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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. Simplify (a^2 + b)^2 - (a^2 - b)^2
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
4a^2(b)
Reciprocal

2. Legs 5 - 12. Hypotenuse?
.0004809 X 10^11
13
(a - b)^2
N! / (k!)(n-k)!

3. What are the roots of the quadrinomial x^2 + 2x + 1?
6
The two xes after factoring.
1
Two (Ø×2=Ø)

4. Reduce: 4.8 : 0.8 : 1.6
A chord is a line segment joining two points on a circle.
1
6 : 1 : 2
P(E) = 1/1 = 1

5. Vertical lines
12sqrt2
87.5%
2 & 3/7
Do not have slopes!

6. What is a central angle?
A central angle is an angle formed by 2 radii.
1
18
y = (x + 5)/2

7. The percent decrease of a quantity
Smallest positive integer
A=½bh
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
= (actual decrease/Original amount) x 100%

8. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
2
(a + b)^2
12sqrt2
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.

9. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
The greatest value minus the smallest.
F(x) + c
1 & 37/132
2 & 3/7

10. Ø divided by 7
Ø
1/x
A= (1/2) b*h
130pi

11. If a product of two numbers is Ø - one number must be
2
V=Lwh
Ø
180°

12. How to determine percent decrease?
(pi)r²
1:sqrt3:2
(base*height) / 2
(amount of decrease/original price) x 100%

13. What is a minor arc?

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14. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
N! / (k!)(n-k)!
500
The set of input values for a function.

15. 5/6 in percent?
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
The sum of the digits is a multiple of 9.
y2-y1/x2-x1
83.333%

16. What is the 'Range' of a function?
The set of output values for a function.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
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)
x - x+1 - x+2

17. The only number that is equal to its opposite
Members or elements
441000 = 1 10 10 10 21 * 21
Positive
Ø Ø=Ø

18. A quadrilateral where two diagonals bisect each other
500
6
Parallelogram
Subtract them. i.e (5^7)/(5^3)= 5^4

19. In a Rectangle - each angles measures
Be Zero!
9 & 6/7
90°
C=2 x pi x r OR pi x D

20. Area of a triangle
(x+y)(x-y)
A= (1/2) b*h
A = length x width
(a - b)(a + b)

21. A number is divisible by 4 is...
Its last two digits are divisible by 4.
Pi(diameter)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
10! / (10-3)! = 720

22. Define a 'monomial'
x^(4+7) = x^11
An expression with just one term (-6x - 2a^2)
1/a^6
True

23. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
An arc is a portion of a circumference of a circle.
2
180

24. What is the 'union' of A and B?
The sum of its digits is divisible by 3.
The set of elements which can be found in either A or B.
P(E) = ø
Infinite.

25. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
28. n = 8 - k = 2. n! / k!(n-k)!
8
(rate)(time) d=rt
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50

26. What is the 'Range' of a series of numbers?
M
The empty set - denoted by a circle with a diagonal through it.
3
The greatest value minus the smallest.

27. 8.84 / 5.2
180
90
288 (8 9 4)
1.7

28. Important properties of a 30-60-90 triangle?
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
Ø
3 - 4 - 5
$11 -448

29. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
.0004809 X 10^11
1
The sum of its digits is divisible by 3.

30. Simplify the expression (p^2 - q^2)/ -5(q - p)
$11 -448
A = pi(r^2)
(p + q)/5
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.

31. 30< all primes<40
31 - 37
V=Lwh
A+c<b+c
(a - b)^2

32. What is the graph of f(x) shifted upward c units or spaces?
Every number
C=2 x pi x r OR pi x D
F(x) + c
(pi)r²

33. Solve the quadratic equation ax^2 + bx + c= 0
A set with a number of elements which can be counted.
F(x + c)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
4.25 - 6 - 22

34. (2²)³
26
48
Members or elements
X

35. (x-y)²
x^(4+7) = x^11
x²-2xy+y²
5
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

36. 60 < all primes <70
Ab+ac
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
28
61 - 67

37. factored binomial product of (x-y)²
An infinite set.
x²-2xy+y²
71 - 73 - 79
4a^2(b)

38. How to find the circumference of a circle which circumscribes a square?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
67 - 71 - 73
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
26

39. What is the name of set with a number of elements which cannot be counted?
A set with a number of elements which can be counted.
8
An infinite set.
26

40. 10^6 has how many zeroes?
1.0843 X 10^11
1.7
6
An is positive

41. Ø is a multiple of
Ø
288 (8 9 4)
N! / (k!)(n-k)!
Two (Ø×2=Ø)

42. If a is negative and n is even then an is (positive or negative?)
Ø
(a - b)^2
90pi
An is positive

43. What is a tangent?
Even prime number
11 - 13 - 17 - 19
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
A tangent is a line that only touches one point on the circumference of a circle.

44. When does a function automatically have a restricted domain (2)?
B?b?b (where b is used as a factor n times)
N! / (k!)(n-k)!
Even prime number
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

45. Area of a circle
The union of A and B.
2sqrt6
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A=pi*(r^2)

46. 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?
1/x
10! / 3!(10-3)! = 120
4725
The longest arc between points A and B on a circle'S diameter.

47. Define a 'Term' -
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.
(rate)(time) d=rt
Two equal sides and two equal angles.
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)

48. If an inequality is multiplied or divided by a negative number....
Relationship cannot be determined (what if x is negative?)
The direction of the inequality is reversed.
zero
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

49. 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?
(x+y)(x-y)
No - only like radicals can be added.
The interesection of A and B.
N! / (n-k)!

50. Whats the difference between factors and multiples?
62.5%
A grouping of the members within a set based on a shared characteristic.
Factors are few - multiples are many.
16.6666%