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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. ز
(a - b)^2
Ø
A=½bh
A tangent is a line that only touches one point on the circumference of a circle.
2. 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.
28
A=½bh
The sum of the digits is a multiple of 9.
3. If a lamp increases from $80 to $100 - what is the percent increase?
1
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
8
3x - 4x - 5x
4. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
Triangles with same measure and same side lengths.
83.333%
2 & 3/7
P(E) = ø
5. What is the slope of a vertical line?
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183
6. An Angle that'S 180°
Straight Angle
Add them. i.e. (5^7) * (5^3) = 5^10
NOT A PRIME
A chord is a line segment joining two points on a circle.
7. Can you add sqrt 3 and sqrt 5?
1:1:sqrt2
1 - P(E)
Ab+ac
No - only like radicals can be added.
8. a(b-c)
Ab-ac
X
(length)(width)(height)
26
9. formula for the volume of a cube
The overlapping sections.
V=side³
$11 -448
(amount of decrease/original price) x 100%
10. Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
Smallest positive integer
A grouping of the members within a set based on a shared characteristic.
A-b is positive
11. Area of a circle
A=pi*(r^2)
Undefined - because we can'T divide by 0.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1 - P(E)
12. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
55%
Every number
V=l×w×h
13. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
x²+2xy+y²
A 30-60-90 triangle.
Every number
Edge³
14. Factor a^2 + 2ab + b^2
(a + b)^2
Can be negative - zero - or positive
Positive
(a - b)^2
15. (2²)³
0
26
Indeterminable.
An expression with just one term (-6x - 2a^2)
16. If a is positive - an is
Positive
13
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Its last two digits are divisible by 4.
17. Area of a Parallelogram:
1:sqrt3:2
A=(base)(height)
x²+2xy+y²
Ø=P(E)=1
18. Evaluate (4^3)^2
F(x) + c
12.5%
1
4096
19. Area of a rectangle
A = length x width
71 - 73 - 79
5 OR -5
Arc length = (n/360) x pi(2r) where n is the number of degrees.
20. Slope of any line that goes up from left to right
x^(4+7) = x^11
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.)
1
Positive
21. 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?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
N! / (k!)(n-k)!
Cd
Every number
22. 5x^2 - 35x -55 = 0
12.5%
180 degrees
Ø Ø=Ø
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
23. If a is inversely porportional to b - what does it equal?
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)
4096
The shortest arc between points A and B on a circle'S diameter.
Ab=k (k is a constant)
24. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
A=(base)(height)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
y2-y1/x2-x1
25. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
2.592 kg
6
Distance=rate×time or d=rt
x - x+1 - x+2
26. Formula for the area of a circle?
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
A = pi(r^2)
Be Zero!
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
27. When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
1
The point of intersection of the systems.
23 - 29
28. If a<b - then
D=rt so r= d/t and t=d/r
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
.0004809 X 10^11
A+c<b+c
29. A number is divisible by 6 if...
12! / 5!7! = 792
(a + b)^2
Its divisible by 2 and by 3.
27
30. What is an exterior angle?
An angle which is supplementary to an interior angle.
An is positive
Ø
(x+y)(x+y)
31. How to recognize a # as a multiple of 3
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)
(pi)r²
Cd
A+c<b+c
32. 1/2 divided by 3/7 is the same as
1/2 times 7/3
C = 2(pi)r
A reflection about the origin.
A reflection about the axis.
33. 5/8 in percent?
62.5%
An expression with just one term (-6x - 2a^2)
3 - 4 - 5
2sqrt6
34. What is the graph of f(x) shifted right c units or spaces?
The point of intersection of the systems.
F(x-c)
Yes - like radicals can be added/subtracted.
55%
35. 20<all primes<30
Straight Angle
(x+y)(x-y)
23 - 29
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
36. What is the graph of f(x) shifted upward c units or spaces?
62.5%
F(x) + c
Two equal sides and two equal angles.
The sum of its digits is divisible by 3.
37. 25^(1/2) or sqrt. 25 =
5 OR -5
C = 2(pi)r
Negative
28. n = 8 - k = 2. n! / k!(n-k)!
38. If a product of two numbers is Ø - one number must be
Ø
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The sum of its digits is divisible by 3.
27^(-4)
39. What is the graph of f(x) shifted downward c units or spaces?
6
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
F(x) - c
Positive
40. The sum of the angles in a quadrilateral is
360°
M= (Y1-Y2)/(X1-X2)
Even
11 - 13 - 17 - 19
41. a(b+c)
Ø
5 OR -5
Ab+ac
A set with a number of elements which can be counted.
42. 30 60 90
A tangent is a line that only touches one point on the circumference of a circle.
Pi is the ratio of a circle'S circumference to its diameter.
x - x(SR3) - 2x
Indeterminable.
43. What is the ratio of the sides of an isosceles right triangle?
Be Zero!
1:1:sqrt2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The steeper the slope.
44. (x+y)²
1.7
x²+2xy+y²
x²-2xy+y²
6 : 1 : 2
45. For any number x
Can be negative - zero - or positive
The set of elements found in both A and B.
ODD number
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
46. Factor x^2 - xy + x.
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)
x(x - y + 1)
Do not have slopes!
N! / (n-k)!
47. a^2 - b^2
The union of A and B.
(a - b)(a + b)
(length)(width)(height)
3 - 4 - 5
48. Acute Angle
5 - 12 - 13
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)
an angle that is less than 90°
Even prime number
49. 1n
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.)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
360°
1
50. Product of any number and Ø is
0
Ø
M
75:11