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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. What is the graph of f(x) shifted downward c units or spaces?
41 - 43 - 47
F(x) - c
Positive or Negative
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

2. Obtuse Angle
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
A natural number greater than 1 that has no positive divisors other than 1 and itself
A=pi*(r^2)
angle that is greater than 90° but less than 180°

3. If a is negative and n is even then an is (positive or negative?)
9
53 - 59
An is positive
1/a^6

4. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
(distance)/(rate) d/r
67 - 71 - 73
1 & 37/132

5. The Perimeter of a Square
P=4s (s=side)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
An expression with just one term (-6x - 2a^2)
A=(base)(height)

6. 5/8 in percent?
6
= (actual decrease/Original amount) x 100%
Do not have slopes!
62.5%

7. If a lamp decreases to $80 - from $100 - what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
... the square of the ratios of the corresponding sides.
4725
18

8. 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)]?
Ab+ac
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
True
Two equal sides and two equal angles.

9. Vertical lines
Factors are few - multiples are many.
Do not have slopes!
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Ab=k (k is a constant)

10. (x-y)(x+y)
(x+y)(x+y)
(n-2) x 180
Every number
x²-y²

11. For any number x
Be Zero!
(base*height) / 2
Can be negative - zero - or positive
3

12. Factor x^2 - xy + x.
4.25 - 6 - 22
x(x - y + 1)
Ø=P(E)=1
180

13. The product of any number x and its reciprocal
The objects within a set.
x²-2xy+y²
1
Every number

14. Consecutive integers
x - x+1 - x+2
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
500
180

15. (a^-1)/a^5
Null
Can be negative - zero - or positive
1/a^6
10! / (10-3)! = 720

16. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
12.5%
Distance=rate×time or d=rt
4725

17. 5x^2 - 35x -55 = 0
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.)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
M
A=(base)(height)

18. How to recognize a multiple of 6
Sum of digits is a multiple of 3 and the last digit is even.
360/n
Even
55%

19. Simplify the expression (p^2 - q^2)/ -5(q - p)
Ø
Edge³
Two angles whose sum is 180.
(p + q)/5

20. What percent of 40 is 22?
55%
3 - 4 - 5
441000 = 1 10 10 10 21 * 21
ODD number

21. Slope
P=2(l+w)
(length)(width)(height)
y2-y1/x2-x1
A tangent is a line that only touches one point on the circumference of a circle.

22. Legs 6 - 8. Hypotenuse?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
10
y/x is a constant
18

23. What is the side length of an equilateral triangle with altitude 6?
27
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...
True
2 & 3/7

24. What is the name for a grouping of the members within a set based on a shared characteristic?
10! / (10-3)! = 720
A subset.
An is positive
1 & 37/132

25. What are the members or elements of a set?
Its divisible by 2 and by 3.
31 - 37
The objects within a set.
9 : 25

26. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
B?b?b (where b is used as a factor n times)
20.5
A reflection about the origin.

27. First 10 prime #s
Positive
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
20.5
1

28. 1/2 divided by 3/7 is the same as
1/2 times 7/3
27
A= (1/2) b*h
90pi

29. Convert 0.7% to a fraction.
7 / 1000
2^9 / 2 = 256
1
Its divisible by 2 and by 3.

30. The sum of the angles in a quadrilateral is
12! / 5!7! = 792
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
D/t (distance)/(time)
360°

31. How to determine percent decrease?
A central angle is an angle formed by 2 radii.
83.333%
The shortest arc between points A and B on a circle'S diameter.
(amount of decrease/original price) x 100%

32. The reciprocal of any non-zero #x is
P(E) = 1/1 = 1
A chord is a line segment joining two points on a circle.
1/x
Triangles with same measure and same side lengths.

33. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
3 - 4 - 5
360°
4:5
x^(4+7) = x^11

34. The ratio of the areas of two similar polygons is ...
180
... the square of the ratios of the corresponding sides.
An arc is a portion of a circumference of a circle.
13

35. What is the set of elements which can be found in either A or B?
The union of A and B.
(n-2) x 180
D/t (distance)/(time)
1/a^6

36. Whats the difference between factors and multiples?
C = 2(pi)r
Factors are few - multiples are many.
1:1:sqrt2
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

37. Important properties of a 30-60-90 triangle?
The empty set - denoted by a circle with a diagonal through it.
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
1
4:5

38. Legs: 3 - 4. Hypotenuse?
Two angles whose sum is 180.
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.)
23 - 29
5

39. 25/2³
2²
1
x²-2xy+y²
1

40. x^4 + x^7 =
Negative
x^(4+7) = x^11
2.592 kg
1

41. Simplify the expression [(b^2 - c^2) / (b - c)]
(a + b)^2
(b + c)
y = (x + 5)/2
The greatest value minus the smallest.

42. What is an isoceles triangle?
NOT A PRIME
Two equal sides and two equal angles.
Relationship cannot be determined (what if x is negative?)
The point of intersection of the systems.

43. formula for the volume of a cube
Triangles with same measure and same side lengths.
V=side³
180 degrees
90

44. 70 < all primes< 80
71 - 73 - 79
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 grouping of the members within a set based on a shared characteristic.
N! / (n-k)!

45. 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?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Negative
The two xes after factoring.
N! / (n-k)!

46. What is the measure of an exterior angle of a regular pentagon?
Indeterminable.
6 : 1 : 2
90°
72

47. A number is divisible by 9 if...
The sum of digits is divisible by 9.
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
3 - 4 - 5
(a - b)(a + b)

48. 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?
A subset.
N! / (k!)(n-k)!
48
2 & 3/7

49. What are complementary angles?
M
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...
F(x-c)
Two angles whose sum is 90.

50. In a Rectangle - each angles measures
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
Every number
6 : 1 : 2
90°