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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. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
1
180
P=4s (s=side)

2. The Perimeter of a rectangle
180
$11 -448
Sector area = (n/360) X (pi)r^2
P=2(l+w)

3. Rate
(a + b)^2
Its divisible by 2 and by 3.
D/t (distance)/(time)
360°

4. What is the graph of f(x) shifted right c units or spaces?
Add them. i.e. (5^7) * (5^3) = 5^10
3/2 - 5/3
A-b is negative
F(x-c)

5. Legs 5 - 12. Hypotenuse?
4725
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
V=l×w×h
13

6. What is a set with no members called?
A natural number greater than 1 that has no positive divisors other than 1 and itself
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
1
The empty set - denoted by a circle with a diagonal through it.

7. Simplify the expression [(b^2 - c^2) / (b - c)]
$3 -500 in the 9% and $2 -500 in the 7%.
The objects within a set.
(b + c)
Pi is the ratio of a circle'S circumference to its diameter.

8. What percent of 40 is 22?
55%
10! / 3!(10-3)! = 120
A reflection about the axis.
Factors are few - multiples are many.

9. What is an exterior angle?
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.
A=pi*(r^2)
1.7
An angle which is supplementary to an interior angle.

10. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
x²+2xy+y²
A reflection about the origin.
A<-b
5 - 12 - 13

11. Area of a Parallelogram:
x - x(SR3) - 2x
y = 2x^2 - 3
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
A=(base)(height)

12. Which is greater? 27^(-4) or 9^(-8)
The steeper the slope.
Ø=P(E)=1
A = length x width
27^(-4)

13. Product of any number and Ø is
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
x - x(SR3) - 2x
Undefined
Ø

14. Legs 6 - 8. Hypotenuse?
1.0843 X 10^11
10
90pi
72

15. 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)!
28. n = 8 - k = 2. n! / k!(n-k)!
(a - b)(a + b)
180

16. formula for distance problems
10! / (10-3)! = 720
C = 2(pi)r
A percent is a fraction whose denominator is 100.
Distance=rate×time or d=rt

17. Area of a circle
... the square of the ratios of the corresponding sides.
A=pi*(r^2)
F(x-c)
x²+2xy+y²

18. What are the real numbers?
(p + q)/5
A²+b²=c²
4.25 - 6 - 22
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)

19. How to find the circumference of a circle which circumscribes a square?
(rate)(time) d=rt
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
13pi / 2
Relationship cannot be determined (what if x is negative?)

20. What is a minor arc?

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21. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
(a + b)^2
(base*height) / 2
Ab-ac

22. 20<all primes<30
The sum of the digits is a multiple of 9.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
23 - 29
All numbers multiples of 1.

23. What is the 'Range' of a function?
An arc is a portion of a circumference of a circle.
The set of output values for a function.
An expression with just one term (-6x - 2a^2)
Triangles with same measure and same side lengths.

24. 5/6 in percent?
The objects within a set.
83.333%
360/n
EVEN

25. To decrease a number by x%
3 - 4 - 5
9 & 6/7
The steeper the slope.
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50

26. binomial product of (x+y)²
(x+y)(x+y)
(distance)/(rate) d/r
Ab=k (k is a constant)
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

27. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
A percent is a fraction whose denominator is 100.
Add them. i.e. (5^7) * (5^3) = 5^10
8

28. Factor a^2 + 2ab + b^2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A natural number greater than 1 that has no positive divisors other than 1 and itself
The set of elements which can be found in either A or B.
(a + b)^2

29. The sum of the measures of the n angles in a polygon with n sides
(n-2) x 180
6
6 : 1 : 2
Null

30. formula for volume of a rectangular solid
Edge³
90°
V=l×w×h
(x+y)(x+y)

31. What is the sum of the angles of a triangle?
All numbers multiples of 1.
12sqrt2
An is positive
180 degrees

32. Formula to find a circle'S circumference from its radius?
The direction of the inequality is reversed.
180
Ø
C = 2(pi)r

33. 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?
75:11
90
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.)
A = length x width

34. Ø²
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
y = (x + 5)/2
500
Ø

35. a^2 - 2ab + b^2
12.5%
1:1:sqrt2
Can be negative - zero - or positive
(a - b)^2

36. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
Two angles whose sum is 90.
10! / 3!(10-3)! = 120
A 30-60-90 triangle.

37. A number is divisible by 6 if...
9 & 6/7
90pi
Its divisible by 2 and by 3.
11 - 13 - 17 - 19

38. What is the maximum value for the function g(x) = (-2x^2) -1?
1
Ab+ac
72
NOT A PRIME

39. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
C = 2(pi)r
P= 2L + 2w
y = (x + 5)/2
A 30-60-90 triangle.

40. Formula for the area of a sector of a circle?
A multiple of every integer
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
5
Sector area = (n/360) X (pi)r^2

41. What is the set of elements found in both A and B?
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
The interesection of A and B.
Two equal sides and two equal angles.
Move the decimal point to the right x places

42. 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?
The sum of digits is divisible by 9.
4096
10! / (10-3)! = 720
The overlapping sections.

43. Perfect Squares 1-15
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
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.
x^(2(4)) =x^8 = (x^4)^2
A reflection about the axis.

44. What is the measure of an exterior angle of a regular pentagon?
Ab=k (k is a constant)
Ø
N! / (k!)(n-k)!
72

45. The negative exponent x?n is equivalent to what?
D=rt so r= d/t and t=d/r
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
5
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

46. Can you add sqrt 3 and sqrt 5?
An arc is a portion of a circumference of a circle.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
No - only like radicals can be added.
Pi is the ratio of a circle'S circumference to its diameter.

47. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
(pi)r²
2.592 kg
10! / 3!(10-3)! = 120
A reflection about the origin.

48. X is the opposite of
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
X
Positive
10! / (10-3)! = 720

49. What are the roots of the quadrinomial x^2 + 2x + 1?
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
The two xes after factoring.
The sum of the digits is a multiple of 9.
The second graph is less steep.

50. In a Regular Polygon - the measure of each exterior angle
360/n
(rate)(time) d=rt
87.5%
A reflection about the axis.