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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. 3/8 in percent?
37.5%
A set with a number of elements which can be counted.
52
1
2. If a lamp increases from $80 to $100 - what is the percent increase?
Parallelogram
P(E) = ø
The objects within a set.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
3. How to determine percent decrease?
an angle that is less than 90°
(amount of decrease/original price) x 100%
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1/x
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.
7 / 1000
5. Formula to calculate arc length?
A-b is positive
Arc length = (n/360) x pi(2r) where n is the number of degrees.
X
y = 2x^2 - 3
6. The sum of all angles around a point
1/2 times 7/3
A=(base)(height)
2
360°
7. What is the 'Solution' for a system of linear equations?
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.
28. n = 8 - k = 2. n! / k!(n-k)!
M
The point of intersection of the systems.
8. Acute Angle
an angle that is less than 90°
10
1
An infinite set.
9. -3³
Two (Ø×2=Ø)
27
A²+b²=c²
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
10. When dividing exponential #s with the same base - you do this to the exponents...
(x+y)(x+y)
Ø=P(E)=1
55%
Subtract them. i.e (5^7)/(5^3)= 5^4
11. To increase a number by x%
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(b + c)
1/a^6
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
12. 7/8 in percent?
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 set of input values for a function.
87.5%
y2-y1/x2-x1
13. Volume of a rectangular solid
x(x - y + 1)
5 OR -5
(length)(width)(height)
9
14. x^2 = 9. What is the value of x?
3 - -3
x^(6-3) = x^3
10! / 3!(10-3)! = 120
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
15. Area of a Parallelogram:
A=(base)(height)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Negative
C = 2(pi)r
16. 2³×7³
1
2
(2x7)³
5
17. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
(a - b)(a + b)
2^9 / 2 = 256
Null
87.5%
18. The percent decrease of a quantity
P=4s (s=side)
M= (Y1-Y2)/(X1-X2)
D=rt so r= d/t and t=d/r
= (actual decrease/Original amount) x 100%
19. Can you add sqrt 3 and sqrt 5?
An infinite set.
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
No - only like radicals can be added.
The set of elements found in both A and B.
20. Formula to find a circle'S circumference from its diameter?
C = (pi)d
5
3 - 4 - 5
C=2 x pi x r OR pi x D
21. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
Its divisible by 2 and by 3.
20.5
Infinite.
22. What is the name for a grouping of the members within a set based on a shared characteristic?
41 - 43 - 47
(a - b)(a + b)
Its divisible by 2 and by 3.
A subset.
23. What is a tangent?
70
A grouping of the members within a set based on a shared characteristic.
A tangent is a line that only touches one point on the circumference of a circle.
C = (pi)d
24. Whats the difference between factors and multiples?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Factors are few - multiples are many.
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
67 - 71 - 73
25. 1/2 divided by 3/7 is the same as
1/2 times 7/3
360°
x^(2(4)) =x^8 = (x^4)^2
x²-y²
26. b¹
1
A= (1/2) b*h
Distance=rate×time or d=rt
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
27. a^2 - b^2 =
8
(a - b)(a + b)
The two xes after factoring.
A set with a number of elements which can be counted.
28. 50 < all primes< 60
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
53 - 59
V=l×w×h
4:5
29. If a<b - then
2 & 3/7
D/t (distance)/(time)
A+c<b+c
The shortest arc between points A and B on a circle'S diameter.
30. Simplify 9^(1/2) X 4^3 X 2^(-6)?
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
Pi(diameter)
X
3
31. A quadrilateral where two diagonals bisect each other
Parallelogram
EVEN
A+c<b+c
Ø
32. Factor x^2 - xy + x.
x(x - y + 1)
1
A = pi(r^2)
Ab+ac
33. To multiply a number by 10^x
3x - 4x - 5x
Move the decimal point to the right x places
(n-2) x 180
Undefined
34. What does scientific notation mean?
13
A+c<b+c
A = length x width
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
35. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
20.5
A set with no members - denoted by a circle with a diagonal through it.
A reflection about the origin.
90
36. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
48
An angle which is supplementary to an interior angle.
55%
37. A number is divisible by 3 if ...
The sum of its digits is divisible by 3.
N! / (k!)(n-k)!
(pi)r²
The sum of the digits is a multiple of 9.
38. If a is inversely porportional to b - what does it equal?
C=2 x pi x r OR pi x D
Ab=k (k is a constant)
Two equal sides and two equal angles.
53 - 59
39. Reduce: 4.8 : 0.8 : 1.6
The point of intersection of the systems.
Ø
3 - -3
6 : 1 : 2
40. 8.84 / 5.2
31 - 37
The set of elements found in both A and B.
Smallest positive integer
1.7
41. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
N! / (n-k)!
Null
The sum of its digits is divisible by 3.
Two equal sides and two equal angles.
42. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
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)
Ø
180
An isosceles right triangle.
43. 7 divided by Ø
0
360°
(p + q)/5
Null
44. 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)!
C = (pi)d
P(E) = number of favorable outcomes/total number of possible outcomes
500
45. 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).
3
Every number
(a - b)^2
46. The product of odd number of negative numbers
The point of intersection of the systems.
Negative
3
90°
47. 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?
4a^2(b)
10! / 3!(10-3)! = 120
6 : 1 : 2
75:11
48. 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?
1
... the square of the ratios of the corresponding sides.
The direction of the inequality is reversed.
2.592 kg
49. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
The sum of its digits is divisible by 3.
An isosceles right triangle.
x(x - y + 1)
50. Ø is
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
A=½bh
Even
(p + q)/5