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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. What is an isoceles triangle?
90pi
Two equal sides and two equal angles.
y = 2x^2 - 3
Right
2. 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?
A<-b
Negative
A natural number greater than 1 that has no positive divisors other than 1 and itself
500
3. (2²)³
26
1
= (actual decrease/Original amount) x 100%
2²
4. Simplify (a^2 + b)^2 - (a^2 - b)^2
(base*height) / 2
x²-2xy+y²
4a^2(b)
Ø
5. Area of a Parallelogram:
A=(base)(height)
Parallelogram
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
D/t (distance)/(time)
6. What is a tangent?
The two xes after factoring.
A tangent is a line that only touches one point on the circumference of a circle.
4:5
72
7. The only number that is equal to its opposite
x²-y²
An infinite set.
D/t (distance)/(time)
Ø Ø=Ø
8. 30 60 90
N! / (n-k)!
Two (Ø×2=Ø)
D=rt so r= d/t and t=d/r
x - x(SR3) - 2x
9. What percent of 40 is 22?
The interesection of A and B.
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
x²+2xy+y²
55%
10. Slope of any line that goes up from left to right
P(E) = ø
10! / 3!(10-3)! = 120
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
11. The reciprocal of any non-zero number is
1/x
Ø Ø=Ø
3
The set of output values for a function.
12. 5/6 in percent?
Subtract them. i.e (5^7)/(5^3)= 5^4
x²-y²
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)
83.333%
13. One is (a prime or not?)
The empty set - denoted by a circle with a diagonal through it.
NOT A PRIME
288 (8 9 4)
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
14. What is the area of a regular hexagon with side 6?
13pi / 2
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
A=½bh
An isosceles right triangle.
15. Define a 'monomial'
Two angles whose sum is 180.
Edge³
8
An expression with just one term (-6x - 2a^2)
16. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
360°
x^(2(4)) =x^8 = (x^4)^2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A 30-60-90 triangle.
17. b¹
1
130pi
28
3 - -3
18. (x+y)²
EVEN
13pi / 2
An infinite set.
x²+2xy+y²
19. What is the intersection of A and B?
Null
A-b is positive
The set of elements found in both A and B.
Ab+ac
20. Important properties of a 30-60-90 triangle?
F(x + c)
P(E) = number of favorable outcomes/total number of possible outcomes
The sum of digits is divisible by 9.
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
21. What number between 70 & 75 - inclusive - has the greatest number of factors?
Positive or Negative
P(E) = ø
5 OR -5
72
22. In a rectangle - all angles are
Right
V=side³
Negative
(amount of decrease/original price) x 100%
23. Ø is
F(x) - c
zero
Smallest positive integer
Even
24. x^2 = 9. What is the value of x?
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
20.5
3 - -3
(distance)/(rate) d/r
25. (12sqrt15) / (2sqrt5) =
2^9 / 2 = 256
Ø Ø=Ø
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Negative
26. Slope
A= (1/2) b*h
y2-y1/x2-x1
75:11
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
27. Positive integers that have exactly 2 positive divisors are
(a + b)^2
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Add them. i.e. (5^7) * (5^3) = 5^10
28. If an inequality is multiplied or divided by a negative number....
2²
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
The direction of the inequality is reversed.
ODD number
29. How to recognize a # as a multiple of 4
(x+y)(x+y)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
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-y²
30. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
180°
26
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
28. n = 8 - k = 2. n! / k!(n-k)!
31. What is the 'Range' of a function?
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.)
1/a^6
The set of output values for a function.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
32. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
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)
Ø
Ø
33. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
No - only like radicals can be added.
x²-y²
The sum of the digits is a multiple of 9.
52
34. 4.809 X 10^7 =
x - x+1 - x+2
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
12.5%
.0004809 X 10^11
35. 50 < all primes< 60
53 - 59
A-b is positive
Add them. i.e. (5^7) * (5^3) = 5^10
Pi(diameter)
36. the slope of a line in y=mx+b
27
1/2 times 7/3
M
The two xes after factoring.
37. The objects in a set are called two names:
1
The set of output values for a function.
Members or elements
Straight Angle
38. 25/2³
3
2²
10! / (10-3)! = 720
F(x + c)
39. Circumference of a circle?
Diameter(Pi)
Undefined - because we can'T divide by 0.
70
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
40. 8.84 / 5.2
(amount of decrease/original price) x 100%
Smallest positive integer
The set of elements found in both A and B.
1.7
41. Dividing by a number is the same as multiplying it by its
x - x+1 - x+2
Reciprocal
3x - 4x - 5x
Two angles whose sum is 90.
42. Acute Angle
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
an angle that is less than 90°
Infinite.
Reciprocal
43. 25^(1/2) or sqrt. 25 =
360/n
5 OR -5
A=(base)(height)
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
44. Legs 5 - 12. Hypotenuse?
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
13
27^(-4)
23 - 29
45. 1 is the
90
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)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Smallest positive integer
46. x^6 / x^3
x^(6-3) = x^3
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.)
Infinite.
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
47. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
True
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
EVEN
A central angle is an angle formed by 2 radii.
48. Which is greater? 27^(-4) or 9^(-8)
180°
The overlapping sections.
The set of input values for a function.
27^(-4)
49. factored binomial product of (x+y)²
A=(base)(height)
Ø
A+c<b+c
x²+2xy+y²
50. How to recognize if a # is a multiple of 12
55%
4a^2(b)
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.)
13