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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. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
70
A-b is negative
The sum of its digits is divisible by 3.
2^9 / 2 = 256
2. How to find the circumference of a circle which circumscribes a square?
Yes - like radicals can be added/subtracted.
An infinite set.
an angle that is less than 90°
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
3. A number is divisible by 4 is...
(rate)(time) d=rt
Its last two digits are divisible by 4.
Move the decimal point to the right x places
Every number
4. ز
V=l×w×h
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
Ø
2sqrt6
5. Time
(distance)/(rate) d/r
A natural number greater than 1 that has no positive divisors other than 1 and itself
The sum of digits is divisible by 9.
83.333%
6. What is the ratio of the sides of an isosceles right triangle?
90pi
1:1:sqrt2
An angle which is supplementary to an interior angle.
y2-y1/x2-x1
7. Circumference of a Circle
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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)
C=2 x pi x r OR pi x D
8. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
A subset.
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
angle that is greater than 90° but less than 180°
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
9. How to recognize a # as a multiple of 3
441000 = 1 10 10 10 21 * 21
18
Negative
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)
10. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
4725
y = 2x^2 - 3
F(x-c)
D/t (distance)/(time)
11. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
2.592 kg
75:11
(a - b)^2
1/x
12. Area of a triangle?
D/t (distance)/(time)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(base*height) / 2
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
13. What is the name of set with a number of elements which cannot be counted?
10! / 3!(10-3)! = 120
C = 2(pi)r
An infinite set.
Do not have slopes!
14. (x^2)^4
x(x - y + 1)
F(x-c)
x^(2(4)) =x^8 = (x^4)^2
An isosceles right triangle.
15. Rate
Ø=P(E)=1
D/t (distance)/(time)
Edge³
Indeterminable.
16. To decrease a number by x%
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
16.6666%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
P= 2L + 2w
17. Define an 'expression'.
31 - 37
360°
13
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)
18. x^4 + x^7 =
4a^2(b)
Even prime number
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...
x^(4+7) = x^11
19. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
All numbers multiples of 1.
5 OR -5
2
F(x + c)
20. What is the measure of an exterior angle of a regular pentagon?
72
The objects within a set.
C = 2(pi)r
The direction of the inequality is reversed.
21. What is the slope of a horizontal line?
The second graph is less steep.
0
V=side³
Parallelogram
22. Legs 6 - 8. Hypotenuse?
Lies opposite the greater angle
12! / 5!7! = 792
90
10
23. a(b-c)
18
1/a^6
Positive
Ab-ac
24. What are the smallest three prime numbers greater than 65?
A 30-60-90 triangle.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
67 - 71 - 73
Every number
25. What is a set with no members called?
y = 2x^2 - 3
The empty set - denoted by a circle with a diagonal through it.
Be Zero!
x(x - y + 1)
26. If a<b - then
1
2(pi)r
Ab+ac
A+c<b+c
27. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
The second graph is less steep.
Null
Sector area = (n/360) X (pi)r^2
28. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
A-b is positive
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
90pi
2 & 3/7
29. What is the sum of the angles of a triangle?
1
180 degrees
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
61 - 67
30. If a is negative and n is even then an is (positive or negative?)
P=4s (s=side)
Ø
An is positive
Reciprocal
31. If the two sides of a triangle are unequal then the longer side.................
Lies opposite the greater angle
x^(4+7) = x^11
4a^2(b)
Triangles with same measure and same side lengths.
32. a>b then a - b is positive or negative?
4096
180°
Right
A-b is positive
33. First 10 prime #s
A-b is positive
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
The union of A and B.
(pi)r²
34. 8.84 / 5.2
Ab+ac
x²-2xy+y²
1.7
7 / 1000
35. In a Regular Polygon - the measure of each exterior angle
0
Ab=k (k is a constant)
x^(2(4)) =x^8 = (x^4)^2
360/n
36. formula for area of a triangle
Members or elements
A natural number greater than 1 that has no positive divisors other than 1 and itself
Triangles with same measure and same side lengths.
A=½bh
37. Simplify (a^2 + b)^2 - (a^2 - b)^2
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
4a^2(b)
Subtract them. i.e (5^7)/(5^3)= 5^4
x²-y²
38. A quadrilateral where two diagonals bisect each other
90pi
A= (1/2) b*h
Parallelogram
The point of intersection of the systems.
39. What is a subset?
The empty set - denoted by a circle with a diagonal through it.
A grouping of the members within a set based on a shared characteristic.
Negative
An infinite set.
40. The perimeter of a square is 48 inches. The length of its diagonal is:
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
12sqrt2
A-b is positive
360°
41. 25^(1/2) or sqrt. 25 =
5 OR -5
Triangles with same measure and same side lengths.
10
V=l×w×h
42. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
The sum of digits is divisible by 9.
(b + c)
4:5
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
43. 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?
N! / (n-k)!
18
Null
Its divisible by 2 and by 3.
44. Simplify the expression (p^2 - q^2)/ -5(q - p)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
A subset.
(p + q)/5
360°
45. 30 60 90
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
3x - 4x - 5x
Add them. i.e. (5^7) * (5^3) = 5^10
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.
46. P and r are factors of 100. What is greater - pr or 100?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Indeterminable.
4a^2(b)
3 - -3
47. What is the graph of f(x) shifted right c units or spaces?
A-b is negative
4725
F(x-c)
A reflection about the axis.
48. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
C=2 x pi x r OR pi x D
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
23 - 29
52
49. What is the area of a regular hexagon with side 6?
(pi)r²
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
441000 = 1 10 10 10 21 * 21
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
50. 40 < all primes<50
C=2 x pi x r OR pi x D
9
41 - 43 - 47
NOT A PRIME