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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. 60 < all primes <70
P=2(l+w)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
An expression with just one term (-6x - 2a^2)
61 - 67

2. What is the 'domain' of a function?
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
Negative
The set of input values for a function.
Ø

3. Legs: 3 - 4. Hypotenuse?
5
$11 -448
A 30-60-90 triangle.
1

4. Describe the relationship between the graphs of x^2 and (1/2)x^2
P(E) = ø
NOT A PRIME
All numbers multiples of 1.
The second graph is less steep.

5. -3²
Even
2 & 3/7
1/a^6
9

6. 7/8 in percent?
A=pi*(r^2)
87.5%
C = 2(pi)r
500

7. What is the set of elements which can be found in either A or B?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
Factors are few - multiples are many.
(a - b)^2
The union of A and B.

8. Slope of any line that goes down as you move from left to right is
1
Triangles with same measure and same side lengths.
The two xes after factoring.
Negative

9. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
1 & 37/132
Indeterminable.
N! / (n-k)!

10. If a is positive - an is
The sum of its digits is divisible by 3.
A = length x width
61 - 67
Positive

11. Volume of a cube
Edge³
An angle which is supplementary to an interior angle.
90
3 - 4 - 5

12. What is the ratio of the sides of a 30-60-90 triangle?
20.5
1:sqrt3:2
13pi / 2
(n-2) x 180

13. What is the empty set?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
A set with no members - denoted by a circle with a diagonal through it.
The interesection of A and B.
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)

14. Area of a triangle
A= (1/2) b*h
41 - 43 - 47
360°
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

15. Simplify the expression [(b^2 - c^2) / (b - c)]
M
Negative
71 - 73 - 79
(b + c)

16. 3 is the opposite of
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
3
53 - 59
y = 2x^2 - 3

17. 1/Ø=null If a>b then
(x+y)(x-y)
A<-b
61 - 67
1:sqrt3:2

18. Distance
(x+y)(x+y)
$11 -448
(rate)(time) d=rt
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

19. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
37.5%
Ø
0
A-b is positive

20. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
The longest arc between points A and B on a circle'S diameter.
9 : 25
2 & 3/7
53 - 59

21. The reciprocal of any non-zero number is
53 - 59
Straight Angle
1/x
27

22. What is an exterior angle?
18
Even
An angle which is supplementary to an interior angle.
A<-b

23. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
500
72
(distance)/(rate) d/r
x²-y²

24. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Relationship cannot be determined (what if x is negative?)
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)
28. n = 8 - k = 2. n! / k!(n-k)!
Ø

25. The negative exponent x?n is equivalent to what?
F(x) - c
20.5
Negative
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008

26. 5x^2 - 35x -55 = 0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Ø=P(E)=1
The greatest value minus the smallest.
M

27. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
1:sqrt3:2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
1

28. a<b then a - b is positive or negative?
Every number
A-b is negative
x(x - y + 1)
Two (Ø×2=Ø)

29. What is the 'union' of A and B?
61 - 67
9 & 6/7
(a - b)(a + b)
The set of elements which can be found in either A or B.

30. a(b-c)
Triangles with same measure and same side lengths.
Negative
Ab-ac
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)

31. 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?
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
55%
4:5
A set with a number of elements which can be counted.

32. Find the surface area of a cylinder with radius 3 and height 12.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
180 degrees
90pi
A<-b

33. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
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.
48
F(x) - c
1

34. factored binomial product of (x-y)²
x²-2xy+y²
(x+y)(x+y)
Ø
Lies opposite the greater angle

35. Simplify (a^2 + b)^2 - (a^2 - b)^2
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
A natural number greater than 1 that has no positive divisors other than 1 and itself
Sector area = (n/360) X (pi)r^2
4a^2(b)

36. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
D=rt so r= d/t and t=d/r
(2x7)³
$3 -500 in the 9% and $2 -500 in the 7%.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

37. If an inequality is multiplied or divided by a negative number....
A-b is positive
Positive or Negative
V=Lwh
The direction of the inequality is reversed.

38. A number is divisible by 4 is...
A=pi*(r^2)
The direction of the inequality is reversed.
70
Its last two digits are divisible by 4.

39. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
1.7
90pi
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

40. What is an arc of a circle?
An arc is a portion of a circumference of a circle.
A-b is positive
Even
1/x

41. Area of a Parallelogram:
M= (Y1-Y2)/(X1-X2)
The union of A and B.
2^9 / 2 = 256
A=(base)(height)

42. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
A 30-60-90 triangle.
2
A+c<b+c
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)

43. 70 < all primes< 80
Ø Ø=Ø
130pi
71 - 73 - 79
3

44. Time
y/x is a constant
A=pi*(r^2)
(distance)/(rate) d/r
The steeper the slope.

45. formula for area of a triangle
A=½bh
Ø Ø=Ø
angle that is greater than 90° but less than 180°
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.)

46. (x-y)²
The set of elements found in both A and B.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
1/2 times 7/3
x²-2xy+y²

47. Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
Null
A natural number greater than 1 that has no positive divisors other than 1 and itself
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

48. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
26
180°
Ab-ac

49. (6sqrt3) x (2sqrt5) =
F(x) + c
Pi(diameter)
y2-y1/x2-x1
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

50. What is a minor arc?

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