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Test your basic knowledge |
GRE Math: All In One
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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. formula for area of a triangle
9
P=2(l+w)
A=½bh
The two xes after factoring.
2. What is the side length of an equilateral triangle with altitude 6?
5
4.25 - 6 - 22
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...
13pi / 2
3. Positive integers that have exactly 2 positive divisors are
P(E) = 1/1 = 1
A = length x width
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
The greatest value minus the smallest.
4. What is the area of a regular hexagon with side 6?
1
180°
zero
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
5. Number of degrees in a triangle
180
x^(6-3) = x^3
The point of intersection of the systems.
(pi)r²
6. A number is divisible by 6 if...
F(x-c)
Lies opposite the greater angle
Its divisible by 2 and by 3.
x²-y²
7. Write 10 -843 X 10^7 in scientific notation
Diameter(Pi)
12! / 5!7! = 792
1.0843 X 10^11
D=rt so r= d/t and t=d/r
8. Ø divided by 7
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.
Ø
Be Zero!
18
9. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
(length)(width)(height)
Even
2 & 3/7
Two angles whose sum is 180.
10. Rate
D/t (distance)/(time)
Infinite.
Undefined - because we can'T divide by 0.
x(x - y + 1)
11. Reduce: 4.8 : 0.8 : 1.6
Ø=P(E)=1
6 : 1 : 2
Relationship cannot be determined (what if x is negative?)
C = 2(pi)r
12. (x-y)²
x²-2xy+y²
3
1.0843 X 10^11
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.)
13. 5/6 in percent?
41 - 43 - 47
83.333%
M= (Y1-Y2)/(X1-X2)
(base*height) / 2
14. Formula to find a circle'S circumference from its radius?
A²+b²=c²
1 - P(E)
1.7
C = 2(pi)r
15. 1/8 in percent?
x^(2(4)) =x^8 = (x^4)^2
Ab-ac
The sum of the digits is a multiple of 9.
12.5%
16. To increase a number by x%
A<-b
16.6666%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
3
17. 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?
3
1
48
1/a^6
18. Find the surface area of a cylinder with radius 3 and height 12.
All numbers multiples of 1.
360°
90pi
Null
19. In a Rectangle - each angles measures
3
9 : 25
90°
62.5%
20. The percent decrease of a quantity
Lies opposite the greater angle
4725
= (actual decrease/Original amount) x 100%
27^(-4)
21. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
2 & 3/7
2sqrt6
37.5%
22. If a<b - then
$3 -500 in the 9% and $2 -500 in the 7%.
A+c<b+c
ODD number
Factors are few - multiples are many.
23. 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?
The shortest arc between points A and B on a circle'S diameter.
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
10
52
24. x^2 = 9. What is the value of x?
Ø
x²-y²
3 - -3
(amount of decrease/original price) x 100%
25. 2³×7³
180°
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
$11 -448
(2x7)³
26. How many multiples does a given number have?
53 - 59
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The two xes after factoring.
Infinite.
27. 4.809 X 10^7 =
12sqrt2
Be Zero!
.0004809 X 10^11
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.)
28. the measure of a straight angle
The sum of the digits is a multiple of 9.
90
180°
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.)
29. Formula to find a circle'S circumference from its diameter?
C = (pi)d
C = 2(pi)r
Ø
A tangent is a line that only touches one point on the circumference of a circle.
30. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
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.
A= (1/2) b*h
2^9 / 2 = 256
F(x-c)
31. Convert 0.7% to a fraction.
zero
7 / 1000
The objects within a set.
31 - 37
32. Evaluate 3& 2/7 / 1/3
9 & 6/7
72
A percent is a fraction whose denominator is 100.
A reflection about the origin.
33. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
180°
53 - 59
4096
34. In any polygon - all external angles equal up to
360°
180
x²+2xy+y²
A=pi*(r^2)
35. Define a 'monomial'
The set of output values for a function.
Ø
An expression with just one term (-6x - 2a^2)
18
36. What is a set with no members called?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The empty set - denoted by a circle with a diagonal through it.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
An angle which is supplementary to an interior angle.
37. 25^(1/2) or sqrt. 25 =
A<-b
5 OR -5
3/2 - 5/3
A set with a number of elements which can be counted.
38. A quadrilateral where two diagonals bisect each other
x²-y²
Parallelogram
4096
x²-2xy+y²
39. What is a central angle?
An infinite set.
A central angle is an angle formed by 2 radii.
Edge³
3/2 - 5/3
40. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
Every number
52
(base*height) / 2
N! / (n-k)!
41. 5x^2 - 35x -55 = 0
A reflection about the origin.
4725
Pi is the ratio of a circle'S circumference to its diameter.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
42. b¹
180
A percent is a fraction whose denominator is 100.
The shortest arc between points A and B on a circle'S diameter.
1
43. Vertical lines
87.5%
Do not have slopes!
Every number
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
44. What are the integers?
Parallelogram
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Ab-ac
All numbers multiples of 1.
45. 3 is the opposite of
1
2(pi)r
2
3
46. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
1.0843 X 10^11
4725
2^9 / 2 = 256
Cd
47. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
12! / 5!7! = 792
11 - 13 - 17 - 19
y = 2x^2 - 3
48. Area of a rectangle
A = length x width
A-b is positive
1/x
71 - 73 - 79
49. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
62.5%
(distance)/(rate) d/r
Two angles whose sum is 180.
13pi / 2
50. Circumference of a Circle
1:sqrt3:2
180
C=2 x pi x r OR pi x D
3
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