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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. What are the roots of the quadrinomial x^2 + 2x + 1?
.0004809 X 10^11
1 - P(E)
The two xes after factoring.
P(E) = ø
2. How to recognize a # as a multiple of 4
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.)
(n-2) x 180
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)
Positive
3. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
An is positive
C = (pi)d
X
True
4. The objects in a set are called two names:
Ø
The sum of its digits is divisible by 3.
Members or elements
1/x
5. Formula to find a circle'S circumference from its diameter?
F(x-c)
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
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.)
C = (pi)d
6. 25+2³
(a - b)(a + b)
A natural number greater than 1 that has no positive divisors other than 1 and itself
28
(x+y)(x-y)
7. Consecutive integers
x - x+1 - x+2
A grouping of the members within a set based on a shared characteristic.
Straight Angle
A = pi(r^2)
8. What is the surface area of a cylinder with radius 5 and height 8?
2
x - x(SR3) - 2x
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
130pi
9. x^2 = 9. What is the value of x?
4a^2(b)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
A chord is a line segment joining two points on a circle.
3 - -3
10. What is the ratio of the sides of a 30-60-90 triangle?
(p + q)/5
1:sqrt3:2
x - x(SR3) - 2x
4a^2(b)
11. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
130pi
1
Sector area = (n/360) X (pi)r^2
x - x+1 - x+2
12. How to find the circumference of a circle which circumscribes a square?
27
The set of output values for a function.
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)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
13. What are complementary angles?
Smallest positive integer
Two angles whose sum is 90.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
6
14. (a^-1)/a^5
2²
1/a^6
23 - 29
Null
15. a<b then a - b is positive or negative?
V=Lwh
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
1/x
A-b is negative
16. What are congruent triangles?
NOT A PRIME
x²+2xy+y²
Triangles with same measure and same side lengths.
130pi
17. What is the sum of the angles of a triangle?
180 degrees
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)
70
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
18. Dividing by a number is the same as multiplying it by its
Reciprocal
Straight Angle
180 degrees
A<-b
19. 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))?
An angle which is supplementary to an interior angle.
2sqrt6
20.5
1:sqrt3:2
20. A quadrilateral where two diagonals bisect each other
x(x - y + 1)
(p + q)/5
(amount of decrease/original price) x 100%
Parallelogram
21. What are the irrational numbers?
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183
22. What is a minor arc?
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23. Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
A = length x width
90
A 30-60-90 triangle.
24. 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?
ODD number
90°
48
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
25. 1 is a divisor of
1
An is positive
Every number
F(x-c)
26. When multiplying exponential #s with the same base - you do this to the exponents...
1.7
Add them. i.e. (5^7) * (5^3) = 5^10
The sum of the digits is a multiple of 9.
(length)(width)(height)
27. Simplify the expression [(b^2 - c^2) / (b - c)]
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 set of output values for a function.
Two angles whose sum is 180.
(b + c)
28. If a<b - then
70
NOT A PRIME
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
A+c<b+c
29. Volume of a rectangular solid
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
V=l×w×h
9 : 25
(length)(width)(height)
30. 30 60 90
3x - 4x - 5x
C = (pi)d
The set of elements which can be found in either A or B.
Ø Ø=Ø
31. If a is negative and n is even then an is (positive or negative?)
A<-b
(length)(width)(height)
An is positive
37.5%
32. 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
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)
N! / (k!)(n-k)!
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
33. What are the smallest three prime numbers greater than 65?
Members or elements
P=4s (s=side)
X
67 - 71 - 73
34. Formula for the area of a circle?
A subset.
6
(distance)/(rate) d/r
A = pi(r^2)
35. 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?
Two equal sides and two equal angles.
3/2 - 5/3
90
N! / (k!)(n-k)!
36. factored binomial product of (x-y)²
90
A+c<b+c
0
x²-2xy+y²
37. If a is inversely porportional to b - what does it equal?
Ø
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Sector area = (n/360) X (pi)r^2
Ab=k (k is a constant)
38. Evaluate 4/11 + 11/12
72
Diameter(Pi)
The longest arc between points A and B on a circle'S diameter.
1 & 37/132
39. Circumference of a Circle
12.5%
A<-b
C=2 x pi x r OR pi x D
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
40. What is a subset?
NOT A PRIME
A grouping of the members within a set based on a shared characteristic.
An expression with just one term (-6x - 2a^2)
1
41. Whats the difference between factors and multiples?
Lies opposite the greater angle
Factors are few - multiples are many.
y = (x + 5)/2
Yes - like radicals can be added/subtracted.
42. What is the 'union' of A and B?
23 - 29
The set of elements which can be found in either A or B.
6
Undefined
43. Vertical lines
31 - 37
1:1:sqrt2
55%
Do not have slopes!
44. The Denominator can never
All numbers multiples of 1.
Be Zero!
Can be negative - zero - or positive
The direction of the inequality is reversed.
45. (x-y)²
D=rt so r= d/t and t=d/r
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
1.7
x²-2xy+y²
46. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
The two xes after factoring.
A-b is negative
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
47. Simplify 9^(1/2) X 4^3 X 2^(-6)?
A 30-60-90 triangle.
A = length x width
3
72
48. Legs: 3 - 4. Hypotenuse?
5
The sum of its digits is divisible by 3.
The set of elements which can be found in either A or B.
3 - -3
49. Slope
y2-y1/x2-x1
A+c<b+c
62.5%
A percent is a fraction whose denominator is 100.
50. 30< all primes<40
V=Lwh
31 - 37
7 / 1000
72