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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. 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?
10! / 3!(10-3)! = 120
x^(6-3) = x^3
V=l×w×h
M= (Y1-Y2)/(X1-X2)
2. The negative exponent x?n is equivalent to what?
A central angle is an angle formed by 2 radii.
Right
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
2(pi)r
3. Dividing by a number is the same as multiplying it by its
The direction of the inequality is reversed.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Reciprocal
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
4. Solve the quadratic equation ax^2 + bx + c= 0
An expression with just one term (-6x - 2a^2)
ODD number
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Lies opposite the greater angle
5. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
5 - 12 - 13
Null
2.592 kg
6. The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
The shortest arc between points A and B on a circle'S diameter.
Every number
Ø
7. How to determine percent decrease?
360°
(amount of decrease/original price) x 100%
(a + b)^2
The two xes after factoring.
8. (a^-1)/a^5
Ø
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
1/a^6
P=2(l+w)
9. -3²
7 / 1000
The sum of digits is divisible by 9.
9
P=4s (s=side)
10. 3/8 in percent?
Ø Ø=Ø
37.5%
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Negative
11. What is the name of set with a number of elements which cannot be counted?
9 & 6/7
180
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
An infinite set.
12. Area of a circle
A=pi*(r^2)
A=½bh
Negative
Positive
13. Perfect Squares 1-15
x - x+1 - x+2
360/n
Arc length = (n/360) x pi(2r) where n is the number of degrees.
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
14. What is the graph of f(x) shifted right c units or spaces?
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.)
x²-2xy+y²
F(x-c)
72
15. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
4.25 - 6 - 22
A percent is a fraction whose denominator is 100.
N! / (k!)(n-k)!
y/x is a constant
16. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
3x - 4x - 5x
Cd
P=4s (s=side)
(amount of decrease/original price) x 100%
17. What is the ratio of the sides of an isosceles right triangle?
6
1:1:sqrt2
7 / 1000
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
18. The sum of the measures of the n angles in a polygon with n sides
1
(distance)/(rate) d/r
61 - 67
(n-2) x 180
19. A number is divisible by 9 if...
The sum of digits is divisible by 9.
360°
4.25 - 6 - 22
B?b?b (where b is used as a factor n times)
20. 1/6 in percent?
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
16.6666%
0
13pi / 2
21. Distance
Subtract them. i.e (5^7)/(5^3)= 5^4
N! / (n-k)!
(rate)(time) d=rt
V=Lwh
22. 2³×7³
4725
The sum of digits is divisible by 9.
360/n
(2x7)³
23. Formula to calculate arc length?
A natural number greater than 1 that has no positive divisors other than 1 and itself
y = 2x^2 - 3
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The sum of the digits is a multiple of 9.
24. (12sqrt15) / (2sqrt5) =
x²+2xy+y²
Negative
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A reflection about the axis.
25. (6sqrt3) x (2sqrt5) =
$11 -448
2(pi)r
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
70
26. What is the empty set?
A central angle is an angle formed by 2 radii.
A set with no members - denoted by a circle with a diagonal through it.
90pi
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
27. 30 60 90
Two angles whose sum is 180.
0
True
5 - 12 - 13
28. First 10 prime #s
441000 = 1 10 10 10 21 * 21
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
y = (x + 5)/2
A percent is a fraction whose denominator is 100.
29. Circumference of a circle
2(pi)r
180
20.5
(a - b)(a + b)
30. Circumference of a circle?
Positive or Negative
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
4096
Diameter(Pi)
31. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
Be Zero!
Ø
1
32. Ø Is
N! / (k!)(n-k)!
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
7 / 1000
EVEN
33. 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))?
4:5
20.5
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
34. Simplify the expression (p^2 - q^2)/ -5(q - p)
4:5
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
(p + q)/5
75:11
35. The product of any number x and its reciprocal
1
Ø
x²-y²
P(E) = 1/1 = 1
36. If a is positive - an is
y/x is a constant
Positive
Cd
1/x
37. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
Two angles whose sum is 180.
288 (8 9 4)
Undefined
38. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
75:11
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)
Negative
39. What is a major arc?
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on line
183
40. Consecutive integers
x²-y²
y = (x + 5)/2
x - x+1 - x+2
20.5
41. The reciprocal of any non-zero number is
P(E) = ø
1/x
P=4s (s=side)
61 - 67
42. In a Regular Polygon - the measure of each exterior angle
The steeper the slope.
x²+2xy+y²
72
360/n
43. Reduce: 4.8 : 0.8 : 1.6
180
180°
6
6 : 1 : 2
44. Can you add sqrt 3 and sqrt 5?
Distance=rate×time or d=rt
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
C = (pi)d
No - only like radicals can be added.
45. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
A+c<b+c
The two xes after factoring.
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
46. If a<b - then
A+c<b+c
20.5
The direction of the inequality is reversed.
1 - P(E)
47. What are the rational numbers?
D/t (distance)/(time)
An infinite set.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
An is positive
48. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
48
28. n = 8 - k = 2. n! / k!(n-k)!
72
49. 30 60 90
An infinite set.
3 - 4 - 5
A reflection about the origin.
x²-y²
50. The reciprocal of any non-zero #x is
1/x
1.7
180
A=(base)(height)