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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. Simplify the expression [(b^2 - c^2) / (b - c)]
1
$3 -500 in the 9% and $2 -500 in the 7%.
C = (pi)d
(b + c)
2. What is the graph of f(x) shifted upward c units or spaces?
Pi(diameter)
13pi / 2
The steeper the slope.
F(x) + c
3. Which is greater? 200x^295 or 10x^294?
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
F(x) + c
A subset.
Relationship cannot be determined (what if x is negative?)
4. 1 is an
Straight Angle
ODD number
The set of elements found in both A and B.
2sqrt6
5. When dividing exponential #s with the same base - you do this to the exponents...
x²-y²
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
87.5%
Subtract them. i.e (5^7)/(5^3)= 5^4
6. 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)
X
4.25 - 6 - 22
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...
75:11
7. Define an 'expression'.
Every number
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)
C = 2(pi)r
y2-y1/x2-x1
8. x^2 = 9. What is the value of x?
The sum of its digits is divisible by 3.
3 - -3
Pi is the ratio of a circle'S circumference to its diameter.
Its divisible by 2 and by 3.
9. How many 3-digit positive integers are even and do not contain the digit 4?
1/x
55%
288 (8 9 4)
(length)(width)(height)
10. In a Rectangle - each angles measures
The sum of its digits is divisible by 3.
180
90°
27
11. (6sqrt3) x (2sqrt5) =
Distance=rate×time or d=rt
20.5
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
12. factored binomial product of (x-y)²
x²-2xy+y²
The two xes after factoring.
5
F(x) + c
13. Ø is a multiple of
An angle which is supplementary to an interior angle.
y = (x + 5)/2
Two (Ø×2=Ø)
$3 -500 in the 9% and $2 -500 in the 7%.
14. 3 is the opposite of
A natural number greater than 1 that has no positive divisors other than 1 and itself
A=pi*(r^2)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
3
15. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
A+c<b+c
A = length x width
52
16. What are the roots of the quadrinomial x^2 + 2x + 1?
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
Relationship cannot be determined (what if x is negative?)
P=2(l+w)
The two xes after factoring.
17. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
The sum of the digits is a multiple of 9.
The set of input values for a function.
ODD number
18. Slope of any line that goes up from left to right
Smallest positive integer
The interesection of A and B.
Positive
Ø
19. 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?
500
83.333%
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
A 30-60-90 triangle.
20. (x^2)^4
x^(6-3) = x^3
A 30-60-90 triangle.
180°
x^(2(4)) =x^8 = (x^4)^2
21. binomial product of (x-y)²
(x+y)(x-y)
Sector area = (n/360) X (pi)r^2
Positive
N! / (n-k)!
22. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
Its divisible by 2 and by 3.
A multiple of every integer
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)
23. 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?
1.0843 X 10^11
90
10! / 3!(10-3)! = 120
2sqrt6
24. Volume of a cube
12.5%
Edge³
A= (1/2) b*h
The set of elements found in both A and B.
25. What are the real numbers?
18
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)
(b + c)
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...
26. Area of a circle
1
3
Null
A=pi*(r^2)
27. Ø divided by 7
y/x is a constant
B?b?b (where b is used as a factor n times)
Ø
90°
28. Pi is a ratio of what to what?
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183
29. What are complementary angles?
A reflection about the origin.
1
N! / (k!)(n-k)!
Two angles whose sum is 90.
30. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
61 - 67
A multiple of every integer
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
31. What is the 'Solution' for a system of linear equations?
1
The point of intersection of the systems.
Sector area = (n/360) X (pi)r^2
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
32. Describe the relationship between 3x^2 and 3(x - 1)^2
x^(2(4)) =x^8 = (x^4)^2
Two equal sides and two equal angles.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
3
33. The negative exponent x?n is equivalent to what?
V=Lwh
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
A tangent is a line that only touches one point on the circumference of a circle.
ODD number
34. (12sqrt15) / (2sqrt5) =
(n-2) x 180
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The second graph is less steep.
An isosceles right triangle.
35. What does scientific notation mean?
3
Pi is the ratio of a circle'S circumference to its diameter.
3
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
36. What are the integers?
Ab-ac
P(E) = ø
1:sqrt3:2
All numbers multiples of 1.
37. The important properties of a 45-45-90 triangle?
0
A reflection about the axis.
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.
360°
38. Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
Edge³
3/2 - 5/3
Ø
39. Which is greater? 27^(-4) or 9^(-8)
8
27^(-4)
9 & 6/7
The second graph is less steep.
40. Find distance when given time and rate
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
12sqrt2
D=rt so r= d/t and t=d/r
$11 -448
41. Acute Angle
10! / (10-3)! = 720
1/x
an angle that is less than 90°
NOT A PRIME
42. Pythagorean theorem
20.5
A²+b²=c²
Even
Null
43. 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)?
3 - 4 - 5
61 - 67
y = (x + 5)/2
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
44. 20<all primes<30
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
23 - 29
Positive
(amount of decrease/original price) x 100%
45. Convert 0.7% to a fraction.
7 / 1000
A²+b²=c²
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
V=l×w×h
46. Legs: 3 - 4. Hypotenuse?
1/x
12! / 5!7! = 792
Its last two digits are divisible by 4.
5
47. b¹
130pi
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
1
Distance=rate×time or d=rt
48. What is a percent?
All numbers multiples of 1.
A percent is a fraction whose denominator is 100.
27
6
49. Ø Is neither
A grouping of the members within a set based on a shared characteristic.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Positive or Negative
1/2 times 7/3
50. Write 10 -843 X 10^7 in scientific notation
Two angles whose sum is 180.
1.0843 X 10^11
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.)
360°