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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. (x-y)(x+y)
x²-y²
(a - b)^2
Infinite.
1/x

2. formula for volume of a rectangular solid
360°
4a^2(b)
4096
V=l×w×h

3. Number of degrees in a triangle
360°
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
C=2 x pi x r OR pi x D
180

4. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
1/x
1/a^6
1:sqrt3:2

5. Area of a circle
(pi)r²
1
3 - -3
Null

6. One is (a prime or not?)
The objects within a set.
Can be negative - zero - or positive
6 : 1 : 2
NOT A PRIME

7. What is an isoceles triangle?
288 (8 9 4)
Two equal sides and two equal angles.
D=rt so r= d/t and t=d/r
1.0843 X 10^11

8. First 10 prime #s
27^(-4)
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
11 - 13 - 17 - 19
5 - 12 - 13

9. 70 < all primes< 80
71 - 73 - 79
130pi
31 - 37
28

10. 30 60 90
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
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.
3 - 4 - 5
An is positive

11. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
F(x + c)
48
A-b is negative
An infinite set.

12. When does a function automatically have a restricted domain (2)?
Ab-ac
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
67 - 71 - 73
P(E) = ø

13. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1/2 times 7/3
D=rt so r= d/t and t=d/r
1
P=4s (s=side)

14. What is the graph of f(x) shifted downward c units or spaces?
The longest arc between points A and B on a circle'S diameter.
x^(2(4)) =x^8 = (x^4)^2
F(x) - c
1

15. What is the area of a regular hexagon with side 6?
F(x) + c
An arc is a portion of a circumference of a circle.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

16. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
... the square of the ratios of the corresponding sides.
75:11
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
87.5%

17. (a^-1)/a^5
an angle that is less than 90°
130pi
1/a^6
Factors are few - multiples are many.

18. Slope given 2 points
A<-b
A percent is a fraction whose denominator is 100.
(a + b)^2
M= (Y1-Y2)/(X1-X2)

19. 2³×7³
A-b is positive
x - x+1 - x+2
4a^2(b)
(2x7)³

20. In a Regular Polygon - the measure of each exterior angle
N! / (k!)(n-k)!
360/n
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

21. What is a central angle?
1/x
37.5%
A central angle is an angle formed by 2 radii.
1

22. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
(n-2) x 180
P=4s (s=side)
A 30-60-90 triangle.
6

23. How to find the circumference of a circle which circumscribes a square?
1/a^6
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
5 - 12 - 13
x²+2xy+y²

24. An Angle that'S 180°
$11 -448
Straight Angle
The longest arc between points A and B on a circle'S diameter.
Even

25. 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...
B?b?b (where b is used as a factor n times)
N! / (n-k)!
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)

26. a>b then a - b is positive or negative?
A-b is positive
1:sqrt3:2
Straight Angle
N! / (n-k)!

27. What are the real numbers?
(a - b)(a + b)
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)
180
The overlapping sections.

28. The product of odd number of negative numbers
Negative
EVEN
An expression with just one term (-6x - 2a^2)
F(x-c)

29. Volume of a rectangular box
37.5%
A²+b²=c²
V=Lwh
48

30. Any Horizontal line slope
zero
1:sqrt3:2
Indeterminable.
A=½bh

31. 30< all primes<40
Distance=rate×time or d=rt
C = (pi)d
31 - 37
An infinite set.

32. If an inequality is multiplied or divided by a negative number....
All numbers multiples of 1.
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)
The direction of the inequality is reversed.
5

33. Pi is a ratio of what to what?

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34. The percent decrease of a quantity
52
Two (Ø×2=Ø)
= (actual decrease/Original amount) x 100%
Pi is the ratio of a circle'S circumference to its diameter.

35. 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?
2(pi)r
1
y = (x + 5)/2
10! / (10-3)! = 720

36. 1/2 divided by 3/7 is the same as
Two equal sides and two equal angles.
1/2 times 7/3
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.)
P(E) = 1/1 = 1

37. How to recognize if a # is a multiple of 12
Factors are few - multiples are many.
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.)
Diameter(Pi)
P(E) = ø

38. What is the empty set?
90
A set with no members - denoted by a circle with a diagonal through it.
11 - 13 - 17 - 19
13

39. Volume of a cube
The empty set - denoted by a circle with a diagonal through it.
1/x
Edge³
V=side³

40. The consecutive angles in a parallelogram equal
A²+b²=c²
180°
441000 = 1 10 10 10 21 * 21
An infinite set.

41. If y is directly proportional to x - what does it equal?
12sqrt2
A<-b
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
y/x is a constant

42. To increase a number by x%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
1
x²-2xy+y²
0

43. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
Members or elements
zero
Positive or Negative
2

44. 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))?
27^(-4)
Ø
20.5
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.

45. Legs: 3 - 4. Hypotenuse?
Null
A multiple of every integer
5
The sum of its digits is divisible by 3.

46. 30 60 90
x - x(SR3) - 2x
The shortest arc between points A and B on a circle'S diameter.
3
(length)(width)(height)

47. The important properties of a 45-45-90 triangle?
0
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.
4:5
y = (x + 5)/2

48. Ø Is neither
Positive or Negative
5
3 - -3
Parallelogram

49. When dividing exponential #s with the same base - you do this to the exponents...
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.
Diameter(Pi)
Subtract them. i.e (5^7)/(5^3)= 5^4
Undefined - because we can'T divide by 0.

50. What is a major arc?

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