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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. (x+y)²
Null
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x²+2xy+y²
180°
2. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
A percent is a fraction whose denominator is 100.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
3. 3 is the opposite of
B?b?b (where b is used as a factor n times)
180°
3
1:1:sqrt2
4. If a product of two numbers is Ø - one number must be
27
3
Ø
Lies opposite the greater angle
5. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
4a^2(b)
The sum of the digits is a multiple of 9.
$3 -500 in the 9% and $2 -500 in the 7%.
6. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
4:5
A natural number greater than 1 that has no positive divisors other than 1 and itself
V=Lwh
7. (6sqrt3) x (2sqrt5) =
180
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
2(pi)r
A central angle is an angle formed by 2 radii.
8. To multiply a number by 10^x
Move the decimal point to the right x places
4:5
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
A natural number greater than 1 that has no positive divisors other than 1 and itself
9. Ø is
An angle which is supplementary to an interior angle.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Even
V=l×w×h
10. x^4 + x^7 =
x^(4+7) = x^11
Undefined
41 - 43 - 47
$3 -500 in the 9% and $2 -500 in the 7%.
11. What is the set of elements found in both A and B?
Be Zero!
The interesection of A and B.
Sector area = (n/360) X (pi)r^2
Triangles with same measure and same side lengths.
12. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
75:11
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
90pi
x^(2(4)) =x^8 = (x^4)^2
13. x^6 / x^3
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
x^(6-3) = x^3
D=rt so r= d/t and t=d/r
The overlapping sections.
14. 5/6 in percent?
83.333%
Positive or Negative
10! / (10-3)! = 720
67 - 71 - 73
15. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
52
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
4.25 - 6 - 22
Ø
16. the slope of a line in y=mx+b
M
4a^2(b)
53 - 59
10! / (10-3)! = 720
17. -3²
9
A reflection about the origin.
4:5
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
18. 7/8 in percent?
87.5%
1 - P(E)
31 - 37
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)
19. 5x^2 - 35x -55 = 0
Do not have slopes!
F(x + c)
Undefined
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
20. 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?
y = 2x^2 - 3
y/x is a constant
90°
A=(base)(height)
21. (2²)³
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
P=2(l+w)
ODD number
26
22. Write 10 -843 X 10^7 in scientific notation
1/2 times 7/3
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
1.0843 X 10^11
The point of intersection of the systems.
23. A quadrilateral where two diagonals bisect each other
P(E) = 1/1 = 1
Lies opposite the greater angle
Parallelogram
M
24. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
x²+2xy+y²
Move the decimal point to the right x places
0
25. To increase a number by x%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Ø
441000 = 1 10 10 10 21 * 21
180°
26. Area of a circle
angle that is greater than 90° but less than 180°
Yes - like radicals can be added/subtracted.
(a - b)(a + b)
(pi)r²
27. To decrease a number by x%
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.
6
55%
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
28. Pi is a ratio of what to what?
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29. 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?
360/n
48
Two equal sides and two equal angles.
y2-y1/x2-x1
30. (x^2)^4
The two xes after factoring.
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...
x^(2(4)) =x^8 = (x^4)^2
90pi
31. 10^6 has how many zeroes?
x²+2xy+y²
3
The objects within a set.
6
32. Product of any number and Ø is
Ø
An infinite set.
y/x is a constant
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)
33. In a Regular Polygon - the measure of each exterior angle
360/n
An angle which is supplementary to an interior angle.
N! / (n-k)!
9
34. -3³
x²-y²
27
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)
D/t (distance)/(time)
35. When dividing exponential #s with the same base - you do this to the exponents...
87.5%
180°
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Subtract them. i.e (5^7)/(5^3)= 5^4
36. What are complementary angles?
Two angles whose sum is 90.
360/n
Parallelogram
The sum of digits is divisible by 9.
37. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
360°
12! / 5!7! = 792
1/a^6
Ø
38. 30 60 90
3x - 4x - 5x
27^(-4)
Its last two digits are divisible by 4.
1/x
39. The product of any number x and its reciprocal
1
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1.0843 X 10^11
A set with a number of elements which can be counted.
40. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
7 / 1000
1.0843 X 10^11
4.25 - 6 - 22
3
41. 25^(1/2) or sqrt. 25 =
5 OR -5
(a - b)(a + b)
28
Ab+ac
42. The ratio of the areas of two similar polygons is ...
360°
... the square of the ratios of the corresponding sides.
1
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
43. Positive integers that have exactly 2 positive divisors are
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
A = length x width
$11 -448
Sum of digits is a multiple of 3 and the last digit is even.
44. Legs: 3 - 4. Hypotenuse?
x - x(SR3) - 2x
5
A = pi(r^2)
3 - 4 - 5
45. How many sides does a hexagon have?
Ø
6
Even
N! / (n-k)!
46. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
20.5
N! / (k!)(n-k)!
x²-y²
10
47. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
A subset.
13pi / 2
x²-2xy+y²
3/2 - 5/3
48. Is 0 even or odd?
Even
5
V=side³
72
49. formula for distance problems
Distance=rate×time or d=rt
180°
A<-b
V=side³
50. What is an isoceles triangle?
Two equal sides and two equal angles.
(amount of decrease/original price) x 100%
x(x - y + 1)
(rate)(time) d=rt