph is less steep.
NOT A PRIME
Ø

30. 50 < all primes< 60
53 - 59
87.5%
(2x7)³
The set of output values for a function.

31. Solve the quadratic equation ax^2 + bx + c= 0
90pi
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
P(E) = number of favorable outcomes/total number of possible outcomes

32. a>b then a - b is positive or negative?
Infinite.
90°
A-b is positive
4.25 - 6 - 22

33. A number is divisible by 6 if...
Its divisible by 2 and by 3.
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...
A=(base)(height)
1

34. What is the maximum value for the function g(x) = (-2x^2) -1?
0
1
The second graph is less steep.
3

35. 6w^2 - w - 15 = 0
8
6 : 1 : 2
... the square of the ratios of the corresponding sides.
3/2 - 5/3

36. b¹
1 & 37/132
1
Distance=rate×time or d=rt
C=2 x pi x r OR pi x D

37. What is a tangent?
A set with a number of elements which can be counted.
7 / 1000
288 (8 9 4)
A tangent is a line that only touches one point on the circumference of a circle.

38. First 10 prime #s
Ab+ac
D=rt so r= d/t and t=d/r
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
Negative

39. Ø is a multiple of
P=2(l+w)
Two (Ø×2=Ø)
A=½bh
500

40. 1 is a divisor of
Be Zero!
Ab=k (k is a constant)
Every number
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

41. Ø is
A grouping of the members within a set based on a shared characteristic.
A multiple of every integer
1
3/2 - 5/3

42. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
6
360°
52
The two xes after factoring.

43. Define an 'expression'.
F(x + c)
(x+y)(x-y)
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)
A tangent is a line that only touches one point on the circumference of a circle.

44. 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?
Sector area = (n/360) X (pi)r^2
A=pi*(r^2)
The sum of its digits is divisible by 3.
y = 2x^2 - 3

45. 25/2³
A=½bh
1
2²
18

46. (x-y)(x+y)
Null
The interesection of A and B.
x²-y²
41 - 43 - 47

47. What is the slope of a vertical line?

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48. (x-y)²
x²-2xy+y²
Ø
(a - b)^2
13

49. Pi is a ratio of what to what?

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50. 1 is an
ODD number
Parallelogram
Even
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50