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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. The Perimeter of a rectangle
x²-2xy+y²
P=2(l+w)
A chord is a line segment joining two points on a circle.
P(E) = 1/1 = 1
2. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
F(x-c)
P(E) = number of favorable outcomes/total number of possible outcomes
(x+y)(x-y)
y = (x + 5)/2
3. bn
441000 = 1 10 10 10 21 * 21
13pi / 2
Right
B?b?b (where b is used as a factor n times)
4. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
360°
62.5%
5. 3/8 in percent?
7 / 1000
Can be negative - zero - or positive
37.5%
D/t (distance)/(time)
6. A quadrilateral where two diagonals bisect each other
x²-y²
y2-y1/x2-x1
Parallelogram
2sqrt6
7. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
Negative
2sqrt6
x^(2(4)) =x^8 = (x^4)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
8. Describe the relationship between the graphs of x^2 and (1/2)x^2
P=2(l+w)
The second graph is less steep.
Do not have slopes!
1:sqrt3:2
9. Whats the difference between factors and multiples?
Two angles whose sum is 180.
5
70
Factors are few - multiples are many.
10. What is an exterior angle?
N! / (k!)(n-k)!
1 - P(E)
An angle which is supplementary to an interior angle.
360°
11. Pi is a ratio of what to what?
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183
12. 1 is an
A central angle is an angle formed by 2 radii.
ODD number
The sum of its digits is divisible by 3.
6 : 1 : 2
13. 5/6 in percent?
83.333%
1
13pi / 2
True
14. Formula for the area of a sector of a circle?
All numbers multiples of 1.
Move the decimal point to the right x places
.0004809 X 10^11
Sector area = (n/360) X (pi)r^2
15. binomial product of (x+y)²
(x+y)(x+y)
P=4s (s=side)
The greatest value minus the smallest.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
16. formula for volume of a rectangular solid
A 30-60-90 triangle.
180
V=l×w×h
Negative
17. Consecutive integers
x - x+1 - x+2
N! / (n-k)!
The interesection of A and B.
(x+y)(x+y)
18. To decrease a number by x%
Null
(distance)/(rate) d/r
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
180
19. In a Regular Polygon - the measure of each exterior angle
12sqrt2
A grouping of the members within a set based on a shared characteristic.
Two (Ø×2=Ø)
360/n
20. If a<b - then
ODD number
Distance=rate×time or d=rt
An is positive
A+c<b+c
21. The Denominator can never
Be Zero!
The objects within a set.
Factors are few - multiples are many.
F(x-c)
22. One is (a prime or not?)
C = (pi)d
NOT A PRIME
Do not have slopes!
The point of intersection of the systems.
23. Is 0 even or odd?
8
1:sqrt3:2
Even
2
24. To increase a number by x%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
The second graph is less steep.
1
$3 -500 in the 9% and $2 -500 in the 7%.
25. the slope of a line in y=mx+b
M
Positive
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Move the decimal point to the right x places
26. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
x^(2(4)) =x^8 = (x^4)^2
2^9 / 2 = 256
Negative
27. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
61 - 67
2.592 kg
Sector area = (n/360) X (pi)r^2
28. n = 8 - k = 2. n! / k!(n-k)!
28. The sum of the angles in a quadrilateral is
0
F(x-c)
Relationship cannot be determined (what if x is negative?)
360°
29. How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
28. n = 8 - k = 2. n! / k!(n-k)!
8
90°
30. Distance
2^9 / 2 = 256
(rate)(time) d=rt
55%
A set with no members - denoted by a circle with a diagonal through it.
31. If a lamp decreases to $80 - from $100 - what is the decrease in price?
Yes - like radicals can be added/subtracted.
x^(2(4)) =x^8 = (x^4)^2
8
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
32. x^4 + x^7 =
An expression with just one term (-6x - 2a^2)
4725
x^(4+7) = x^11
Ø Ø=Ø
33. factored binomial product of (x+y)²
F(x) - c
2²
(length)(width)(height)
x²+2xy+y²
34. What are the smallest three prime numbers greater than 65?
F(x) + c
67 - 71 - 73
A²+b²=c²
Can be negative - zero - or positive
35. A number is divisible by 9 if...
The sum of digits is divisible by 9.
A-b is negative
(2x7)³
Pi(diameter)
36. Which is greater? 64^5 or 16^8
The sum of digits is divisible by 9.
Two equal sides and two equal angles.
The greatest value minus the smallest.
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
37. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
4096
Cd
0
38. What is a set with no members called?
3
Two (Ø×2=Ø)
The empty set - denoted by a circle with a diagonal through it.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
39. Slope given 2 points
A percent is a fraction whose denominator is 100.
M= (Y1-Y2)/(X1-X2)
1 - P(E)
Move the decimal point to the right x places
40. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2^9 / 2 = 256
A=pi*(r^2)
2 & 3/7
A = pi(r^2)
41. 1/Ø=null If a>b then
360°
Edge³
A<-b
$11 -448
42. 1n
angle that is greater than 90° but less than 180°
9 : 25
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.
1
43. 5/8 in percent?
62.5%
M
441000 = 1 10 10 10 21 * 21
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
44. 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 = length x width
10
3
45. What is the side length of an equilateral triangle with altitude 6?
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...
F(x + c)
A= (1/2) b*h
angle that is greater than 90° but less than 180°
46. -3²
9
67 - 71 - 73
10! / (10-3)! = 720
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.)
47. Formula to find a circle'S circumference from its radius?
2sqrt6
C = 2(pi)r
28. n = 8 - k = 2. n! / k!(n-k)!
V=l×w×h
48. Solve the quadratic equation ax^2 + bx + c= 0
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The second graph is less steep.
y = (x + 5)/2
49. Positive integers that have exactly 2 positive divisors are
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
P=2(l+w)
Distance=rate×time or d=rt
= (actual decrease/Original amount) x 100%
50. 20<all primes<30
23 - 29
M= (Y1-Y2)/(X1-X2)
A reflection about the axis.
(rate)(time) d=rt