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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. How to find the circumference of a circle which circumscribes a square?
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
16.6666%
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
2. What is the area of a regular hexagon with side 6?
Two angles whose sum is 180.
9 & 6/7
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
180°
3. What percent of 40 is 22?
55%
4.25 - 6 - 22
11 - 13 - 17 - 19
C = 2(pi)r
4. If a<b - then
13pi / 2
A+c<b+c
3
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
5. Circumference of a Circle
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
D=rt so r= d/t and t=d/r
The set of elements found in both A and B.
C=2 x pi x r OR pi x D
6. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
70
1
13pi / 2
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
7. 2 is the only
10
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Even prime number
The sum of the digits is a multiple of 9.
8. What is the ratio of the sides of a 30-60-90 triangle?
27^(-4)
1:sqrt3:2
x²-y²
4:5
9. What is the sum of the angles of a triangle?
180 degrees
13pi / 2
23 - 29
A subset.
10. 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))?
x²-2xy+y²
0
20.5
x(x - y + 1)
11. What is an exterior angle?
An angle which is supplementary to an interior angle.
2.592 kg
Members or elements
61 - 67
12. 1/Ø=null If a>b then
A<-b
Reciprocal
(b + c)
Ø
13. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
13pi / 2
1
3
F(x) - c
14. Vertical lines
Do not have slopes!
(a - b)(a + b)
441000 = 1 10 10 10 21 * 21
28
15. What is the graph of f(x) shifted upward c units or spaces?
N! / (n-k)!
52
F(x) + c
20.5
16. Probability of Event all cases
90
27
The steeper the slope.
Ø=P(E)=1
17. Slope
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The set of elements which can be found in either A or B.
A percent is a fraction whose denominator is 100.
y2-y1/x2-x1
18. When multiplying exponential #s with the same base - you do this to the exponents...
A tangent is a line that only touches one point on the circumference of a circle.
Add them. i.e. (5^7) * (5^3) = 5^10
Even prime number
Move the decimal point to the right x places
19. How to recognize a # as a multiple of 3
1:sqrt3:2
P= 2L + 2w
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)
3x - 4x - 5x
20. 50 < all primes< 60
x - x(SR3) - 2x
Negative
(x+y)(x-y)
53 - 59
21. First 10 prime #s
52
Positive or Negative
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
The objects within a set.
22. Formula to find a circle'S circumference from its diameter?
11 - 13 - 17 - 19
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Even prime number
C = (pi)d
23. -3³
37.5%
M= (Y1-Y2)/(X1-X2)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
27
24. 6w^2 - w - 15 = 0
Two angles whose sum is 90.
Its last two digits are divisible by 4.
3/2 - 5/3
3 - 4 - 5
25. When dividing exponential #s with the same base - you do this to the exponents...
V=side³
(a - b)^2
Subtract them. i.e (5^7)/(5^3)= 5^4
28. n = 8 - k = 2. n! / k!(n-k)!
26. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
Two equal sides and two equal angles.
An isosceles right triangle.
x - x(SR3) - 2x
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
27. Pi is a ratio of what to what?
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28. What is the empty set?
Infinite.
2 & 3/7
A set with no members - denoted by a circle with a diagonal through it.
B?b?b (where b is used as a factor n times)
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?
Ø
48
An arc is a portion of a circumference of a circle.
1
30. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
11 - 13 - 17 - 19
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
90pi
31. Distance
(rate)(time) d=rt
Members or elements
10! / 3!(10-3)! = 120
Ø Ø=Ø
32. What number between 70 & 75 - inclusive - has the greatest number of factors?
Ab-ac
Positive
72
EVEN
33. In a rectangle - all angles are
Edge³
13pi / 2
Right
0
34. Formula to find a circle'S circumference from its radius?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
C = 2(pi)r
6
35. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
(n-2) x 180
90
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
(b + c)
36. What is the set of elements which can be found in either A or B?
The set of elements found in both A and B.
Lies opposite the greater angle
The union of A and B.
3
37. What is a tangent?
Ø
A tangent is a line that only touches one point on the circumference of a circle.
The set of input values for a function.
Parallelogram
38. What are the roots of the quadrinomial x^2 + 2x + 1?
Cd
C = (pi)d
The two xes after factoring.
Add them. i.e. (5^7) * (5^3) = 5^10
39. What is the 'Solution' for a system of linear equations?
An infinite set.
Even
The point of intersection of the systems.
(a - b)(a + b)
40. What is a finite set?
A set with a number of elements which can be counted.
A-b is positive
70
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)
41. 60 < all primes <70
= (actual decrease/Original amount) x 100%
Sector area = (n/360) X (pi)r^2
Diameter(Pi)
61 - 67
42. Legs 5 - 12. Hypotenuse?
70
13
3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
43. 25/2³
26
Subtract them. i.e (5^7)/(5^3)= 5^4
C = (pi)d
2²
44. 8.84 / 5.2
1.7
P=2(l+w)
Even prime number
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
45. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
Ø
P= 2L + 2w
Edge³
46. Ø is a multiple of
(a - b)(a + b)
Two (Ø×2=Ø)
0
(distance)/(rate) d/r
47. Important properties of a 30-60-90 triangle?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
4725
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
4096
48. The Denominator can never
Be Zero!
Even
6 : 1 : 2
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)
49. What is a subset?
Sum of digits is a multiple of 3 and the last digit is even.
Edge³
A grouping of the members within a set based on a shared characteristic.
12! / 5!7! = 792
50. A prime number (or a prime)
1 & 37/132
4:5
A natural number greater than 1 that has no positive divisors other than 1 and itself
$11 -448