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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 the expression [(b^2 - c^2) / (b - c)]
(b + c)
37.5%
D/t (distance)/(time)
72

2. 6w^2 - w - 15 = 0
3/2 - 5/3
The objects within a set.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
(a - b)(a + b)

3. Can you simplify sqrt72?
Members or elements
NOT A PRIME
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
x²-2xy+y²

4. 2³×7³
(2x7)³
1/x
3 - -3
4725

5. a^2 - 2ab + b^2
1.7
2(pi)r
(a - b)^2
1/x

6. If the two sides of a triangle are unequal then the longer side.................
1/a^6
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
Lies opposite the greater angle
A reflection about the axis.

7. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
20.5
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.)
M

8. Is 0 even or odd?
5 - 12 - 13
Even
$3 -500 in the 9% and $2 -500 in the 7%.
87.5%

9. In any polygon - all external angles equal up to
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
360°
V=l×w×h
x - x+1 - x+2

10. Solve the quadratic equation ax^2 + bx + c= 0
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
$11 -448
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
31 - 37

11. The important properties of a 45-45-90 triangle?
x^(2(4)) =x^8 = (x^4)^2
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.
4.25 - 6 - 22
Smallest positive integer

12. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
180°
The sum of its digits is divisible by 3.
1/x

13. What is the set of elements which can be found in either A or B?
1
The union of A and B.
Pi is the ratio of a circle'S circumference to its diameter.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

14. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
Sector area = (n/360) X (pi)r^2
(a + b)^2
3
Diameter(Pi)

15. 30 60 90
3 - 4 - 5
12sqrt2
1/x
Positive

16. Area of a triangle?
(base*height) / 2
Every number
90
y = (x + 5)/2

17. The larger the absolute value of the slope...
6
The steeper the slope.
Negative
y = (x + 5)/2

18. Slope
y2-y1/x2-x1
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Undefined - because we can'T divide by 0.
130pi

19. Volume of a rectangular solid
7 / 1000
180°
(length)(width)(height)
An angle which is supplementary to an interior angle.

20. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
28. n = 8 - k = 2. n! / k!(n-k)!
(pi)r²
67 - 71 - 73
Positive

21. What is the intersection of A and B?
(base*height) / 2
Edge³
The set of elements found in both A and B.
(a - b)^2

22. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
= (actual decrease/Original amount) x 100%
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
441000 = 1 10 10 10 21 * 21

23. When multiplying exponential #s with the same base - you do this to the exponents...
Add them. i.e. (5^7) * (5^3) = 5^10
A chord is a line segment joining two points on a circle.
Ab=k (k is a constant)
48

24. How many sides does a hexagon have?
41 - 43 - 47
6
A+c<b+c
130pi

25. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
An arc is a portion of a circumference of a circle.
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.
A subset.

26. Simplify 9^(1/2) X 4^3 X 2^(-6)?
Even
3
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
(a + b)^2

27. (x-y)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)
x²-2xy+y²
Ø
Diameter(Pi)

28. x^4 + x^7 =
EVEN
x^(4+7) = x^11
90°
180

29. What is a percent?
A percent is a fraction whose denominator is 100.
The greatest value minus the smallest.
.0004809 X 10^11
y = 2x^2 - 3

30. What are the integers?
All numbers multiples of 1.
(a - b)(a + b)
18
x²+2xy+y²

31. 10^6 has how many zeroes?
(p + q)/5
6
70
F(x) - c

32. What are 'Supplementary angles?'
Two angles whose sum is 180.
180
2sqrt6
EVEN

33. 2 is the only
71 - 73 - 79
Even prime number
B?b?b (where b is used as a factor n times)
An is positive

34. What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
A = length x width
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
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.)

35. If an inequality is multiplied or divided by a negative number....
Parallelogram
The direction of the inequality is reversed.
A percent is a fraction whose denominator is 100.
Lies opposite the greater angle

36. Can you add sqrt 3 and sqrt 5?
Ø
No - only like radicals can be added.
(a - b)(a + b)
3

37. Whats the difference between factors and multiples?
F(x-c)
3 - -3
Factors are few - multiples are many.
Can be negative - zero - or positive

38. What is the surface area of a cylinder with radius 5 and height 8?
9 & 6/7
130pi
A+c<b+c
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

39. Legs: 3 - 4. Hypotenuse?
A reflection about the origin.
An arc is a portion of a circumference of a circle.
5
x^(6-3) = x^3

40. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
500
y = (x + 5)/2
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
71 - 73 - 79

41. Number of degrees in a triangle
180
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.
1/2 times 7/3
52

42. The perimeter of a square is 48 inches. The length of its diagonal is:
90°
(p + q)/5
12sqrt2
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

43. factored binomial product of (x-y)²
x²-2xy+y²
(x+y)(x-y)
441000 = 1 10 10 10 21 * 21
= (actual decrease/Original amount) x 100%

44. Define an 'expression'.
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)
F(x + c)
C=2 x pi x r OR pi x D
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

45. The product of odd number of negative numbers
A+c<b+c
The steeper the slope.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Negative

46. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The set of input values for a function.
10! / (10-3)! = 720
61 - 67

47. What is the side length of an equilateral triangle with altitude 6?
2 & 3/7
5 OR -5
(n-2) x 180
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...

48. formula for area of a triangle
A=½bh
A reflection about the origin.
A=(base)(height)
The sum of the digits is a multiple of 9.

49. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
The set of output values for a function.
A 30-60-90 triangle.
An angle which is supplementary to an interior angle.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60

50. Area of a triangle
N! / (n-k)!
1 - P(E)
4a^2(b)
A= (1/2) b*h