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GRE Math: All In One

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 add sqrt 3 and sqrt 5?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
No - only like radicals can be added.
The empty set - denoted by a circle with a diagonal through it.
90

2. 5x^2 - 35x -55 = 0
x^(4+7) = x^11
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Pi is the ratio of a circle'S circumference to its diameter.
13pi / 2

3. Ø is a multiple of
A reflection about the axis.
A grouping of the members within a set based on a shared characteristic.
A²+b²=c²
Two (Ø×2=Ø)

4. What is a percent?
A percent is a fraction whose denominator is 100.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The greatest value minus the smallest.
y2-y1/x2-x1

5. formula for distance problems
Distance=rate×time or d=rt
... the square of the ratios of the corresponding sides.
3
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

6. a^2 + 2ab + b^2
90°
(a + b)^2
4:5
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

7. a^0 =
Every number
Every number
X
1

8. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
2^9 / 2 = 256
An arc is a portion of a circumference of a circle.
28. n = 8 - k = 2. n! / k!(n-k)!
23 - 29

9. What is the 'Solution' for a set of inequalities.
The overlapping sections.
Factors are few - multiples are many.
(a + b)^2
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)

10. -3³
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
27
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
27^(-4)

11. Factor a^2 + 2ab + b^2
A= (1/2) b*h
(a + b)^2
A=pi*(r^2)
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60

12. a(b+c)
Ab+ac
An arc is a portion of a circumference of a circle.
1.0843 X 10^11
13pi / 2

13. Simplify (a^2 + b)^2 - (a^2 - b)^2
P(E) = number of favorable outcomes/total number of possible outcomes
Members or elements
4a^2(b)
67 - 71 - 73

14. What are congruent triangles?
4:5
1
Triangles with same measure and same side lengths.
67 - 71 - 73

15. A number is divisible by 6 if...
180°
Straight Angle
$11 -448
Its divisible by 2 and by 3.

16. Circumference of a circle
2(pi)r
An expression with just one term (-6x - 2a^2)
500
41 - 43 - 47

17. Area of a Parallelogram:
A=(base)(height)
Parallelogram
Ab-ac
F(x-c)

18. Rate
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
an angle that is less than 90°
A percent is a fraction whose denominator is 100.
D/t (distance)/(time)

19. the slope of a line in y=mx+b
The shortest arc between points A and B on a circle'S diameter.
F(x) - c
The sum of the digits is a multiple of 9.
M

20. The product of any number x and its reciprocal
An infinite set.
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)
1/a^6

21. What number between 70 & 75 - inclusive - has the greatest number of factors?
An is positive
M
EVEN
72

22. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
y = (x + 5)/2
P= 2L + 2w
Ø

23. If y is directly proportional to x - what does it equal?
y/x is a constant
(pi)r²
Triangles with same measure and same side lengths.
1

24. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A+c<b+c
Relationship cannot be determined (what if x is negative?)
The shortest arc between points A and B on a circle'S diameter.
A reflection about the origin.

25. 3 is the opposite of
x - x(SR3) - 2x
(a - b)(a + b)
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
3

26. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
The shortest arc between points A and B on a circle'S diameter.
Even
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

27. What are the integers?
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.)
All numbers multiples of 1.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
1 - P(E)

28. The objects in a set are called two names:
Members or elements
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.
28. n = 8 - k = 2. n! / k!(n-k)!
An is positive

29. a(b-c)
Ab-ac
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
3
Triangles with same measure and same side lengths.

30. Is 0 even or odd?
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
(pi)r²
The overlapping sections.
Even

31. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Reciprocal
6
2^9 / 2 = 256

32. Ø²
Ø
Every number
52
Can be negative - zero - or positive

33. (x^2)^4
180 degrees
x^(2(4)) =x^8 = (x^4)^2
180°
Ab-ac

34. Describe the relationship between 3x^2 and 3(x - 1)^2
4096
2 & 3/7
The shortest arc between points A and B on a circle'S diameter.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

35. What is the 'Range' of a function?
Every number
... the square of the ratios of the corresponding sides.
(2x7)³
The set of output values for a function.

36. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
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.
130pi
Ab+ac
Smallest positive integer

37. 30 60 90
A=pi*(r^2)
3 - 4 - 5
31 - 37
M

38. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
The union of A and B.
70
Yes - like radicals can be added/subtracted.
.0004809 X 10^11

39. x^4 + x^7 =
x²-2xy+y²
1
x^(4+7) = x^11
Arc length = (n/360) x pi(2r) where n is the number of degrees.

40. 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?
23 - 29
$3 -500 in the 9% and $2 -500 in the 7%.
ODD number
An arc is a portion of a circumference of a circle.

41. Simplify 9^(1/2) X 4^3 X 2^(-6)?
The sum of digits is divisible by 9.
41 - 43 - 47
Positive
3

42. One is (a prime or not?)
NOT A PRIME
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.
1:1:sqrt2
Ø

43. 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))?
28
Cd
zero
20.5

44. a^2 - b^2 =
x - x+1 - x+2
Two angles whose sum is 90.
Sector area = (n/360) X (pi)r^2
(a - b)(a + b)

45. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
The sum of digits is divisible by 9.
1/a^6
V=l×w×h

46. 5/8 in percent?
Two (Ø×2=Ø)
62.5%
87.5%
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

47. What is the ratio of the sides of a 30-60-90 triangle?
180°
A central angle is an angle formed by 2 radii.
(p + q)/5
1:sqrt3:2

48. Slope of any line that goes up from left to right
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Positive
Even prime number
90pi

49. Legs 6 - 8. Hypotenuse?
The second graph is less steep.
Positive or Negative
9
10

50. What are the smallest three prime numbers greater than 65?
1 & 37/132
Positive or Negative
Its divisible by 2 and by 3.
67 - 71 - 73

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GRE Math: All In One

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