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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. a^2 - b^2
(a - b)(a + b)
4725
Yes - like radicals can be added/subtracted.
83.333%

2. 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?
441000 = 1 10 10 10 21 * 21
x²-y²
Even
1

3. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
Positive
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
1
4725

4. (x^2)^4
3 - -3
The two xes after factoring.
F(x + c)
x^(2(4)) =x^8 = (x^4)^2

5. Slope of any line that goes up from left to right
Arc length = (n/360) x pi(2r) where n is the number of degrees.
10! / (10-3)! = 720
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Positive

6. a^0 =
1
1/a^6
An infinite set.
Do not have slopes!

7. 1/8 in percent?
12.5%
55%
Triangles with same measure and same side lengths.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

8. What is the ratio of the sides of a 30-60-90 triangle?
A= (1/2) b*h
Two angles whose sum is 180.
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
1:sqrt3:2

9. Is 0 even or odd?
An isosceles right triangle.
C=2 x pi x r OR pi x D
Positive or Negative
Even

10. The percent decrease of a quantity
90pi
(n-2) x 180
= (actual decrease/Original amount) x 100%
A = length x width

11. 0^0
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.)
Ø
Undefined
26

12. What is the sum of the angles of a triangle?
Ø
180 degrees
0
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

13. The only number that is equal to its opposite
The greatest value minus the smallest.
Ø Ø=Ø
The interesection of A and B.
Null

14. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
3/2 - 5/3
The objects within a set.
A reflection about the axis.

15. How to determine percent decrease?
(amount of decrease/original price) x 100%
1:sqrt3:2
V=side³
87.5%

16. (x-y)²
x²-2xy+y²
... the square of the ratios of the corresponding sides.
360°
A 30-60-90 triangle.

17. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
90
Subtract them. i.e (5^7)/(5^3)= 5^4
The set of elements which can be found in either A or B.

18. Define a 'Term' -
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)
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
D/t (distance)/(time)
Lies opposite the greater angle

19. The ratio of the areas of two similar polygons is ...
10! / 3!(10-3)! = 120
Lies opposite the greater angle
The two xes after factoring.
... the square of the ratios of the corresponding sides.

20. a^2 - 2ab + b^2
Its divisible by 2 and by 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
(a - b)^2
3

21. The larger the absolute value of the slope...
An infinite set.
V=l×w×h
The steeper the slope.
2(pi)r

22. How do you solve proportions? a/b=c/d
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
The set of input values for a function.
V=l×w×h
61 - 67

23. (2²)³
26
x²-y²
4725
Two angles whose sum is 90.

24. Ø is
True
A multiple of every integer
An is positive
A+c<b+c

25. What is the area of a regular hexagon with side 6?
F(x-c)
x - x(SR3) - 2x
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
y = 2x^2 - 3

26. What is a subset?
A grouping of the members within a set based on a shared characteristic.
The set of elements found in both A and B.
2sqrt6
1/a^6

27. 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?
10! / 3!(10-3)! = 120
90pi
2^9 / 2 = 256
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...

28. How many 3-digit positive integers are even and do not contain the digit 4?
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
2²
288 (8 9 4)
Ø

29. Which is greater? 200x^295 or 10x^294?
A multiple of every integer
Relationship cannot be determined (what if x is negative?)
5 - 12 - 13
Positive

30. What is a finite set?
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)
5
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)
A set with a number of elements which can be counted.

31. 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))?
12! / 5!7! = 792
A reflection about the origin.
20.5
Distance=rate×time or d=rt

32. What is the side length of an equilateral triangle with altitude 6?
10! / (10-3)! = 720
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 set of elements found in both A and B.
71 - 73 - 79

33. Area of a circle
1/x
(pi)r²
Arc length = (n/360) x pi(2r) where n is the number of degrees.
6

34. First 10 prime #s
20.5
The sum of digits is divisible by 9.
1/x
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29

35. 25+2³
12sqrt2
28
The two xes after factoring.
The objects within a set.

36. To increase a number by x%
180
Even
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
P=2(l+w)

37. What is the maximum value for the function g(x) = (-2x^2) -1?
1
Two angles whose sum is 180.
.0004809 X 10^11
C = 2(pi)r

38. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
x²-2xy+y²
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.
Sector area = (n/360) X (pi)r^2
Ø

39. Positive integers that have exactly 2 positive divisors are
(amount of decrease/original price) x 100%
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
zero
52

40. For any number x
P(E) = number of favorable outcomes/total number of possible outcomes
Can be negative - zero - or positive
F(x) + c
The set of elements found in both A and B.

41. Perimeter of a rectangle
P= 2L + 2w
y = 2x^2 - 3
2^9 / 2 = 256
Pi(diameter)

42. What is the surface area of a cylinder with radius 5 and height 8?
NOT A PRIME
(pi)r²
31 - 37
130pi

43. Write 10 -843 X 10^7 in scientific notation
A+c<b+c
0
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
1.0843 X 10^11

44. How many sides does a hexagon have?
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...
x²-y²
4.25 - 6 - 22

45. Ø divided by 7
9 & 6/7
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
M
Ø

46. (12sqrt15) / (2sqrt5) =
N! / (k!)(n-k)!
1:1:sqrt2
an angle that is less than 90°
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

47. Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
4:5
71 - 73 - 79
(amount of decrease/original price) x 100%

48. 3 is the opposite of
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
3
Infinite.
4096

49. Volume of a rectangular box
4.25 - 6 - 22
1 - P(E)
V=Lwh
Pi is the ratio of a circle'S circumference to its diameter.

50. 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)
Positive or Negative
23 - 29
(amount of decrease/original price) x 100%