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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. What is the side length of an equilateral triangle with altitude 6?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
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...
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.
The two xes after factoring.

2. Slope
y2-y1/x2-x1
(x+y)(x+y)
1/2 times 7/3
1

3. Solve the quadratic equation ax^2 + bx + c= 0
26
90°
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

4. 25^(1/2) or sqrt. 25 =
Negative
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)
5 OR -5
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

5. What is a finite set?
A tangent is a line that only touches one point on the circumference of a circle.
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
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A set with a number of elements which can be counted.

6. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
Ab=k (k is a constant)
Undefined - because we can'T divide by 0.
V=l×w×h

7. The Denominator can never
The sum of digits is divisible by 9.
Be Zero!
A=½bh
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

8. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
x²-2xy+y²
An arc is a portion of a circumference of a circle.
A grouping of the members within a set based on a shared characteristic.
4725

9. 1/2 divided by 3/7 is the same as
1
The interesection of A and B.
1/2 times 7/3
x²-y²

10. What is the graph of f(x) shifted left c units or spaces?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(p + q)/5
F(x + c)
Positive

11. One is (a prime or not?)
A= (1/2) b*h
1/x
NOT A PRIME
The set of elements found in both A and B.

12. (x-y)²
3
An isosceles right triangle.
x²-2xy+y²
(a - b)(a + b)

13. The product of odd number of negative numbers
(x+y)(x-y)
x²+2xy+y²
(2x7)³
Negative

14. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
8
(p + q)/5
Do not have slopes!
C=2 x pi x r OR pi x D

15. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
180
An is positive
(b + c)

16. If E is certain
P(E) = 1/1 = 1
360°
(a + b)^2
Triangles with same measure and same side lengths.

17. Area of a rectangle
The set of input values for a function.
A = length x width
x²+2xy+y²
The union of A and B.

18. The product of any number x and its reciprocal
28. n = 8 - k = 2. n! / k!(n-k)!
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)
Two angles whose sum is 90.
1

19. b¹
2.592 kg
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
F(x) + c
1

20. What is the slope of a horizontal line?
0
3 - 4 - 5
Undefined - because we can'T divide by 0.
62.5%

21. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
A 30-60-90 triangle.
Even prime number
1

22. Which is greater? 27^(-4) or 9^(-8)
A=(base)(height)
Infinite.
Negative
27^(-4)

23. An Angle that'S 180°
Smallest positive integer
A reflection about the origin.
Straight Angle
(distance)/(rate) d/r

24. a^2 - 2ab + b^2
A percent is a fraction whose denominator is 100.
M= (Y1-Y2)/(X1-X2)
C=2 x pi x r OR pi x D
(a - b)^2

25. x^4 + x^7 =
Two equal sides and two equal angles.
16.6666%
x^(4+7) = x^11
The point of intersection of the systems.

26. 1/Ø=null If a>b then
P(E) = ø
A<-b
9
Right

27. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
The overlapping sections.
2
A<-b
13

28. How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
NOT A PRIME
Even
1:1:sqrt2

29. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
6
90°
A 30-60-90 triangle.
x²+2xy+y²

30. What is the name of set with a number of elements which cannot be counted?
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
71 - 73 - 79
An infinite set.
P=4s (s=side)

31. 1 is a divisor of
Every number
Even
7 / 1000
360/n

32. 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?
13
$3 -500 in the 9% and $2 -500 in the 7%.
x²-y²
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29

33. bn
B?b?b (where b is used as a factor n times)
A central angle is an angle formed by 2 radii.
6
A=pi*(r^2)

34. How to determine percent decrease?
A reflection about the origin.
Two angles whose sum is 180.
(amount of decrease/original price) x 100%
Negative

35. 6w^2 - w - 15 = 0
(x+y)(x+y)
9 & 6/7
3/2 - 5/3
True

36. x^6 / x^3
x^(6-3) = x^3
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Ø=P(E)=1
Infinite.

37. What is the 'domain' of a function?
x^(2(4)) =x^8 = (x^4)^2
(a - b)(a + b)
A reflection about the axis.
The set of input values for a function.

38. Evaluate 3& 2/7 / 1/3
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
9 & 6/7
A²+b²=c²
An isosceles right triangle.

39. What is the name for a grouping of the members within a set based on a shared characteristic?
The sum of the digits is a multiple of 9.
Subtract them. i.e (5^7)/(5^3)= 5^4
A subset.
12! / 5!7! = 792

40. formula for the volume of a cube
4096
Triangles with same measure and same side lengths.
V=side³
3x - 4x - 5x

41. a^2 + 2ab + b^2
(a + b)^2
Even prime number
90pi
Null

42. The Perimeter of a rectangle
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
1 & 37/132
P=2(l+w)

43. Probability of E not occurring:
1 - P(E)
10! / (10-3)! = 720
y = (x + 5)/2
y/x is a constant

44. A number is divisible by 6 if...
Do not have slopes!
y2-y1/x2-x1
Its divisible by 2 and by 3.
13

45. 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?
3/2 - 5/3
x(x - y + 1)
N! / (k!)(n-k)!
Undefined - because we can'T divide by 0.

46. What is the graph of f(x) shifted downward c units or spaces?
Undefined - because we can'T divide by 0.
F(x) - c
Sum of digits is a multiple of 3 and the last digit is even.
12sqrt2

47. Legs 5 - 12. Hypotenuse?
angle that is greater than 90° but less than 180°
The steeper the slope.
Ø
13

48. Describe the relationship between the graphs of x^2 and (1/2)x^2
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
The second graph is less steep.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
P(E) = ø

49. Reduce: 4.8 : 0.8 : 1.6
2^9 / 2 = 256
6 : 1 : 2
4a^2(b)
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

50. factored binomial product of (x-y)²
28
The set of output values for a function.
x²-2xy+y²
An arc is a portion of a circumference of a circle.

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GRE Math: All In One

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