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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. 50 < all primes< 60
180
90
16.6666%
53 - 59
2. The negative exponent x?n is equivalent to what?
0
Straight Angle
16.6666%
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
3. How do you solve proportions? a/b=c/d
x²-y²
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
B?b?b (where b is used as a factor n times)
3 - 4 - 5
4. 40 < all primes<50
41 - 43 - 47
6 : 1 : 2
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
28
5. Simplify the expression (p^2 - q^2)/ -5(q - p)
4:5
(p + q)/5
The union of A and B.
Pi(diameter)
6. A prime number (or a prime)
Triangles with same measure and same side lengths.
A natural number greater than 1 that has no positive divisors other than 1 and itself
Factors are few - multiples are many.
The steeper the slope.
7. What is a percent?
A percent is a fraction whose denominator is 100.
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.)
Factors are few - multiples are many.
C = 2(pi)r
8. a<b then a - b is positive or negative?
A-b is negative
Even
Two angles whose sum is 90.
(a - b)(a + b)
9. What is the maximum value for the function g(x) = (-2x^2) -1?
A percent is a fraction whose denominator is 100.
10
1
75:11
10. Ø Is
A=pi*(r^2)
1
EVEN
Infinite.
11. Whats the difference between factors and multiples?
Factors are few - multiples are many.
P= 2L + 2w
Null
4:5
12. What is the area of a regular hexagon with side 6?
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Distance=rate×time or d=rt
18
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
13. What is the 'Solution' for a set of inequalities.
The overlapping sections.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
2 & 3/7
P=2(l+w)
14. 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)
9 & 6/7
27^(-4)
62.5%
4.25 - 6 - 22
15. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
Sector area = (n/360) X (pi)r^2
1/x
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.
10! / (10-3)! = 720
16. How to recognize a # as a multiple of 9
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The sum of the digits is a multiple of 9.
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)
V=side³
17. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
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.)
$11 -448
18. The Perimeter of a rectangle
Smallest positive integer
P=2(l+w)
Two equal sides and two equal angles.
A<-b
19. What is a minor arc?
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183
20. What are 'Supplementary angles?'
All numbers multiples of 1.
Two angles whose sum is 180.
1
x(x - y + 1)
21. The Perimeter of a Square
P=4s (s=side)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
23 - 29
360/n
22. Circumference of a circle
Ø=P(E)=1
2(pi)r
3
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
23. What is the empty set?
C=2 x pi x r OR pi x D
(a - b)(a + b)
A set with no members - denoted by a circle with a diagonal through it.
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)
24. formula for the volume of a cube
441000 = 1 10 10 10 21 * 21
1.7
V=side³
The longest arc between points A and B on a circle'S diameter.
25. What are the smallest three prime numbers greater than 65?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
67 - 71 - 73
The set of elements which can be found in either A or B.
26. Which is greater? 64^5 or 16^8
(n-2) x 180
X
52
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
27. Legs 5 - 12. Hypotenuse?
13
1
12.5%
28
28. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
x²-2xy+y²
The set of output values for a function.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
72
29. 1 is the
1
6 : 1 : 2
Smallest positive integer
72
30. What are complementary angles?
Positive
Two angles whose sum is 90.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
y/x is a constant
31. What are congruent triangles?
Can be negative - zero - or positive
Triangles with same measure and same side lengths.
180 degrees
Pi is the ratio of a circle'S circumference to its diameter.
32. 30 60 90
M
3 - 4 - 5
A=(base)(height)
Add them. i.e. (5^7) * (5^3) = 5^10
33. 30 60 90
5 - 12 - 13
2
6 : 1 : 2
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
34. a>b then a - b is positive or negative?
A-b is positive
F(x) - c
(pi)r²
The two xes after factoring.
35. 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?
A= (1/2) b*h
x²+2xy+y²
1/a^6
52
36. x^6 / x^3
x^(6-3) = x^3
Straight Angle
NOT A PRIME
A set with a number of elements which can be counted.
37. Simplify the expression [(b^2 - c^2) / (b - c)]
(x+y)(x-y)
(b + c)
Can be negative - zero - or positive
48
38. To increase a number by x%
Right
1 & 37/132
A natural number greater than 1 that has no positive divisors other than 1 and itself
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
39. Circumference of a circle?
x - x+1 - x+2
Diameter(Pi)
2
The set of output values for a function.
40. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
441000 = 1 10 10 10 21 * 21
5
Two (Ø×2=Ø)
18
41. Area of a triangle
A= (1/2) b*h
Undefined
an angle that is less than 90°
x^(4+7) = x^11
42. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
Factors are few - multiples are many.
The sum of its digits is divisible by 3.
An isosceles right triangle.
43. An Angle that'S 180°
y = (x + 5)/2
Straight Angle
71 - 73 - 79
3 - -3
44. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
F(x + c)
Two (Ø×2=Ø)
Cd
Smallest positive integer
45. What is the name of set with a number of elements which cannot be counted?
1/x
360°
An infinite set.
Ø
46. bn
1
1
B?b?b (where b is used as a factor n times)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
47. A number is divisible by 6 if...
Can be negative - zero - or positive
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Its divisible by 2 and by 3.
A natural number greater than 1 that has no positive divisors other than 1 and itself
48. What are the real numbers?
70
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)
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
A= (1/2) b*h
49. Area of a Parallelogram:
Sector area = (n/360) X (pi)r^2
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
A=(base)(height)
y = 2x^2 - 3
50. Formula for the area of a sector of a circle?
x²-y²
Sector area = (n/360) X (pi)r^2
360/n
A-b is negative