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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 percent of 40 is 22?
55%
18
5 - 12 - 13
A set with a number of elements which can be counted.
2. 3/8 in percent?
180
37.5%
Relationship cannot be determined (what if x is negative?)
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
3. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
Sum of digits is a multiple of 3 and the last digit is even.
An arc is a portion of a circumference of a circle.
A set with no members - denoted by a circle with a diagonal through it.
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
4. Ø is
x^(2(4)) =x^8 = (x^4)^2
P=4s (s=side)
A multiple of every integer
An expression with just one term (-6x - 2a^2)
5. Simplify (a^2 + b)^2 - (a^2 - b)^2
P= 2L + 2w
(x+y)(x+y)
Ab-ac
4a^2(b)
6. x^4 + x^7 =
x^(4+7) = x^11
V=side³
Pi(diameter)
M
7. What is the intersection of A and B?
The set of elements found in both A and B.
1 - P(E)
500
EVEN
8. What is the name for a grouping of the members within a set based on a shared characteristic?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A 30-60-90 triangle.
A subset.
26
9. What does scientific notation mean?
x²-2xy+y²
Ab-ac
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
2 & 3/7
10. Ø Is neither
F(x + c)
(base*height) / 2
Positive or Negative
angle that is greater than 90° but less than 180°
11. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
EVEN
(x+y)(x-y)
1/a^6
12. When does a function automatically have a restricted domain (2)?
Positive or Negative
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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)
A=pi*(r^2)
13. Convert 0.7% to a fraction.
7 / 1000
A=½bh
1
1
14. How to recognize if a # is a multiple of 12
The sum of digits is divisible by 9.
Do not have slopes!
180°
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.)
15. How do you solve proportions? a/b=c/d
y = 2x^2 - 3
The longest arc between points A and B on a circle'S diameter.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
Even
16. If y is directly proportional to x - what does it equal?
A = length x width
y/x is a constant
83.333%
The union of A and B.
17. What are the integers?
All numbers multiples of 1.
13
The direction of the inequality is reversed.
V=side³
18. 10^6 has how many zeroes?
6
Positive
90°
83.333%
19. 60 < all primes <70
70
61 - 67
1
(rate)(time) d=rt
20. Describe the relationship between 3x^2 and 3(x - 1)^2
An infinite set.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
4725
D=rt so r= d/t and t=d/r
21. Slope of any line that goes up from left to right
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
130pi
C = 2(pi)r
Positive
22. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
y/x is a constant
4:5
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
12.5%
23. 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?
N! / (k!)(n-k)!
A 30-60-90 triangle.
1/a^6
Relationship cannot be determined (what if x is negative?)
24. Distance
Add them. i.e. (5^7) * (5^3) = 5^10
(rate)(time) d=rt
180
(x+y)(x-y)
25. 20<all primes<30
The point of intersection of the systems.
23 - 29
(pi)r²
y = 2x^2 - 3
26. The Denominator can never
A²+b²=c²
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Two angles whose sum is 180.
Be Zero!
27. The only number that is equal to its opposite
90°
Ø Ø=Ø
1/a^6
$3 -500 in the 9% and $2 -500 in the 7%.
28. If a lamp decreases to $80 - from $100 - what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
2.592 kg
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The greatest value minus the smallest.
29. a^2 + 2ab + b^2
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
zero
(a + b)^2
The steeper the slope.
30. Reduce: 4.8 : 0.8 : 1.6
28. n = 8 - k = 2. n! / k!(n-k)!
6 : 1 : 2
16.6666%
Yes - like radicals can be added/subtracted.
31. Whats the difference between factors and multiples?
A²+b²=c²
Factors are few - multiples are many.
6
Subtract them. i.e (5^7)/(5^3)= 5^4
32. What are the roots of the quadrinomial x^2 + 2x + 1?
1 & 37/132
No - only like radicals can be added.
The two xes after factoring.
an angle that is less than 90°
33. Ø Is
Factors are few - multiples are many.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
C = 2(pi)r
EVEN
34. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
D/t (distance)/(time)
67 - 71 - 73
5 - 12 - 13
Cd
35. The Perimeter of a Square
26
A=(base)(height)
P=4s (s=side)
C = 2(pi)r
36. The objects in a set are called two names:
Members or elements
61 - 67
Ø=P(E)=1
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
37. The product of any number x and its reciprocal
4:5
1
75:11
$3 -500 in the 9% and $2 -500 in the 7%.
38. 2³×7³
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(2x7)³
A chord is a line segment joining two points on a circle.
(length)(width)(height)
39. 1/6 in percent?
x²-y²
(a + b)^2
1
16.6666%
40. Consecutive integers
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
C=2 x pi x r OR pi x D
The set of input values for a function.
x - x+1 - x+2
41. How many 3-digit positive integers are even and do not contain the digit 4?
x²-y²
180°
180 degrees
288 (8 9 4)
42. Can you subtract 3sqrt4 from sqrt4?
P(E) = number of favorable outcomes/total number of possible outcomes
A percent is a fraction whose denominator is 100.
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Yes - like radicals can be added/subtracted.
43. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
10! / (10-3)! = 720
3
44. The sum of all angles around a point
An isosceles right triangle.
Even
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
360°
45. What are 'Supplementary angles?'
D/t (distance)/(time)
Two angles whose sum is 180.
71 - 73 - 79
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)
46. 30 60 90
Right
x - x(SR3) - 2x
A-b is negative
90pi
47. Probability of Event all cases
28
Ø=P(E)=1
C = 2(pi)r
37.5%
48. Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
0
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x^(2(4)) =x^8 = (x^4)^2
49. Slope
52
y2-y1/x2-x1
Every number
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
50. What is the measure of an exterior angle of a regular pentagon?
Add them. i.e. (5^7) * (5^3) = 5^10
72
2sqrt6
37.5%