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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. If a=-1 and b=3 - what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
X
2.592 kg
A²+b²=c²
20.5
2. If a lamp decreases to $80 - from $100 - what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
(x+y)(x+y)
70
(a - b)(a + b)
3. What is the surface area of a cylinder with radius 5 and height 8?
28
The point of intersection of the systems.
130pi
Two equal sides and two equal angles.
4. Factor a^2 + 2ab + b^2
(a + b)^2
Null
x²+2xy+y²
A=(base)(height)
5. What is the graph of f(x) shifted upward c units or spaces?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
75:11
F(x) + c
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.
6. Formula to find a circle'S circumference from its diameter?
180°
Ab=k (k is a constant)
C = (pi)d
x^(2(4)) =x^8 = (x^4)^2
7. -3²
(n-2) x 180
9
28. n = 8 - k = 2. n! / k!(n-k)!
4:5
8. (6sqrt3) x (2sqrt5) =
48
6 : 1 : 2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
9. The percent decrease of a quantity
(a - b)^2
53 - 59
= (actual decrease/Original amount) x 100%
(b + c)
10. What is the slope of a vertical line?
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183
11. (x-y)(x+y)
zero
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
x²-y²
Pi(diameter)
12. What is the measure of an exterior angle of a regular pentagon?
31 - 37
180°
zero
72
13. For any number x
3/2 - 5/3
x²-y²
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.
Can be negative - zero - or positive
14. Volume of a cube
2^9 / 2 = 256
3
Edge³
12! / 5!7! = 792
15. formula for volume of a rectangular solid
V=l×w×h
.0004809 X 10^11
3 - 4 - 5
A chord is a line segment joining two points on a circle.
16. How to determine percent decrease?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
(amount of decrease/original price) x 100%
A central angle is an angle formed by 2 radii.
67 - 71 - 73
17. Area of a rectangle
A = length x width
N! / (k!)(n-k)!
1
(n-2) x 180
18. If a lamp increases from $80 to $100 - what is the percent increase?
1/a^6
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
19. Convert 0.7% to a fraction.
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)
The set of elements found in both A and B.
an angle that is less than 90°
7 / 1000
20. What is the order of operations?
A=(base)(height)
9 & 6/7
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Cd
21. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
360/n
0
13
22. One is (a prime or not?)
N! / (n-k)!
72
NOT A PRIME
500
23. 10^6 has how many zeroes?
Ab=k (k is a constant)
90
6
1:1:sqrt2
24. The larger the absolute value of the slope...
Even prime number
Ø Ø=Ø
$3 -500 in the 9% and $2 -500 in the 7%.
The steeper the slope.
25. Define a 'Term' -
Positive or Negative
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)
Diameter(Pi)
x^(2(4)) =x^8 = (x^4)^2
26. Perimeter of a rectangle
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
The direction of the inequality is reversed.
23 - 29
P= 2L + 2w
27. (x^2)^4
72
.0004809 X 10^11
The interesection of A and B.
x^(2(4)) =x^8 = (x^4)^2
28. Write 10 -843 X 10^7 in scientific notation
Be Zero!
Subtract them. i.e (5^7)/(5^3)= 5^4
1.0843 X 10^11
Ø=P(E)=1
29. Number of degrees in a triangle
180
The greatest value minus the smallest.
A=pi*(r^2)
(pi)r²
30. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
75:11
Every number
3
31. 1 is an
9 : 25
The sum of the digits is a multiple of 9.
ODD number
V=side³
32. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
P(E) = 1/1 = 1
1
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Triangles with same measure and same side lengths.
33. How many 3-digit positive integers are even and do not contain the digit 4?
(amount of decrease/original price) x 100%
288 (8 9 4)
Ab+ac
x - x(SR3) - 2x
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?
Two angles whose sum is 90.
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
Straight Angle
10! / 3!(10-3)! = 120
35. When dividing exponential #s with the same base - you do this to the exponents...
Subtract them. i.e (5^7)/(5^3)= 5^4
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.)
A chord is a line segment joining two points on a circle.
6
36. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
1
1:sqrt3:2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
8
37. Vertical lines
20.5
Do not have slopes!
Lies opposite the greater angle
P(E) = 1/1 = 1
38. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
4a^2(b)
Move the decimal point to the right x places
Positive
39. If a is positive - an is
71 - 73 - 79
1:sqrt3:2
72
Positive
40. What is the graph of f(x) shifted right c units or spaces?
Lies opposite the greater angle
13pi / 2
(a - b)(a + b)
F(x-c)
41. Describe the relationship between the graphs of x^2 and (1/2)x^2
Negative
Factors are few - multiples are many.
The second graph is less steep.
Undefined - because we can'T divide by 0.
42. Ø Is
EVEN
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.)
A=pi*(r^2)
A central angle is an angle formed by 2 radii.
43. 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
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
x²-2xy+y²
y = (x + 5)/2
44. binomial product of (x-y)²
52
(x+y)(x-y)
3
288 (8 9 4)
45. What are congruent triangles?
x²-2xy+y²
6
Triangles with same measure and same side lengths.
Reciprocal
46. What is an isoceles triangle?
Two equal sides and two equal angles.
Two angles whose sum is 180.
1.7
x²+2xy+y²
47. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
87.5%
V=Lwh
Members or elements
2^9 / 2 = 256
48. 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?
5
N! / (n-k)!
A reflection about the origin.
The set of elements which can be found in either A or B.
49. 2 is the only
8
Even prime number
27
61 - 67
50. Which is greater? 200x^295 or 10x^294?
... the square of the ratios of the corresponding sides.
Relationship cannot be determined (what if x is negative?)
12! / 5!7! = 792
A=pi*(r^2)