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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 recognize a # as a multiple of 4
2sqrt6
The last 2 digits are a multiple of 4. (i.e 144 .... 44 is a multiple of 4 - so 144 must also be a multiple of 4.)
Ø
4725
2. -3²
9
A natural number greater than 1 that has no positive divisors other than 1 and itself
441000 = 1 10 10 10 21 * 21
A=pi*(r^2)
3. Vertical lines
13pi / 2
Do not have slopes!
13
0
4. What are complementary angles?
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)
Two angles whose sum is 90.
1/2 times 7/3
20.5
5. A number is divisible by 4 is...
2^9 / 2 = 256
Its last two digits are divisible by 4.
1:sqrt3:2
Ø=P(E)=1
6. What is a central angle?
500
P= 2L + 2w
A central angle is an angle formed by 2 radii.
x - x+1 - x+2
7. Acute Angle
an angle that is less than 90°
Two equal sides and two equal angles.
The union of A and B.
An is positive
8. When multiplying exponential #s with the same base - you do this to the exponents...
Add them. i.e. (5^7) * (5^3) = 5^10
A tangent is a line that only touches one point on the circumference of a circle.
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.
Smallest positive integer
9. How to recognize a # as a multiple of 9
1 & 37/132
The sum of the digits is a multiple of 9.
5
180°
10. Legs 6 - 8. Hypotenuse?
(n-2) x 180
The sum of the digits is a multiple of 9.
10
C=2 x pi x r OR pi x D
11. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
x²-y²
A = pi(r^2)
(base*height) / 2
12. 1 is the
B?b?b (where b is used as a factor n times)
(x+y)(x+y)
28. n = 8 - k = 2. n! / k!(n-k)!
Smallest positive integer
13. (12sqrt15) / (2sqrt5) =
3
x^(2(4)) =x^8 = (x^4)^2
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Two angles whose sum is 180.
14. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
(x+y)(x+y)
The empty set - denoted by a circle with a diagonal through it.
Ø Ø=Ø
15. (x^2)^4
1/x
1/a^6
48
x^(2(4)) =x^8 = (x^4)^2
16. What is the graph of f(x) shifted upward c units or spaces?
(rate)(time) d=rt
6 : 1 : 2
F(x) + c
288 (8 9 4)
17. What is the empty set?
10
V=side³
3
A set with no members - denoted by a circle with a diagonal through it.
18. If a lamp decreases to $80 - from $100 - what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
(a + b)^2
4:5
True
19. What are the rational numbers?
3 - -3
Ab-ac
P=2(l+w)
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
20. What is the surface area of a cylinder with radius 5 and height 8?
130pi
V=l×w×h
Lies opposite the greater angle
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)
21. a^2 - 2ab + b^2
(a - b)^2
(2x7)³
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
x^(2(4)) =x^8 = (x^4)^2
22. How do you solve proportions? a/b=c/d
360°
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
Undefined - because we can'T divide by 0.
1.7
23. 3 is the opposite of
3
11 - 13 - 17 - 19
x^(4+7) = x^11
(b + c)
24. Can you subtract 3sqrt4 from sqrt4?
A set with no members - denoted by a circle with a diagonal through it.
C = (pi)d
12! / 5!7! = 792
Yes - like radicals can be added/subtracted.
25. binomial product of (x+y)(x-y)
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A central angle is an angle formed by 2 radii.
x²-y²
1/2 times 7/3
26. The Denominator can never
The sum of its digits is divisible by 3.
(a + b)^2
Be Zero!
The sum of the digits is a multiple of 9.
27. Is 0 even or odd?
V=Lwh
2
Even
12! / 5!7! = 792
28. 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?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
C=2 x pi x r OR pi x D
52
Can be negative - zero - or positive
29. 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?
A= (1/2) b*h
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.
N! / (n-k)!
The set of elements which can be found in either A or B.
30. formula for area of a triangle
1 - P(E)
Two angles whose sum is 90.
A=½bh
Positive
31. What is a subset?
(p + q)/5
A grouping of the members within a set based on a shared characteristic.
3/2 - 5/3
The point of intersection of the systems.
32. -3³
x²-y²
F(x-c)
27
83.333%
33. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
A=(base)(height)
72
34. The Perimeter of a Square
P=4s (s=side)
D/t (distance)/(time)
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...
(a + b)^2
35. One is (a prime or not?)
N! / (k!)(n-k)!
Relationship cannot be determined (what if x is negative?)
NOT A PRIME
2(pi)r
36. 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?
10! / (10-3)! = 720
1 - P(E)
x²-2xy+y²
F(x) + c
37. The only number that is equal to its opposite
A tangent is a line that only touches one point on the circumference of a circle.
N! / (k!)(n-k)!
Ø Ø=Ø
Positive
38. 7 divided by Ø
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Null
A= (1/2) b*h
72
39. 1/6 in percent?
The greatest value minus the smallest.
P= 2L + 2w
X
16.6666%
40. What is an exterior angle?
An angle which is supplementary to an interior angle.
31 - 37
$3 -500 in the 9% and $2 -500 in the 7%.
$11 -448
41. In any polygon - all external angles equal up to
The sum of its digits is divisible by 3.
An expression with just one term (-6x - 2a^2)
360°
The objects within a set.
42. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
An angle which is supplementary to an interior angle.
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
The steeper the slope.
A reflection about the origin.
43. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
The longest arc between points A and B on a circle'S diameter.
Its last two digits are divisible by 4.
(b + c)
44. (x+y)²
x²+2xy+y²
0
x - x+1 - x+2
Positive
45. 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?
48
N! / (k!)(n-k)!
x²-2xy+y²
1/2 times 7/3
46. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
A set with no members - denoted by a circle with a diagonal through it.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
2sqrt6
0
47. (a^-1)/a^5
180 degrees
0
1
1/a^6
48. What number between 70 & 75 - inclusive - has the greatest number of factors?
Subtract them. i.e (5^7)/(5^3)= 5^4
An isosceles right triangle.
72
53 - 59
49. To increase a number by x%
41 - 43 - 47
Undefined
Ab=k (k is a constant)
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
50. What is the maximum value for the function g(x) = (-2x^2) -1?
A= (1/2) b*h
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
1
23 - 29