Test your basic knowledge |

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. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
(b + c)
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.)
Null

2. 1/2 divided by 3/7 is the same as
41 - 43 - 47
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
A grouping of the members within a set based on a shared characteristic.
1/2 times 7/3

3. How to determine percent decrease?
A²+b²=c²
(amount of decrease/original price) x 100%
The two xes after factoring.
A-b is positive

4. a^2 + 2ab + b^2
70
(a + b)^2
90
The two xes after factoring.

5. Product of any number and Ø is
12sqrt2
Edge³
(a - b)(a + b)
Ø

6. 1n
(distance)/(rate) d/r
Distance=rate×time or d=rt
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)
1

7. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
12sqrt2
Even prime number
2sqrt6

8. If a lamp increases from $80 to $100 - what is the percent increase?
x²+2xy+y²
x²-2xy+y²
Triangles with same measure and same side lengths.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

9. a^2 - 2ab + b^2
(a - b)^2
A multiple of every integer
(x+y)(x-y)
The direction of the inequality is reversed.

10. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
8
A = length x width
16.6666%
90°

11. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
9 : 25
61 - 67
NOT A PRIME
62.5%

12. In any polygon - all external angles equal up to
A set with a number of elements which can be counted.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
360°

13. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
The two xes after factoring.
72
10! / 3!(10-3)! = 120

14. One is (a prime or not?)
NOT A PRIME
Two (Ø×2=Ø)
Move the decimal point to the right x places
C=2 x pi x r OR pi x D

15. Which is greater? 64^5 or 16^8
360/n
A = length x width
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
x²+2xy+y²

16. How to find the circumference of a circle which circumscribes a square?
Do not have slopes!
= (actual decrease/Original amount) x 100%
(x+y)(x-y)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

17. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
No - only like radicals can be added.
1
1/a^6

18. When multiplying exponential #s with the same base - you do this to the exponents...
Add them. i.e. (5^7) * (5^3) = 5^10
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
The objects within a set.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

19. Vertical lines
Its last two digits are divisible by 4.
Do not have slopes!
(pi)r²
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

20. How to recognize a # as a multiple of 3
y = (x + 5)/2
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)
F(x) + c
F(x + c)

21. a/Ø
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)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
A central angle is an angle formed by 2 radii.
Null

22. What is the set of elements which can be found in either A or B?
P=4s (s=side)
V=side³
Factors are few - multiples are many.
The union of A and B.

23. x^4 + x^7 =
3 - -3
0
x^(4+7) = x^11
EVEN

24. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
10
31 - 37
y = 2x^2 - 3

25. Slope of any line that goes down as you move from left to right is
x - x+1 - x+2
A= (1/2) b*h
Negative
x²-y²

26. (x^2)^4
(n-2) x 180
The longest arc between points A and B on a circle'S diameter.
A 30-60-90 triangle.
x^(2(4)) =x^8 = (x^4)^2

27. If y is directly proportional to x - what does it equal?
16.6666%
y/x is a constant
Subtract them. i.e (5^7)/(5^3)= 5^4
angle that is greater than 90° but less than 180°

28. What is the graph of f(x) shifted upward c units or spaces?
The sum of its digits is divisible by 3.
1
F(x) + c
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

29. A number is divisible by 3 if ...
The shortest arc between points A and B on a circle'S diameter.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
P= 2L + 2w
The sum of its digits is divisible by 3.

30. What is the side length of an equilateral triangle with altitude 6?
An expression with just one term (-6x - 2a^2)
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
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.
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...

31. What is the graph of f(x) shifted downward c units or spaces?
x^(6-3) = x^3
F(x) - c
26
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

32. 5x^2 - 35x -55 = 0
An arc is a portion of a circumference of a circle.
Straight Angle
an angle that is less than 90°
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

33. What is an exterior angle?
x²-2xy+y²
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
P=4s (s=side)

34. 25^(1/2) or sqrt. 25 =
Its last two digits are divisible by 4.
5 OR -5
zero
y = (x + 5)/2

35. Ø is
16.6666%
90°
A multiple of every integer
(a - b)^2

36. a>b then a - b is positive or negative?
A-b is positive
130pi
2.592 kg
Positive

37. Find distance when given time and rate
(a + b)^2
D=rt so r= d/t and t=d/r
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)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

38. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
360°
62.5%
The direction of the inequality is reversed.
A reflection about the origin.

39. (x-y)²
0
V=l×w×h
A reflection about the axis.
x²-2xy+y²

40. Write 10 -843 X 10^7 in scientific notation
P(E) = number of favorable outcomes/total number of possible outcomes
1.0843 X 10^11
0
Ø Ø=Ø

41. Ø Is neither
Even
Positive or Negative
52
P(E) = 1/1 = 1

42. 70 < all primes< 80
3
A reflection about the axis.
71 - 73 - 79
Null

43. 3/8 in percent?
1/x
37.5%
13
Reciprocal

44. Whats the difference between factors and multiples?
A= (1/2) b*h
9 & 6/7
A<-b
Factors are few - multiples are many.

45. Factor a^2 + 2ab + b^2
F(x) + c
(a + b)^2
12.5%
The sum of the digits is a multiple of 9.

46. When does a function automatically have a restricted domain (2)?
1
7 / 1000
Two equal sides and two equal angles.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

47. Ø is a multiple of
Every number
90
360°
An infinite set.

48. What is the name of set with a number of elements which cannot be counted?
An infinite set.
2^9 / 2 = 256
The shortest arc between points A and B on a circle'S diameter.
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)

49. 30 60 90
Two equal sides and two equal angles.
12sqrt2
180
3 - 4 - 5

50. Evaluate 4/11 + 11/12
1 & 37/132
Sum of digits is a multiple of 3 and the last digit is even.
1 - P(E)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3