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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. A number is divisible by 9 if...
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.)
The sum of digits is divisible by 9.
1.7
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
2. (x-y)²
1 & 37/132
x²-2xy+y²
Add them. i.e. (5^7) * (5^3) = 5^10
Pi is the ratio of a circle'S circumference to its diameter.
3. What are 'Supplementary angles?'
Two angles whose sum is 180.
1:1:sqrt2
A set with no members - denoted by a circle with a diagonal through it.
x²+2xy+y²
4. What are the members or elements of a set?
Two equal sides and two equal angles.
1/2 times 7/3
The objects within a set.
x²-y²
5. What is a set with no members called?
(a + b)^2
The empty set - denoted by a circle with a diagonal through it.
True
180°
6. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
61 - 67
52
Even
7. Ø is a multiple of
Two (Ø×2=Ø)
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.
F(x-c)
Undefined
8. 70 < all primes< 80
x(x - y + 1)
(pi)r²
Members or elements
71 - 73 - 79
9. the measure of a straight angle
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
180°
$3 -500 in the 9% and $2 -500 in the 7%.
Two angles whose sum is 90.
10. 6w^2 - w - 15 = 0
Positive
A central angle is an angle formed by 2 radii.
0
3/2 - 5/3
11. (a^-1)/a^5
Undefined
A 30-60-90 triangle.
1/a^6
(b + c)
12. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
(p + q)/5
C = (pi)d
500
A=pi*(r^2)
13. Probability of E not occurring:
360°
Positive or Negative
A = length x width
1 - P(E)
14. In a rectangle - all angles are
Straight Angle
1/x
Right
True
15. formula for distance problems
1
1.7
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Distance=rate×time or d=rt
16. Legs: 3 - 4. Hypotenuse?
C=2 x pi x r OR pi x D
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.)
5
A chord is a line segment joining two points on a circle.
17. Important properties of a 30-60-90 triangle?
1/a^6
The second graph is less steep.
Positive
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
18. For any number x
The objects within a set.
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)
Can be negative - zero - or positive
Ø Ø=Ø
19. If Event is impossible
Null
P(E) = ø
A chord is a line segment joining two points on a circle.
C = 2(pi)r
20. If a is positive - an is
Every number
Positive
$11 -448
x - x+1 - x+2
21. Slope given 2 points
EVEN
3
Ab+ac
M= (Y1-Y2)/(X1-X2)
22. (x+y)²
360°
(2x7)³
x²+2xy+y²
27
23. formula for area of a triangle
ODD number
(x+y)(x+y)
The empty set - denoted by a circle with a diagonal through it.
A=½bh
24. In a Regular Polygon - the measure of each exterior angle
3 - 4 - 5
5
360/n
12.5%
25. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
Move the decimal point to the right x places
360°
N! / (k!)(n-k)!
1
26. If y is directly proportional to x - what does it equal?
Its last two digits are divisible by 4.
The overlapping sections.
(a - b)(a + b)
y/x is a constant
27. Area of a Parallelogram:
(a - b)(a + b)
Yes - like radicals can be added/subtracted.
Relationship cannot be determined (what if x is negative?)
A=(base)(height)
28. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
4a^2(b)
A reflection about the origin.
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
2
29. To multiply a number by 10^x
Undefined - because we can'T divide by 0.
Sector area = (n/360) X (pi)r^2
Move the decimal point to the right x places
Ø
30. What are the smallest three prime numbers greater than 65?
Lies opposite the greater angle
2
67 - 71 - 73
75:11
31. binomial product of (x+y)(x-y)
The set of output values for a function.
61 - 67
Reciprocal
x²-y²
32. The only number that is equal to its opposite
Do not have slopes!
Ø Ø=Ø
(p + q)/5
Ø
33. What are the integers?
B?b?b (where b is used as a factor n times)
Triangles with same measure and same side lengths.
2(pi)r
All numbers multiples of 1.
34. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
P= 2L + 2w
$11 -448
x - x(SR3) - 2x
10! / 3!(10-3)! = 120
35. a^2 - b^2
(a - b)(a + b)
13pi / 2
4725
Ø=P(E)=1
36. Ø is
Arc length = (n/360) x pi(2r) where n is the number of degrees.
N! / (n-k)!
A multiple of every integer
The set of elements found in both A and B.
37. How to recognize a # as a multiple of 9
9 & 6/7
The steeper the slope.
The sum of the digits is a multiple of 9.
87.5%
38. Ø is
Even
Edge³
(length)(width)(height)
x²-2xy+y²
39. Define an 'expression'.
Two angles whose sum is 180.
180°
10
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)
40. 0^0
2sqrt6
Undefined
= (actual decrease/Original amount) x 100%
72
41. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
NOT A PRIME
Yes - like radicals can be added/subtracted.
Smallest positive integer
42. Evaluate (4^3)^2
4096
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A= (1/2) b*h
87.5%
43. Which is greater? 200x^295 or 10x^294?
x - x(SR3) - 2x
1
Relationship cannot be determined (what if x is negative?)
A subset.
44. The important properties of a 45-45-90 triangle?
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
Ab=k (k is a constant)
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.
1:1:sqrt2
45. a>b then a - b is positive or negative?
A-b is positive
1.0843 X 10^11
Subtract them. i.e (5^7)/(5^3)= 5^4
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)
46. How to determine percent decrease?
90
B?b?b (where b is used as a factor n times)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(amount of decrease/original price) x 100%
47. Formula for the area of a sector of a circle?
31 - 37
(base*height) / 2
Sector area = (n/360) X (pi)r^2
0
48. If an inequality is multiplied or divided by a negative number....
The direction of the inequality is reversed.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
11 - 13 - 17 - 19
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
49. Rate
The point of intersection of the systems.
D/t (distance)/(time)
180°
Move the decimal point to the right x places
50. 8.84 / 5.2
1.7
The greatest value minus the smallest.
Do not have slopes!
= (actual decrease/Original amount) x100% = 20/100x100% = 20%