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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. Simplify the expression [(b^2 - c^2) / (b - c)]
Two angles whose sum is 180.
Ø
3/2 - 5/3
(b + c)

2. In a rectangle - all angles are
N! / (n-k)!
Two equal sides and two equal angles.
Right
53 - 59

3. Define a 'monomial'
3
2.592 kg
An expression with just one term (-6x - 2a^2)
A<-b

4. What does scientific notation mean?
Reciprocal
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
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.)

5. Slope of any line that goes down as you move from left to right is
The shortest arc between points A and B on a circle'S diameter.
An infinite set.
Be Zero!
Negative

6. Factor x^2 - xy + x.
True
Smallest positive integer
The two xes after factoring.
x(x - y + 1)

7. 10^6 has how many zeroes?
6
A-b is positive
20.5
Reciprocal

8. What is the 'Range' of a function?
x²-2xy+y²
A = pi(r^2)
0
The set of output values for a function.

9. a>b then a - b is positive or negative?
.0004809 X 10^11
x²-y²
A-b is positive
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)

10. What are 'Supplementary angles?'
71 - 73 - 79
Two angles whose sum is 180.
A subset.
61 - 67

11. 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?
72
Null
53 - 59
N! / (k!)(n-k)!

12. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
An arc is a portion of a circumference of a circle.
52
M= (Y1-Y2)/(X1-X2)

13. How many multiples does a given number have?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Triangles with same measure and same side lengths.
Infinite.
12sqrt2

14. What are the smallest three prime numbers greater than 65?
C = 2(pi)r
75:11
x(x - y + 1)
67 - 71 - 73

15. A number is divisible by 9 if...
The sum of digits is divisible by 9.
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
Factors are few - multiples are many.
A reflection about the origin.

16. What is the maximum value for the function g(x) = (-2x^2) -1?
The steeper the slope.
2sqrt6
13
1

17. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
1 & 37/132
10! / 3!(10-3)! = 120
53 - 59

18. When multiplying exponential #s with the same base - you do this to the exponents...
V=l×w×h
Add them. i.e. (5^7) * (5^3) = 5^10
zero
90°

19. To decrease a number by x%
A natural number greater than 1 that has no positive divisors other than 1 and itself
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Every number
9

20. Probability of Event all cases
Do not have slopes!
Subtract them. i.e (5^7)/(5^3)= 5^4
A reflection about the origin.
Ø=P(E)=1

21. Formula to find a circle'S circumference from its diameter?
11 - 13 - 17 - 19
x - x+1 - x+2
The point of intersection of the systems.
C = (pi)d

22. x^2 = 9. What is the value of x?
The set of input values for a function.
D/t (distance)/(time)
Two angles whose sum is 90.
3 - -3

23. Ø²
1/x
(p + q)/5
All numbers multiples of 1.
Ø

24. How to recognize a # as a multiple of 3
12sqrt2
X
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)
Its last two digits are divisible by 4.

25. What percent of 40 is 22?
Reciprocal
55%
The objects within a set.
10

26. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
360°

27. How many sides does a hexagon have?
53 - 59
6
All numbers multiples of 1.
Lies opposite the greater angle

28. 1n
F(x) - c
1
y/x is a constant
Pi(diameter)

29. What are the rational numbers?
1:sqrt3:2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
500
Every number

30. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
12sqrt2
360/n
55%

31. The sum of the measures of the n angles in a polygon with n sides
(n-2) x 180
D/t (distance)/(time)
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
13pi / 2

32. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
6 : 1 : 2
4725
16.6666%
C = 2(pi)r

33. What are the irrational numbers?

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34. Define an 'expression'.
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 - b)(a + b)
52
An expression with just one term (-6x - 2a^2)

35. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
y2-y1/x2-x1
True
P(E) = ø
Ab=k (k is a constant)

36. What is an arc of a circle?
N! / (n-k)!
A-b is negative
An arc is a portion of a circumference of a circle.
72

37. 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).
A tangent is a line that only touches one point on the circumference of a circle.
67 - 71 - 73
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

38. The objects in a set are called two names:
31 - 37
70
B?b?b (where b is used as a factor n times)
Members or elements

39. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
(a - b)^2
Straight Angle
Triangles with same measure and same side lengths.

40. What is a tangent?
Reciprocal
87.5%
13
A tangent is a line that only touches one point on the circumference of a circle.

41. Describe the relationship between 3x^2 and 3(x - 1)^2
A set with no members - denoted by a circle with a diagonal through it.
A chord is a line segment joining two points on a circle.
x^(4+7) = x^11
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

42. Probability of an Event
x - x(SR3) - 2x
P(E) = number of favorable outcomes/total number of possible outcomes
F(x-c)
Two (Ø×2=Ø)

43. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
10! / (10-3)! = 720
Even
Sum of digits is a multiple of 3 and the last digit is even.
ODD number

44. The reciprocal of any non-zero #x is
10
1/x
Ab=k (k is a constant)
1

45. Slope of any line that goes up from left to right
(a + b)^2
Positive
83.333%
The shortest arc between points A and B on a circle'S diameter.

46. What is a percent?
A percent is a fraction whose denominator is 100.
10! / 3!(10-3)! = 120
28
27

47. (12sqrt15) / (2sqrt5) =
Members or elements
(rate)(time) d=rt
Ø=P(E)=1
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

48. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
(p + q)/5
Infinite.
4:5
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50

49. Time
(distance)/(rate) d/r
F(x-c)
Ø=P(E)=1
27^(-4)

50. What is the graph of f(x) shifted upward c units or spaces?
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.
The second graph is less steep.
F(x) + c
Straight Angle