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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. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
Straight Angle
180
A chord is a line segment joining two points on a circle.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
2. In a Regular Polygon - the measure of each exterior angle
Straight Angle
360/n
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...
.0004809 X 10^11
3. 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))?
EVEN
20.5
D/t (distance)/(time)
0
4. The larger the absolute value of the slope...
Positive
48
The steeper the slope.
18
5. The negative exponent x?n is equivalent to what?
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
... the square of the ratios of the corresponding sides.
3
An arc is a portion of a circumference of a circle.
6. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
C=2 x pi x r OR pi x D
Add them. i.e. (5^7) * (5^3) = 5^10
Relationship cannot be determined (what if x is negative?)
7. What is the name for a grouping of the members within a set based on a shared characteristic?
An isosceles right triangle.
4:5
180
A subset.
8. 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?
The union of A and B.
23 - 29
8
N! / (k!)(n-k)!
9. Slope of any line that goes down as you move from left to right is
Negative
The longest arc between points A and B on a circle'S diameter.
y = (x + 5)/2
Can be negative - zero - or positive
10. What is the slope of a horizontal line?
4725
0
28. n = 8 - k = 2. n! / k!(n-k)!
A=pi*(r^2)
11. The sum of all angles around a point
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
360°
Undefined - because we can'T divide by 0.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
12. What are the roots of the quadrinomial x^2 + 2x + 1?
0
A reflection about the origin.
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)
The two xes after factoring.
13. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
90
180
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
A reflection about the axis.
14. 30 60 90
3x - 4x - 5x
A=½bh
75:11
Infinite.
15. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
The shortest arc between points A and B on a circle'S diameter.
(pi)r²
2sqrt6
16. a^2 + 2ab + b^2
180°
(a + b)^2
The direction of the inequality is reversed.
1 - P(E)
17. If a is negative and n is even then an is (positive or negative?)
An is positive
Reciprocal
The overlapping sections.
The longest arc between points A and B on a circle'S diameter.
18. a(b-c)
9 & 6/7
4.25 - 6 - 22
Ab-ac
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
19. a^2 - b^2 =
P=4s (s=side)
180 degrees
0
(a - b)(a + b)
20. 7/8 in percent?
130pi
4:5
87.5%
Ø=P(E)=1
21. 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?
No - only like radicals can be added.
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
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.
ODD number
22. What are the rational numbers?
4096
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
28
1
23. How to recognize a # as a multiple of 4
No - only like radicals can be added.
1/a^6
2(pi)r
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.)
24. Find the surface area of a cylinder with radius 3 and height 12.
90pi
x - x+1 - x+2
1/a^6
1
25. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
The set of output values for a function.
28
A subset.
26. The objects in a set are called two names:
x^(2(4)) =x^8 = (x^4)^2
Members or elements
x²-2xy+y²
1:1:sqrt2
27. What is the sum of the angles of a triangle?
180 degrees
A= (1/2) b*h
10
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.)
28. (12sqrt15) / (2sqrt5) =
Ab+ac
The sum of its digits is divisible by 3.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A<-b
29. Describe the relationship between the graphs of x^2 and (1/2)x^2
... the square of the ratios of the corresponding sides.
The second graph is less steep.
NOT A PRIME
Ø
30. 50 < all primes< 60
53 - 59
87.5%
(2x7)³
The set of output values for a function.
31. Solve the quadratic equation ax^2 + bx + c= 0
90pi
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
P(E) = number of favorable outcomes/total number of possible outcomes
32. a>b then a - b is positive or negative?
Infinite.
90°
A-b is positive
4.25 - 6 - 22
33. A number is divisible by 6 if...
Its divisible by 2 and by 3.
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=(base)(height)
1
34. What is the maximum value for the function g(x) = (-2x^2) -1?
0
1
The second graph is less steep.
3
35. 6w^2 - w - 15 = 0
8
6 : 1 : 2
... the square of the ratios of the corresponding sides.
3/2 - 5/3
36. b¹
1 & 37/132
1
Distance=rate×time or d=rt
C=2 x pi x r OR pi x D
37. What is a tangent?
A set with a number of elements which can be counted.
7 / 1000
288 (8 9 4)
A tangent is a line that only touches one point on the circumference of a circle.
38. First 10 prime #s
Ab+ac
D=rt so r= d/t and t=d/r
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
Negative
39. Ø is a multiple of
P=2(l+w)
Two (Ø×2=Ø)
A=½bh
500
40. 1 is a divisor of
Be Zero!
Ab=k (k is a constant)
Every number
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
41. Ø is
A grouping of the members within a set based on a shared characteristic.
A multiple of every integer
1
3/2 - 5/3
42. 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?
6
360°
52
The two xes after factoring.
43. Define an 'expression'.
F(x + c)
(x+y)(x-y)
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)
A tangent is a line that only touches one point on the circumference of a circle.
44. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
Sector area = (n/360) X (pi)r^2
A=pi*(r^2)
The sum of its digits is divisible by 3.
y = 2x^2 - 3
45. 25/2³
A=½bh
1
2²
18
46. (x-y)(x+y)
Null
The interesection of A and B.
x²-y²
41 - 43 - 47
47. What is the slope of a vertical line?
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48. (x-y)²
x²-2xy+y²
Ø
(a - b)^2
13
49. Pi is a ratio of what to what?
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50. 1 is an
ODD number
Parallelogram
Even
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50