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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. The objects in a set are called two names:
Members or elements
1:1:sqrt2
3x - 4x - 5x
(rate)(time) d=rt

2. Slope of any line that goes up from left to right
Positive
90°
x^(2(4)) =x^8 = (x^4)^2
Triangles with same measure and same side lengths.

3. What is a tangent?
... the square of the ratios of the corresponding sides.
A tangent is a line that only touches one point on the circumference of a circle.
x²-y²
N! / (n-k)!

4. The Perimeter of a Square
P=4s (s=side)
y = (x + 5)/2
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 point of intersection of the systems.

5. What is the 'Range' of a function?
The sum of its digits is divisible by 3.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The set of output values for a function.
2²

6. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
5 - 12 - 13
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
(pi)r²
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.

7. 5x^2 - 35x -55 = 0
4a^2(b)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1/x
Every number

8. If a is negative and n is even then an is (positive or negative?)
4.25 - 6 - 22
The greatest value minus the smallest.
An is positive
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...

9. If a is positive - an is
x²+2xy+y²
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
(n-2) x 180
Positive

10. Find the surface area of a cylinder with radius 3 and height 12.
P= 2L + 2w
The shortest arc between points A and B on a circle'S diameter.
27
90pi

11. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
A chord is a line segment joining two points on a circle.
13pi / 2
31 - 37
360/n

12. Positive integers that have exactly 2 positive divisors are
26
x²-y²
Infinite.
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)

13. formula for area of a triangle
A= (1/2) b*h
4a^2(b)
A=½bh
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.

14. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
5 OR -5
x - x+1 - x+2
41 - 43 - 47

15. Define a 'Term' -
1 & 37/132
Add them. i.e. (5^7) * (5^3) = 5^10
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
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)

16. -3²
5 OR -5
Sector area = (n/360) X (pi)r^2
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
9

17. To multiply a number by 10^x
1:1:sqrt2
130pi
Move the decimal point to the right x places
Null

18. 5/8 in percent?
Infinite.
62.5%
The set of input values for a function.
1/x

19. The only number that is equal to its opposite
Ø Ø=Ø
130pi
Even prime number
Sum of digits is a multiple of 3 and the last digit is even.

20. (12sqrt15) / (2sqrt5) =
Pi(diameter)
A subset.
P=4s (s=side)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

21. What are the real numbers?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 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)
Add them. i.e. (5^7) * (5^3) = 5^10
Pi is the ratio of a circle'S circumference to its diameter.

22. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
x²+2xy+y²
500
V=side³
360°

23. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
48
A 30-60-90 triangle.
V=l×w×h

24. When multiplying exponential #s with the same base - you do this to the exponents...
y/x is a constant
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)
Add them. i.e. (5^7) * (5^3) = 5^10
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)

25. Circumference of a circle?
28. n = 8 - k = 2. n! / k!(n-k)!
(length)(width)(height)
Diameter(Pi)
Reciprocal

26. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
1:sqrt3:2
A<-b
1

27. What is the 'Solution' for a set of inequalities.
The overlapping sections.
M= (Y1-Y2)/(X1-X2)
x^(2(4)) =x^8 = (x^4)^2
$3 -500 in the 9% and $2 -500 in the 7%.

28. In a Regular Polygon - the measure of each exterior angle
360/n
4725
F(x + c)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

29. Acute Angle
an angle that is less than 90°
Pi(diameter)
27
An angle which is supplementary to an interior angle.

30. How to recognize a # as a multiple of 3
6 : 1 : 2
A<-b
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)
72

31. Slope given 2 points
M= (Y1-Y2)/(X1-X2)
NOT A PRIME
An angle which is supplementary to an interior angle.
The shortest arc between points A and B on a circle'S diameter.

32. Consecutive integers
12.5%
55%
x²+2xy+y²
x - x+1 - x+2

33. If the two sides of a triangle are unequal then the longer side.................
5 OR -5
5 - 12 - 13
1:1:sqrt2
Lies opposite the greater angle

34. Important properties of a 30-60-90 triangle?
(a - b)^2
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
P(E) = number of favorable outcomes/total number of possible outcomes
F(x) + c

35. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
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.)
1
A = length x width

36. (2²)³
26
Right
12.5%
x²-y²

37. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
P(E) = ø
Edge³
Two angles whose sum is 90.

38. Product of any number and Ø is
Ø
x - x+1 - x+2
Parallelogram
(pi)r²

39. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The greatest value minus the smallest.
F(x-c)
(a - b)(a + b)

40. Volume of a rectangular box
1/x
1
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
V=Lwh

41. 1n
52
... the square of the ratios of the corresponding sides.
1
(length)(width)(height)

42. What are the roots of the quadrinomial x^2 + 2x + 1?
A-b is positive
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The two xes after factoring.

43. 10^6 has how many zeroes?
37.5%
48
75:11
6

44. -3³
Sector area = (n/360) X (pi)r^2
Its last two digits are divisible by 4.
P=2(l+w)
27

45. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
(a - b)(a + b)
x²+2xy+y²

46. The larger the absolute value of the slope...
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.
Lies opposite the greater angle
55%
The steeper the slope.

47. Circumference of a circle
Ø
Positive or Negative
2^9 / 2 = 256
2(pi)r

48. 1/Ø=null If a>b then
A<-b
y = 2x^2 - 3
The steeper the slope.
Even

49. Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
A+c<b+c
Be Zero!
A 30-60-90 triangle.

50. Ø divided by 7
= (actual decrease/Original amount) x 100%
3 - 4 - 5
(2x7)³
Ø