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Test your basic knowledge |
GRE Math: All In One
Start Test
Study First
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. Area of a circle
13pi / 2
(pi)r²
1.0843 X 10^11
2.592 kg
2. What is the empty set?
6
N! / (k!)(n-k)!
B?b?b (where b is used as a factor n times)
A set with no members - denoted by a circle with a diagonal through it.
3. The reciprocal of any non-zero number is
1/x
13
Diameter(Pi)
Ab=k (k is a constant)
4. The product of odd number of negative numbers
Cd
V=l×w×h
Negative
Null
5. 1/2 divided by 3/7 is the same as
Subtract them. i.e (5^7)/(5^3)= 5^4
5
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)
1/2 times 7/3
6. Circumference of a Circle
C=2 x pi x r OR pi x D
Undefined
The interesection of A and B.
31 - 37
7. a/Ø
90°
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
Null
(b + c)
8. Solve the quadratic equation ax^2 + bx + c= 0
1
Move the decimal point to the right x places
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
1/x
9. Pythagorean theorem
6
Be Zero!
(a - b)^2
A²+b²=c²
10. Evaluate (4^3)^2
4096
1
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)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
11. When does a function automatically have a restricted domain (2)?
67 - 71 - 73
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A set with no members - denoted by a circle with a diagonal through it.
A reflection about the axis.
12. 30< all primes<40
Move the decimal point to the right x places
31 - 37
0
Edge³
13. A quadrilateral where two diagonals bisect each other
41 - 43 - 47
180°
(a - b)^2
Parallelogram
14. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
X
2.592 kg
Diameter(Pi)
P(E) = 1/1 = 1
15. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
1
(x+y)(x-y)
y2-y1/x2-x1
16. 8.84 / 5.2
1.7
A percent is a fraction whose denominator is 100.
V=Lwh
4:5
17. If a lamp decreases to $80 - from $100 - what is the decrease in price?
Two angles whose sum is 90.
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
Ab+ac
360°
18. What are 'Supplementary angles?'
Factors are few - multiples are many.
Two angles whose sum is 180.
A subset.
x²+2xy+y²
19. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
B?b?b (where b is used as a factor n times)
All numbers multiples of 1.
Infinite.
52
20. To multiply a number by 10^x
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Move the decimal point to the right x places
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
6 : 1 : 2
21. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
Diameter(Pi)
83.333%
An isosceles right triangle.
M
22. If a lamp increases from $80 to $100 - what is the percent increase?
x²-y²
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Right
2(pi)r
23. 1n
P(E) = number of favorable outcomes/total number of possible outcomes
5 OR -5
1
Ab+ac
24. First 10 prime #s
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
(amount of decrease/original price) x 100%
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
Members or elements
25. What are congruent triangles?
Triangles with same measure and same side lengths.
70
Undefined
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
26. What percent of 40 is 22?
Its last two digits are divisible by 4.
55%
3x - 4x - 5x
Relationship cannot be determined (what if x is negative?)
27. When multiplying exponential #s with the same base - you do this to the exponents...
The direction of the inequality is reversed.
C = (pi)d
360°
Add them. i.e. (5^7) * (5^3) = 5^10
28. In a Rectangle - each angles measures
90°
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
B?b?b (where b is used as a factor n times)
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
29. What is the graph of f(x) shifted upward c units or spaces?
Members or elements
F(x) + c
x²-2xy+y²
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
30. Area of a Parallelogram:
An angle which is supplementary to an interior angle.
A=(base)(height)
360/n
V=side³
31. How to recognize a multiple of 6
Negative
EVEN
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Sum of digits is a multiple of 3 and the last digit is even.
32. Legs 6 - 8. Hypotenuse?
55%
(a + b)^2
(x+y)(x+y)
10
33. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
Every number
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...
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
34. 7/8 in percent?
87.5%
1
D=rt so r= d/t and t=d/r
A central angle is an angle formed by 2 radii.
35. A number is divisible by 3 if ...
The sum of the digits is a multiple of 9.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A grouping of the members within a set based on a shared characteristic.
The sum of its digits is divisible by 3.
36. The sum of the angles in a quadrilateral is
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
360°
Be Zero!
20.5
37. a>b then a - b is positive or negative?
A-b is positive
EVEN
1 & 37/132
Reciprocal
38. 7 divided by Ø
1
26
y = 2x^2 - 3
Null
39. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
P(E) = number of favorable outcomes/total number of possible outcomes
Even prime number
1 - P(E)
40. What does scientific notation mean?
The objects within a set.
F(x) - c
(base*height) / 2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
41. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
4.25 - 6 - 22
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)
13pi / 2
23 - 29
42. b¹
67 - 71 - 73
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
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
43. When dividing exponential #s with the same base - you do this to the exponents...
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
12sqrt2
(distance)/(rate) d/r
Subtract them. i.e (5^7)/(5^3)= 5^4
44. 25^(1/2) or sqrt. 25 =
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
5 OR -5
20.5
... the square of the ratios of the corresponding sides.
45. 2 is the only
Subtract them. i.e (5^7)/(5^3)= 5^4
Even prime number
Ø
2
46. Can you add sqrt 3 and sqrt 5?
Sum of digits is a multiple of 3 and the last digit is even.
75:11
1
No - only like radicals can be added.
47. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
Ø=P(E)=1
... the square of the ratios of the corresponding sides.
M= (Y1-Y2)/(X1-X2)
48. Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
12! / 5!7! = 792
7 / 1000
49. What is the 'union' of A and B?
2²
The set of elements which can be found in either A or B.
5
Move the decimal point to the right x places
50. In any polygon - all external angles equal up to
P(E) = number of favorable outcomes/total number of possible outcomes
Relationship cannot be determined (what if x is negative?)
360°
Negative