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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.
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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. a^2 - b^2 =
72
(a - b)(a + b)
Add them. i.e. (5^7) * (5^3) = 5^10
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)

2. 1 is an
9
ODD number
Negative
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.

3. For any number x
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
P(E) = number of favorable outcomes/total number of possible outcomes
An isosceles right triangle.
Can be negative - zero - or positive

4. The larger the absolute value of the slope...
Smallest positive integer
The steeper the slope.
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)
180

5. Formula to find a circle'S circumference from its radius?
500
Its last two digits are divisible by 4.
C = 2(pi)r
y2-y1/x2-x1

6. How many 3-digit positive integers are even and do not contain the digit 4?
(amount of decrease/original price) x 100%
180 degrees
288 (8 9 4)
C = (pi)d

7. 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)
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The shortest arc between points A and B on a circle'S diameter.
V=side³
4.25 - 6 - 22

8. 6w^2 - w - 15 = 0
An is positive
3/2 - 5/3
A=(base)(height)
9 : 25

9. What is the side length of an equilateral triangle with altitude 6?
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...
(b + c)
12.5%
83.333%

10. Area of a triangle
F(x) + c
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
1:1:sqrt2
A= (1/2) b*h

11. Find distance when given time and rate
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
D=rt so r= d/t and t=d/r
2
360°

12. Area of a Parallelogram:
True
A=(base)(height)
A natural number greater than 1 that has no positive divisors other than 1 and itself
x²-2xy+y²

13. 1 is a divisor of
The sum of its digits is divisible by 3.
13
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Every number

14. What is a central angle?
A central angle is an angle formed by 2 radii.
A natural number greater than 1 that has no positive divisors other than 1 and itself
9
P(E) = number of favorable outcomes/total number of possible outcomes

15. Area of a circle
90
(pi)r²
C = 2(pi)r
y = (x + 5)/2

16. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
1
16.6666%
ODD number
8

17. Perfect Squares 1-15
C = (pi)d
Ø=P(E)=1
3
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

18. a<b then a - b is positive or negative?
A-b is negative
4.25 - 6 - 22
P(E) = number of favorable outcomes/total number of possible outcomes
The two xes after factoring.

19. 3 is the opposite of
x²-y²
Infinite.
A 30-60-90 triangle.
3

20. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
10! / (10-3)! = 720
9 : 25
Can be negative - zero - or positive
71 - 73 - 79

21. What percent of 40 is 22?
37.5%
55%
3
31 - 37

22. What is a major arc?

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23. In any polygon - all external angles equal up to
9 : 25
360°
(p + q)/5
ODD number

24. The objects in a set are called two names:
A = length x width
x - x+1 - x+2
Members or elements
A=½bh

25. Circumference of a circle?
180°
Diameter(Pi)
The second graph is less steep.
28. n = 8 - k = 2. n! / k!(n-k)!

26. The important properties of a 45-45-90 triangle?
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.
Do not have slopes!
(a - b)^2
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

27. A quadrilateral where two diagonals bisect each other
C = (pi)d
(a + b)^2
360°
Parallelogram

28. a(b+c)
Ab+ac
(base*height) / 2
2 & 3/7
A reflection about the axis.

29. One is (a prime or not?)
NOT A PRIME
A=pi*(r^2)
An isosceles right triangle.
An expression with just one term (-6x - 2a^2)

30. Ø²
y = 2x^2 - 3
4.25 - 6 - 22
Two equal sides and two equal angles.
Ø

31. 60 < all primes <70
Cd
61 - 67
360/n
Yes - like radicals can be added/subtracted.

32. (6sqrt3) x (2sqrt5) =
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
x^(6-3) = x^3
1

33. Factor a^2 + 2ab + b^2
A=½bh
... the square of the ratios of the corresponding sides.
5 OR -5
(a + b)^2

34. What is an arc of a circle?
An arc is a portion of a circumference of a circle.
28
180 degrees
Subtract them. i.e (5^7)/(5^3)= 5^4

35. x^2 = 9. What is the value of x?
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.
3 - -3
NOT A PRIME
D/t (distance)/(time)

36. Ø is a multiple of
Two (Ø×2=Ø)
4096
1/x
1/a^6

37. The Perimeter of a Square
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
1
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
P=4s (s=side)

38. A number is divisible by 9 if...
(length)(width)(height)
C = 2(pi)r
The sum of digits is divisible by 9.
Two equal sides and two equal angles.

39. How to recognize a # as a multiple of 3
N! / (n-k)!
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)
2^9 / 2 = 256
Add them. i.e. (5^7) * (5^3) = 5^10

40. To increase a number by x%
4:5
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
(b + c)
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

41. -3²
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The sum of the digits is a multiple of 9.
9
Lies opposite the greater angle

42. What is the sum of the angles of a triangle?
0
1/2 times 7/3
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.)
180 degrees

43. formula for distance problems
3/2 - 5/3
67 - 71 - 73
Distance=rate×time or d=rt
180°

44. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
3
4:5
B?b?b (where b is used as a factor n times)
Add them. i.e. (5^7) * (5^3) = 5^10

45. 8.84 / 5.2
1.7
A=(base)(height)
90
90°

46. the measure of a straight angle
V=side³
180°
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A grouping of the members within a set based on a shared characteristic.

47. Area of a triangle?
23 - 29
(base*height) / 2
A set with a number of elements which can be counted.
The shortest arc between points A and B on a circle'S diameter.

48. a^0 =
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
37.5%
1
90°

49. a^2 - 2ab + b^2
(length)(width)(height)
P(E) = number of favorable outcomes/total number of possible outcomes
(a - b)^2
Ø=P(E)=1

50. 10^6 has how many zeroes?
Undefined
An angle which is supplementary to an interior angle.
6
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.

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GRE Math: All In One

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