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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. 25^(1/2) or sqrt. 25 =
5
5 OR -5
Ø Ø=Ø
360°

2. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
Negative
An isosceles right triangle.
EVEN

3. 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?
70
5 - 12 - 13
75:11
Factors are few - multiples are many.

4. In a Rectangle - each angles measures
1
90°
(x+y)(x+y)
Null

5. What is the graph of f(x) shifted left c units or spaces?
F(x + c)
Positive
C = 2(pi)r
Ab=k (k is a constant)

6. To multiply a number by 10^x
A=½bh
Move the decimal point to the right x places
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.
Undefined - because we can'T divide by 0.

7. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
1
(pi)r²
70
16.6666%

8. Ø Is neither
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
Infinite.
6
Positive or Negative

9. a^2 - 2ab + b^2
V=Lwh
(a - b)^2
3 - 4 - 5
2

10. Volume of a rectangular box
An infinite set.
1:1:sqrt2
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
V=Lwh

11. What are the smallest three prime numbers greater than 65?
Ø
67 - 71 - 73
180
441000 = 1 10 10 10 21 * 21

12. Simplify the expression [(b^2 - c^2) / (b - c)]
1
(b + c)
28
A²+b²=c²

13. What is the surface area of a cylinder with radius 5 and height 8?
28. n = 8 - k = 2. n! / k!(n-k)!
16.6666%
4.25 - 6 - 22
130pi

14. Ø is
3
Even
The direction of the inequality is reversed.
28

15. bn
B?b?b (where b is used as a factor n times)
(n-2) x 180
D=rt so r= d/t and t=d/r
4096

16. 1 is the
x^(2(4)) =x^8 = (x^4)^2
An angle which is supplementary to an interior angle.
3x - 4x - 5x
Smallest positive integer

17. Ø²
$11 -448
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
A subset.
Ø

18. What is a chord of a circle?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
28
A chord is a line segment joining two points on a circle.
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008

19. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
Every number
x^(6-3) = x^3
2sqrt6
B?b?b (where b is used as a factor n times)

20. What is the 'domain' of a function?
Two (Ø×2=Ø)
The set of input values for a function.
A=½bh
360°

21. x^6 / x^3
1
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
x^(6-3) = x^3
87.5%

22. Whats the difference between factors and multiples?
Relationship cannot be determined (what if x is negative?)
A = pi(r^2)
$11 -448
Factors are few - multiples are many.

23. Define an 'expression'.
130pi
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 tangent is a line that only touches one point on the circumference of a circle.
Positive or Negative

24. If a lamp decreases to $80 - from $100 - what is the decrease in price?
P=2(l+w)
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...
71 - 73 - 79
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

25. What is the ratio of the sides of a 30-60-90 triangle?
A = length x width
1:sqrt3:2
(x+y)(x-y)
A-b is positive

26. If a product of two numbers is Ø - one number must be
A central angle is an angle formed by 2 radii.
C = 2(pi)r
Ø
A set with a number of elements which can be counted.

27. Convert 0.7% to a fraction.
31 - 37
10
0
7 / 1000

28. a(b-c)
Ab-ac
Even
4a^2(b)
1

29. To increase a number by x%
1
F(x-c)
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

30. Slope given 2 points
(a + b)^2
Be Zero!
M= (Y1-Y2)/(X1-X2)
Ø

31. formula for the volume of a cube
The two xes after factoring.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
y2-y1/x2-x1
V=side³

32. 1/2 divided by 3/7 is the same as
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
83.333%
2 & 3/7
1/2 times 7/3

33. What is the empty set?
Ab=k (k is a constant)
A=pi*(r^2)
A set with no members - denoted by a circle with a diagonal through it.
an angle that is less than 90°

34. How to find the circumference of a circle which circumscribes a square?
A = pi(r^2)
F(x) + c
6 : 1 : 2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

35. 25+2³
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
62.5%
8
28

36. a>b then a - b is positive or negative?
4.25 - 6 - 22
A-b is positive
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
441000 = 1 10 10 10 21 * 21

37. Ø Is
EVEN
2(pi)r
72
F(x-c)

38. Can you add sqrt 3 and sqrt 5?
2^9 / 2 = 256
A reflection about the origin.
All numbers multiples of 1.
No - only like radicals can be added.

39. Vertical lines
Factors are few - multiples are many.
P(E) = number of favorable outcomes/total number of possible outcomes
Ø
Do not have slopes!

40. The Perimeter of a Square
Positive
A set with no members - denoted by a circle with a diagonal through it.
180
P=4s (s=side)

41. 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?
No - only like radicals can be added.
48
V=side³
x^(4+7) = x^11

42. binomial product of (x+y)²
(x+y)(x+y)
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
6 : 1 : 2

43. 30 60 90
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
3x - 4x - 5x
x^(2(4)) =x^8 = (x^4)^2
F(x) + c

44. Which is greater? 200x^295 or 10x^294?
(b + c)
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...
A = length x width
Relationship cannot be determined (what if x is negative?)

45. One is (a prime or not?)
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
180°
NOT A PRIME
Yes - like radicals can be added/subtracted.

46. 20<all primes<30
23 - 29
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
A=(base)(height)
1.7

47. The sum of all angles around a point
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)
Diameter(Pi)
The union of A and B.
360°

48. Legs 6 - 8. Hypotenuse?
3 - -3
10
A-b is negative
x^(2(4)) =x^8 = (x^4)^2

49. What is a finite set?
A set with a number of elements which can be counted.
A²+b²=c²
True
$11 -448

50. 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)?
Ø
y = (x + 5)/2
31 - 37
Ø=P(E)=1