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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 is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
13
90°
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.
2. Volume of a rectangular box
2sqrt6
(x+y)(x-y)
83.333%
V=Lwh
3. Ø divided by 7
5 OR -5
Ø
27
1
4. 3/8 in percent?
87.5%
37.5%
Add them. i.e. (5^7) * (5^3) = 5^10
2
5. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
48
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
ODD number
1/x
6. In a rectangle - all angles are
Right
20.5
Ø
$3 -500 in the 9% and $2 -500 in the 7%.
7. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
Every number
2(pi)r
4.25 - 6 - 22
2
8. Simplify the expression [(b^2 - c^2) / (b - c)]
90
Its divisible by 2 and by 3.
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)
(b + c)
9. If a is positive - an is
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
180
Positive
y = (x + 5)/2
10. Ø is
Indeterminable.
37.5%
Undefined
A multiple of every integer
11. What are complementary angles?
EVEN
Every number
zero
Two angles whose sum is 90.
12. If E is certain
P(E) = 1/1 = 1
Relationship cannot be determined (what if x is negative?)
3/2 - 5/3
Ø
13. In a Regular Polygon - the measure of each exterior angle
A tangent is a line that only touches one point on the circumference of a circle.
360/n
Move the decimal point to the right x places
1:sqrt3:2
14. 30 60 90
3x - 4x - 5x
12! / 5!7! = 792
90
Ø Ø=Ø
15. 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?
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
A+c<b+c
D=rt so r= d/t and t=d/r
37.5%
16. What is the empty set?
(base*height) / 2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The overlapping sections.
A set with no members - denoted by a circle with a diagonal through it.
17. Pi is a ratio of what to what?
18. P and r are factors of 100. What is greater - pr or 100?
(x+y)(x+y)
Indeterminable.
28. n = 8 - k = 2. n! / k!(n-k)!
An isosceles right triangle.
19. factored binomial product of (x-y)²
A natural number greater than 1 that has no positive divisors other than 1 and itself
Pi(diameter)
x²-2xy+y²
A reflection about the origin.
20. 25^(1/2) or sqrt. 25 =
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
5 OR -5
Indeterminable.
4a^2(b)
21. Can you add sqrt 3 and sqrt 5?
1/x
No - only like radicals can be added.
37.5%
x(x - y + 1)
22. What is the set of elements found in both A and B?
1/x
(x+y)(x+y)
The interesection of A and B.
B?b?b (where b is used as a factor n times)
23. 1/6 in percent?
16.6666%
31 - 37
Two angles whose sum is 90.
10! / (10-3)! = 720
24. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
1
Pi(diameter)
M
x^(4+7) = x^11
25. Area of a triangle
Lies opposite the greater angle
A= (1/2) b*h
(amount of decrease/original price) x 100%
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
26. A quadrilateral where two diagonals bisect each other
(base*height) / 2
Null
(n-2) x 180
Parallelogram
27. x^2 = 9. What is the value of x?
2^9 / 2 = 256
3 - -3
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
The point of intersection of the systems.
28. What is the name for a grouping of the members within a set based on a shared characteristic?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
1.0843 X 10^11
75:11
A subset.
29. Probability of Event all cases
An expression with just one term (-6x - 2a^2)
37.5%
1:1:sqrt2
Ø=P(E)=1
30. What is the 'domain' of a function?
180 degrees
The set of elements which can be found in either A or B.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The set of input values for a function.
31. A number is divisible by 6 if...
Triangles with same measure and same side lengths.
The sum of the digits is a multiple of 9.
Its divisible by 2 and by 3.
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
32. Legs 6 - 8. Hypotenuse?
1
Ø=P(E)=1
10
(amount of decrease/original price) x 100%
33. The larger the absolute value of the slope...
C = 2(pi)r
The steeper the slope.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
An angle which is supplementary to an interior angle.
34. How to find the circumference of a circle which circumscribes a square?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
3/2 - 5/3
Sum of digits is a multiple of 3 and the last digit is even.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
35. The product of odd number of negative numbers
Negative
23 - 29
4:5
(2x7)³
36. What is the 'Range' of a function?
F(x) - c
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The set of output values for a function.
Two angles whose sum is 180.
37. Perfect Squares 1-15
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
The longest arc between points A and B on a circle'S diameter.
(a - b)^2
x²-y²
38. Define a 'monomial'
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
2^9 / 2 = 256
Cd
An expression with just one term (-6x - 2a^2)
39. What is the 'Range' of a series of numbers?
A set with a number of elements which can be counted.
The greatest value minus the smallest.
A = length x width
D=rt so r= d/t and t=d/r
40. Circumference of a circle
Pi(diameter)
(rate)(time) d=rt
Null
52
41. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
M= (Y1-Y2)/(X1-X2)
1 - P(E)
The second graph is less steep.
A reflection about the axis.
42. What is a subset?
Indeterminable.
Ø Ø=Ø
Can be negative - zero - or positive
A grouping of the members within a set based on a shared characteristic.
43. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
1/2 times 7/3
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
An isosceles right triangle.
A-b is negative
44. What are 'Supplementary angles?'
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Yes - like radicals can be added/subtracted.
A 30-60-90 triangle.
Two angles whose sum is 180.
45. the measure of a straight angle
$3 -500 in the 9% and $2 -500 in the 7%.
31 - 37
180°
Smallest positive integer
46. 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)?
y = (x + 5)/2
1/2 times 7/3
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
2
47. 8.84 / 5.2
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
2²
1.7
A=(base)(height)
48. Number of degrees in a triangle
1
The point of intersection of the systems.
180
A 30-60-90 triangle.
49. 1/2 divided by 3/7 is the same as
Pi is the ratio of a circle'S circumference to its diameter.
1/2 times 7/3
0
The union of A and B.
50. A number is divisible by 9 if...
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...
The set of elements which can be found in either A or B.
All numbers multiples of 1.
The sum of digits is divisible by 9.