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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. Evaluate (4^3)^2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
4096
2^9 / 2 = 256
288 (8 9 4)

2. Obtuse Angle
11 - 13 - 17 - 19
61 - 67
Pi is the ratio of a circle'S circumference to its diameter.
angle that is greater than 90° but less than 180°

3. What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
Add them. i.e. (5^7) * (5^3) = 5^10
= (actual decrease/Original amount) x 100%
The longest arc between points A and B on a circle'S diameter.

4. (12sqrt15) / (2sqrt5) =
A grouping of the members within a set based on a shared characteristic.
1.0843 X 10^11
20.5
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

5. What are the real numbers?
1
6
A natural number greater than 1 that has no positive divisors other than 1 and itself
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)

6. A quadrilateral where two diagonals bisect each other
0
360/n
3 - 4 - 5
Parallelogram

7. If Event is impossible
P(E) = ø
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Relationship cannot be determined (what if x is negative?)

8. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
1
72
8

9. What is a chord of a circle?
75:11
(x+y)(x+y)
2
A chord is a line segment joining two points on a circle.

10. What number between 70 & 75 - inclusive - has the greatest number of factors?
y = (x + 5)/2
Positive or Negative
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
72

11. 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?
Distance=rate×time or d=rt
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.
52
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

12. Simplify the expression [(b^2 - c^2) / (b - c)]
53 - 59
(b + c)
V=l×w×h
ODD number

13. Legs 6 - 8. Hypotenuse?
Sector area = (n/360) X (pi)r^2
x²-2xy+y²
P(E) = 1/1 = 1
10

14. When dividing exponential #s with the same base - you do this to the exponents...
87.5%
Subtract them. i.e (5^7)/(5^3)= 5^4
(base*height) / 2
72

15. 60 < all primes <70
6 : 1 : 2
3 - 4 - 5
P(E) = number of favorable outcomes/total number of possible outcomes
61 - 67

16. If a is negative and n is even then an is (positive or negative?)
ODD number
An is positive
7 / 1000
C = 2(pi)r

17. What is a tangent?
71 - 73 - 79
A tangent is a line that only touches one point on the circumference of a circle.
F(x) - c
y = (x + 5)/2

18. 1/Ø=null If a>b then
A<-b
5 - 12 - 13
(a - b)(a + b)
The set of output values for a function.

19. Any Horizontal line slope
C = (pi)d
zero
M= (Y1-Y2)/(X1-X2)
x²-2xy+y²

20. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
(a + b)^2
The greatest value minus the smallest.
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 30-60-90 triangle.

21. (x-y)(x+y)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
x²-y²
Cd
Sector area = (n/360) X (pi)r^2

22. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
Parallelogram
13pi / 2
A-b is positive
90pi

23. What is the 'Range' of a function?
(a - b)(a + b)
y/x is a constant
x - x+1 - x+2
The set of output values for a function.

24. What is the 'Solution' for a system of linear equations?
x - x(SR3) - 2x
55%
The point of intersection of the systems.
A = pi(r^2)

25. Circumference of a circle
Pi(diameter)
Positive
x^(4+7) = x^11
12sqrt2

26. Circumference of a Circle
C=2 x pi x r OR pi x D
1
500
10! / (10-3)! = 720

27. a/Ø
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)
Null
The set of output values for a function.

28. The negative exponent x?n is equivalent to what?
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)
12.5%
Sum of digits is a multiple of 3 and the last digit is even.
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008

29. Important properties of a 30-60-90 triangle?
1 - P(E)
x - x+1 - x+2
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
NOT A PRIME

30. When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
An infinite set.
A+c<b+c
0

31. The sum of the measures of the n angles in a polygon with n sides
(n-2) x 180
2
500
Pi(diameter)

32. 1 is the
Smallest positive integer
A 30-60-90 triangle.
$3 -500 in the 9% and $2 -500 in the 7%.
A percent is a fraction whose denominator is 100.

33. What is the maximum value for the function g(x) = (-2x^2) -1?
The union of A and B.
V=Lwh
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1

34. 25^(1/2) or sqrt. 25 =
72
13pi / 2
5 OR -5
$11 -448

35. formula for distance problems
V=l×w×h
All numbers multiples of 1.
Distance=rate×time or d=rt
C = 2(pi)r

36. Distance
Two (Ø×2=Ø)
The direction of the inequality is reversed.
(rate)(time) d=rt
Ab+ac

37. The product of odd number of negative numbers
Negative
C = (pi)d
3/2 - 5/3
N! / (n-k)!

38. What is a minor arc?

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39. What is a percent?
(base*height) / 2
The point of intersection of the systems.
The sum of digits is divisible by 9.
A percent is a fraction whose denominator is 100.

40. 3/8 in percent?
Pi(diameter)
37.5%
441000 = 1 10 10 10 21 * 21
12! / 5!7! = 792

41. 5/6 in percent?
= (actual decrease/Original amount) x 100%
9
2
83.333%

42. Find distance when given time and rate
True
D=rt so r= d/t and t=d/r
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

43. a<b then a - b is positive or negative?
3
A-b is negative
1
1/2 times 7/3

44. 0^0
1
Null
Undefined
A = length x width

45. What are congruent triangles?
The longest arc between points A and B on a circle'S diameter.
1:sqrt3:2
Triangles with same measure and same side lengths.
37.5%

46. Circumference of a circle?
Even prime number
Diameter(Pi)
M
1

47. 25/2³
2²
(p + q)/5
10
Undefined - because we can'T divide by 0.

48. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
2sqrt6
Undefined - because we can'T divide by 0.
A tangent is a line that only touches one point on the circumference of a circle.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

49. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
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.
Cd
x²+2xy+y²
The longest arc between points A and B on a circle'S diameter.

50. Simplify 9^(1/2) X 4^3 X 2^(-6)?
1
3
Factors are few - multiples are many.
The steeper the slope.