Test your basic knowledge |

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. What is a chord of a circle?
3
1:1:sqrt2
x^(6-3) = x^3
A chord is a line segment joining two points on a circle.

2. What is an isoceles triangle?
X
72
90pi
Two equal sides and two equal angles.

3. (x-y)(x+y)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1:1:sqrt2
y = (x + 5)/2
x²-y²

4. How to find the circumference of a circle which circumscribes a square?
Undefined
3 - -3
75:11
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

5. Time
Reciprocal
180
13
(distance)/(rate) d/r

6. (x-y)²
x²-2xy+y²
A central angle is an angle formed by 2 radii.
Add them. i.e. (5^7) * (5^3) = 5^10
1 & 37/132

7. The ratio of the areas of two similar polygons is ...
8
The greatest value minus the smallest.
... the square of the ratios of the corresponding sides.
X

8. What are complementary angles?
A natural number greater than 1 that has no positive divisors other than 1 and itself
The longest arc between points A and B on a circle'S diameter.
Two angles whose sum is 90.
26

9. What is the graph of f(x) shifted left c units or spaces?
The triangle is a right triangle. The hypotenuse is twice the length of the shorter leg. The ratio of the length of the three sides is x:xv3:2x
Right
3
F(x + c)

10. the measure of a straight angle
7 / 1000
F(x + c)
A natural number greater than 1 that has no positive divisors other than 1 and itself
180°

11. First 10 prime #s
The overlapping sections.
F(x) + c
(a - b)^2
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29

12. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
V=l×w×h
18
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
28. n = 8 - k = 2. n! / k!(n-k)!

13. What is the 'domain' of a function?
The set of input values for a function.
A= (1/2) b*h
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
3

14. Factor x^2 - xy + x.
Negative
An expression with just one term (-6x - 2a^2)
x(x - y + 1)
Ø

15. 5x^2 - 35x -55 = 0
(a - b)(a + b)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
A chord is a line segment joining two points on a circle.
(p + q)/5

16. 1/2 divided by 3/7 is the same as
x - x(SR3) - 2x
Sum of digits is a multiple of 3 and the last digit is even.
1/2 times 7/3
The greatest value minus the smallest.

17. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
The objects within a set.
The interesection of A and B.
B?b?b (where b is used as a factor n times)

18. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
4a^2(b)
3
Factors are few - multiples are many.
Null

19. The sum of the measures of the n angles in a polygon with n sides
1.0843 X 10^11
(n-2) x 180
Triangles with same measure and same side lengths.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

20. What is the 'union' of A and B?
41 - 43 - 47
B?b?b (where b is used as a factor n times)
The interesection of A and B.
The set of elements which can be found in either A or B.

21. 10^6 has how many zeroes?
P=4s (s=side)
6
A<-b
Indeterminable.

22. The product of odd number of negative numbers
P=2(l+w)
The set of elements found in both A and B.
All numbers multiples of 1.
Negative

23. Which is greater? 64^5 or 16^8
y/x is a constant
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
2sqrt6
2²

24. X is the opposite of
X
Even prime number
An is positive
(distance)/(rate) d/r

25. 8.84 / 5.2
1.7
360°
Arc length = (n/360) x pi(2r) where n is the number of degrees.
1

26. If E is certain
75:11
13
P(E) = 1/1 = 1
Triangles with same measure and same side lengths.

27. What are 'Supplementary angles?'
1
x(x - y + 1)
1
Two angles whose sum is 180.

28. How many multiples does a given number have?
Reciprocal
3
Infinite.
70

29. 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?
N! / (n-k)!
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
Positive
3 - -3

30. 4.809 X 10^7 =
(a + b)^2
1
Every number
.0004809 X 10^11

31. (x+y)²
x²+2xy+y²
18
The steeper the slope.
P(E) = number of favorable outcomes/total number of possible outcomes

32. formula for volume of a rectangular solid
An arc is a portion of a circumference of a circle.
V=l×w×h
y2-y1/x2-x1
The steeper the slope.

33. 20<all primes<30
12! / 5!7! = 792
360°
23 - 29
P(E) = number of favorable outcomes/total number of possible outcomes

34. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
28
B?b?b (where b is used as a factor n times)

35. 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?
37.5%
y/x is a constant
10
$3 -500 in the 9% and $2 -500 in the 7%.

36. What is the set of elements found in both A and B?
Two angles whose sum is 90.
(a - b)(a + b)
6 : 1 : 2
The interesection of A and B.

37. Formula to find a circle'S circumference from its diameter?
C = (pi)d
Factors are few - multiples are many.
A chord is a line segment joining two points on a circle.
Lies opposite the greater angle

38. When dividing exponential #s with the same base - you do this to the exponents...
8
Subtract them. i.e (5^7)/(5^3)= 5^4
V=l×w×h
A-b is positive

39. In a Regular Polygon - the measure of each exterior angle
An is positive
360/n
1
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

40. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
4.25 - 6 - 22
Add them. i.e. (5^7) * (5^3) = 5^10
$11 -448
16.6666%

41. A number is divisible by 6 if...
9 : 25
Two equal sides and two equal angles.
Its divisible by 2 and by 3.
y/x is a constant

42. 10<all primes<20
1 - P(E)
11 - 13 - 17 - 19
3
An expression with just one term (-6x - 2a^2)

43. 30< all primes<40
31 - 37
(rate)(time) d=rt
10! / 3!(10-3)! = 120
(a + b)^2

44. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
288 (8 9 4)
10! / 3!(10-3)! = 120
The interesection of A and B.

45. What is the surface area of a cylinder with radius 5 and height 8?
130pi
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
A natural number greater than 1 that has no positive divisors other than 1 and itself
The empty set - denoted by a circle with a diagonal through it.

46. Area of a circle
61 - 67
x^(2(4)) =x^8 = (x^4)^2
4096
A=pi*(r^2)

47. 50 < all primes< 60
Negative
9 & 6/7
Straight Angle
53 - 59

48. 1 is an
Edge³
ODD number
x(x - y + 1)
70

49. 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?
x²-2xy+y²
N! / (k!)(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)
Cd

50. Can you add sqrt 3 and sqrt 5?
x^(6-3) = x^3
No - only like radicals can be added.
83.333%
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)