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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. The Perimeter of a rectangle
x²-2xy+y²
P=2(l+w)
A chord is a line segment joining two points on a circle.
P(E) = 1/1 = 1

2. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
F(x-c)
P(E) = number of favorable outcomes/total number of possible outcomes
(x+y)(x-y)
y = (x + 5)/2

3. bn
441000 = 1 10 10 10 21 * 21
13pi / 2
Right
B?b?b (where b is used as a factor n times)

4. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
360°
62.5%

5. 3/8 in percent?
7 / 1000
Can be negative - zero - or positive
37.5%
D/t (distance)/(time)

6. A quadrilateral where two diagonals bisect each other
x²-y²
y2-y1/x2-x1
Parallelogram
2sqrt6

7. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
Negative
2sqrt6
x^(2(4)) =x^8 = (x^4)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

8. Describe the relationship between the graphs of x^2 and (1/2)x^2
P=2(l+w)
The second graph is less steep.
Do not have slopes!
1:sqrt3:2

9. Whats the difference between factors and multiples?
Two angles whose sum is 180.
5
70
Factors are few - multiples are many.

10. What is an exterior angle?
N! / (k!)(n-k)!
1 - P(E)
An angle which is supplementary to an interior angle.
360°

11. Pi is a ratio of what to what?

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12. 1 is an
A central angle is an angle formed by 2 radii.
ODD number
The sum of its digits is divisible by 3.
6 : 1 : 2

13. 5/6 in percent?
83.333%
1
13pi / 2
True

14. Formula for the area of a sector of a circle?
All numbers multiples of 1.
Move the decimal point to the right x places
.0004809 X 10^11
Sector area = (n/360) X (pi)r^2

15. binomial product of (x+y)²
(x+y)(x+y)
P=4s (s=side)
The greatest value minus the smallest.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

16. formula for volume of a rectangular solid
A 30-60-90 triangle.
180
V=l×w×h
Negative

17. Consecutive integers
x - x+1 - x+2
N! / (n-k)!
The interesection of A and B.
(x+y)(x+y)

18. To decrease a number by x%
Null
(distance)/(rate) d/r
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
180

19. In a Regular Polygon - the measure of each exterior angle
12sqrt2
A grouping of the members within a set based on a shared characteristic.
Two (Ø×2=Ø)
360/n

20. If a<b - then
ODD number
Distance=rate×time or d=rt
An is positive
A+c<b+c

21. The Denominator can never
Be Zero!
The objects within a set.
Factors are few - multiples are many.
F(x-c)

22. One is (a prime or not?)
C = (pi)d
NOT A PRIME
Do not have slopes!
The point of intersection of the systems.

23. Is 0 even or odd?
8
1:sqrt3:2
Even
2

24. To increase a number by x%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
The second graph is less steep.
1
$3 -500 in the 9% and $2 -500 in the 7%.

25. the slope of a line in y=mx+b
M
Positive
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Move the decimal point to the right x places

26. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
x^(2(4)) =x^8 = (x^4)^2
2^9 / 2 = 256
Negative

27. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
61 - 67
2.592 kg
Sector area = (n/360) X (pi)r^2
28. n = 8 - k = 2. n! / k!(n-k)!

28. The sum of the angles in a quadrilateral is
0
F(x-c)
Relationship cannot be determined (what if x is negative?)
360°

29. How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
28. n = 8 - k = 2. n! / k!(n-k)!
8
90°

30. Distance
2^9 / 2 = 256
(rate)(time) d=rt
55%
A set with no members - denoted by a circle with a diagonal through it.

31. If a lamp decreases to $80 - from $100 - what is the decrease in price?
Yes - like radicals can be added/subtracted.
x^(2(4)) =x^8 = (x^4)^2
8
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

32. x^4 + x^7 =
An expression with just one term (-6x - 2a^2)
4725
x^(4+7) = x^11
Ø Ø=Ø

33. factored binomial product of (x+y)²
F(x) - c
2²
(length)(width)(height)
x²+2xy+y²

34. What are the smallest three prime numbers greater than 65?
F(x) + c
67 - 71 - 73
A²+b²=c²
Can be negative - zero - or positive

35. A number is divisible by 9 if...
The sum of digits is divisible by 9.
A-b is negative
(2x7)³
Pi(diameter)

36. Which is greater? 64^5 or 16^8
The sum of digits is divisible by 9.
Two equal sides and two equal angles.
The greatest value minus the smallest.
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16

37. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
4096
Cd
0

38. What is a set with no members called?
3
Two (Ø×2=Ø)
The empty set - denoted by a circle with a diagonal through it.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

39. Slope given 2 points
A percent is a fraction whose denominator is 100.
M= (Y1-Y2)/(X1-X2)
1 - P(E)
Move the decimal point to the right x places

40. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2^9 / 2 = 256
A=pi*(r^2)
2 & 3/7
A = pi(r^2)

41. 1/Ø=null If a>b then
360°
Edge³
A<-b
$11 -448

42. 1n
angle that is greater than 90° but less than 180°
9 : 25
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.
1

43. 5/8 in percent?
62.5%
M
441000 = 1 10 10 10 21 * 21
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

44. When multiplying exponential #s with the same base - you do this to the exponents...
Add them. i.e. (5^7) * (5^3) = 5^10
A = length x width
10
3

45. What is the side length of an equilateral triangle with altitude 6?
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...
F(x + c)
A= (1/2) b*h
angle that is greater than 90° but less than 180°

46. -3²
9
67 - 71 - 73
10! / (10-3)! = 720
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.)

47. Formula to find a circle'S circumference from its radius?
2sqrt6
C = 2(pi)r
28. n = 8 - k = 2. n! / k!(n-k)!
V=l×w×h

48. Solve the quadratic equation ax^2 + bx + c= 0
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The second graph is less steep.
y = (x + 5)/2

49. Positive integers that have exactly 2 positive divisors are
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
P=2(l+w)
Distance=rate×time or d=rt
= (actual decrease/Original amount) x 100%

50. 20<all primes<30
23 - 29
M= (Y1-Y2)/(X1-X2)
A reflection about the axis.
(rate)(time) d=rt