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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 is negative and n is even then an is (positive or negative?)
Ab-ac
The set of elements found in both A and B.
.0004809 X 10^11
An is positive
2. 0^0
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)
90pi
6
Undefined
3. Simplify the expression [(b^2 - c^2) / (b - c)]
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
A chord is a line segment joining two points on a circle.
An isosceles right triangle.
(b + c)
4. Product of any number and Ø is
Ø
F(x-c)
10
Arc length = (n/360) x pi(2r) where n is the number of degrees.
5. Ø divided by 7
1
Ø
y2-y1/x2-x1
Even
6. What are the integers?
52
3x - 4x - 5x
Yes - like radicals can be added/subtracted.
All numbers multiples of 1.
7. (6sqrt3) x (2sqrt5) =
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Sum of digits is a multiple of 3 and the last digit is even.
8. 10^6 has how many zeroes?
0
6
(a - b)^2
1 - P(E)
9. Positive integers that have exactly 2 positive divisors are
Its divisible by 2 and by 3.
V=l×w×h
y = (x + 5)/2
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
10. 40 < all primes<50
5 - 12 - 13
41 - 43 - 47
130pi
The objects within a set.
11. Solve the quadratic equation ax^2 + bx + c= 0
... the square of the ratios of the corresponding sides.
C = (pi)d
4725
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
12. When multiplying exponential #s with the same base - you do this to the exponents...
(a - b)(a + b)
90°
Ø
Add them. i.e. (5^7) * (5^3) = 5^10
13. 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)?
Ab-ac
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
A=pi*(r^2)
y = (x + 5)/2
14. Simplify 9^(1/2) X 4^3 X 2^(-6)?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
x - x(SR3) - 2x
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
3
15. How to find the circumference of a circle which circumscribes a square?
48
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(a + b)^2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
16. 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))?
20.5
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)
Pi(diameter)
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.)
17. 1 is the
Ø Ø=Ø
1
Smallest positive integer
Diameter(Pi)
18. The important properties of a 45-45-90 triangle?
1:sqrt3:2
V=l×w×h
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.
Do not have slopes!
19. What is a major arc?
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on line
183
20. Vertical lines
The union of A and B.
Do not have slopes!
Ø
(pi)r²
21. Area of a circle
y/x is a constant
Can be negative - zero - or positive
(pi)r²
The shortest arc between points A and B on a circle'S diameter.
22. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The shortest arc between points A and B on a circle'S diameter.
An expression with just one term (-6x - 2a^2)
23. An Angle that'S 180°
180°
Straight Angle
12! / 5!7! = 792
10! / 3!(10-3)! = 120
24. Simplify the expression (p^2 - q^2)/ -5(q - p)
D/t (distance)/(time)
(p + q)/5
The second graph is less steep.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
25. What is a minor arc?
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183
26. What percent of 40 is 22?
1 & 37/132
55%
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Positive
27. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
7 / 1000
31 - 37
A reflection about the origin.
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.)
28. How to recognize a multiple of 6
10! / (10-3)! = 720
Sum of digits is a multiple of 3 and the last digit is even.
37.5%
C = 2(pi)r
29. Find distance when given time and rate
72
11 - 13 - 17 - 19
20.5
D=rt so r= d/t and t=d/r
30. In a Regular Polygon - the measure of each exterior angle
360/n
The two xes after factoring.
Move the decimal point to the right x places
Ø
31. Time
12! / 5!7! = 792
Negative
(distance)/(rate) d/r
1
32. (x-y)(x+y)
P(E) = ø
x²-y²
Even
Null
33. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
A+c<b+c
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)
1
34. What are 'Supplementary angles?'
(base*height) / 2
2 & 3/7
Two angles whose sum is 180.
Yes - like radicals can be added/subtracted.
35. Area of a Parallelogram:
53 - 59
A=(base)(height)
2 & 3/7
An infinite set.
36. What is a subset?
The sum of digits is divisible by 9.
1/x
A grouping of the members within a set based on a shared characteristic.
Two angles whose sum is 180.
37. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
1
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Every number
38. Circumference of a Circle
Distance=rate×time or d=rt
10
3 - 4 - 5
C=2 x pi x r OR pi x D
39. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
180°
0
A=½bh
40. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
P=4s (s=side)
4a^2(b)
P= 2L + 2w
9 : 25
41. binomial product of (x-y)²
3/2 - 5/3
(x+y)(x-y)
31 - 37
Infinite.
42. Circumference of a circle
(length)(width)(height)
3
2(pi)r
53 - 59
43. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
0
360°
75:11
4:5
44. -3²
28. n = 8 - k = 2. n! / k!(n-k)!
A multiple of every integer
9
Two angles whose sum is 180.
45. What is the order of operations?
A=½bh
A set with a number of elements which can be counted.
x²-y²
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
46. Ø Is
Undefined - because we can'T divide by 0.
EVEN
4a^2(b)
V=side³
47. 1/6 in percent?
A central angle is an angle formed by 2 radii.
x - x+1 - x+2
(a - b)(a + b)
16.6666%
48. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
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.)
Can be negative - zero - or positive
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A set with no members - denoted by a circle with a diagonal through it.
49. 30 60 90
5 - 12 - 13
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
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.)
12sqrt2
50. (x-y)²
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.
4096
An angle which is supplementary to an interior angle.
x²-2xy+y²