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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. Probability of an Event
Reciprocal
P(E) = number of favorable outcomes/total number of possible outcomes
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)
Indeterminable.
2. Define a 'Term' -
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)
9 & 6/7
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)
2^9 / 2 = 256
3. 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))?
26
Members or elements
52
20.5
4. 3 is the opposite of
An angle which is supplementary to an interior angle.
Ab=k (k is a constant)
A²+b²=c²
3
5. Describe the relationship between 3x^2 and 3(x - 1)^2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
V=Lwh
52
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
6. What is a tangent?
A percent is a fraction whose denominator is 100.
C=2 x pi x r OR pi x D
90°
A tangent is a line that only touches one point on the circumference of a circle.
7. If a is inversely porportional to b - what does it equal?
x²-2xy+y²
Distance=rate×time or d=rt
Ab=k (k is a constant)
Every number
8. If the two sides of a triangle are unequal then the longer side.................
Lies opposite the greater angle
26
x^(2(4)) =x^8 = (x^4)^2
10! / (10-3)! = 720
9. 60 < all primes <70
(x+y)(x+y)
V=Lwh
ODD number
61 - 67
10. Ø is
The sum of the digits is a multiple of 9.
Even
53 - 59
The steeper the slope.
11. Formula to find a circle'S circumference from its diameter?
18
x²-y²
C = (pi)d
6
12. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
180 degrees
... the square of the ratios of the corresponding sides.
$11 -448
441000 = 1 10 10 10 21 * 21
13. 1/8 in percent?
28. n = 8 - k = 2. n! / k!(n-k)!
D/t (distance)/(time)
12.5%
an angle that is less than 90°
14. a/Ø
360°
Null
The longest arc between points A and B on a circle'S diameter.
Add them. i.e. (5^7) * (5^3) = 5^10
15. Volume of a rectangular solid
Reciprocal
(amount of decrease/original price) x 100%
(length)(width)(height)
V=l×w×h
16. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
1 & 37/132
26
1/2 times 7/3
17. If y is directly proportional to x - what does it equal?
y/x is a constant
5 - 12 - 13
1/2 times 7/3
1
18. How to determine percent decrease?
x - x(SR3) - 2x
A natural number greater than 1 that has no positive divisors other than 1 and itself
(amount of decrease/original price) x 100%
1
19. 25+2³
9 : 25
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
28
1
20. a^2 - b^2 =
2 & 3/7
28
Pi(diameter)
(a - b)(a + b)
21. b¹
16.6666%
A central angle is an angle formed by 2 radii.
1
Even
22. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
An expression with just one term (-6x - 2a^2)
10
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
A reflection about the axis.
23. If E is certain
y/x is a constant
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
P(E) = 1/1 = 1
24. 25^(1/2) or sqrt. 25 =
= (actual decrease/Original amount) x 100%
5 OR -5
x(x - y + 1)
(x+y)(x+y)
25. Area of a rectangle
2
Every number
A = length x width
x - x+1 - x+2
26. What is the side length of an equilateral triangle with altitude 6?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
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...
2
1
27. Find the surface area of a cylinder with radius 3 and height 12.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Lies opposite the greater angle
90pi
F(x) - c
28. How to recognize a multiple of 6
The triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.
Sum of digits is a multiple of 3 and the last digit is even.
Add them. i.e. (5^7) * (5^3) = 5^10
Relationship cannot be determined (what if x is negative?)
29. a^2 + 2ab + b^2
(a + b)^2
(amount of decrease/original price) x 100%
23 - 29
Triangles with same measure and same side lengths.
30. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
Positive
x - x+1 - x+2
9 & 6/7
1
31. 7 divided by Ø
1
M
P(E) = ø
Null
32. What are complementary angles?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
an angle that is less than 90°
x²+2xy+y²
Two angles whose sum is 90.
33. formula for area of a triangle
A=½bh
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
V=Lwh
A=(base)(height)
34. One is (a prime or not?)
The point of intersection of the systems.
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
NOT A PRIME
x²+2xy+y²
35. Area of a circle
Its last two digits are divisible by 4.
Ø
A=pi*(r^2)
An is positive
36. Can you add sqrt 3 and sqrt 5?
All numbers multiples of 1.
.0004809 X 10^11
y2-y1/x2-x1
No - only like radicals can be added.
37. The sum of all angles around a point
2sqrt6
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.)
360°
28
38. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
Even
8
10! / 3!(10-3)! = 120
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...
39. (12sqrt15) / (2sqrt5) =
A set with no members - denoted by a circle with a diagonal through it.
The sum of the digits is a multiple of 9.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
P=2(l+w)
40. 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?
52
20.5
360°
9
41. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
1:sqrt3:2
No - only like radicals can be added.
4725
6
42. 6w^2 - w - 15 = 0
A subset.
The sum of its digits is divisible by 3.
Triangles with same measure and same side lengths.
3/2 - 5/3
43. A prime number (or a prime)
A natural number greater than 1 that has no positive divisors other than 1 and itself
P=4s (s=side)
13pi / 2
N! / (n-k)!
44. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
180 degrees
9 & 6/7
72
10! / (10-3)! = 720
45. To increase a number by x%
A multiple of every integer
An expression with just one term (-6x - 2a^2)
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
5
46. What are the members or elements of a set?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The objects within a set.
F(x) + c
180
47. If a product of two numbers is Ø - one number must be
2²
1
Ø
9 & 6/7
48. In a Regular Polygon - the measure of each exterior angle
B?b?b (where b is used as a factor n times)
12.5%
360/n
y2-y1/x2-x1
49. 40 < all primes<50
A multiple of every integer
A<-b
41 - 43 - 47
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...
50. How to recognize if a # is a multiple of 12
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.)
The sum of the digits is a multiple of 9.
52
1/x