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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 are the rational numbers?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Smallest positive integer
Relationship cannot be determined (what if x is negative?)
360°
2. (x+y)²
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x²+2xy+y²
90pi
1 & 37/132
3. What percent of 40 is 22?
55%
EVEN
Undefined
x²-y²
4. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
The greatest value minus the smallest.
Indeterminable.
(a - b)(a + b)
4725
5. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
The steeper the slope.
Ø
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
6. a^2 + 2ab + b^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Parallelogram
(a + b)^2
Be Zero!
7. A number is divisible by 9 if...
41 - 43 - 47
N! / (k!)(n-k)!
The sum of digits is divisible by 9.
The set of elements found in both A and B.
8. What is the intersection of A and B?
Positive or Negative
The set of elements found in both A and B.
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...
All numbers multiples of 1.
9. If a lamp increases from $80 to $100 - what is the percent increase?
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
A= (1/2) b*h
A=pi*(r^2)
Infinite.
10. The larger the absolute value of the slope...
The set of output values for a function.
A multiple of every integer
The set of elements which can be found in either A or B.
The steeper the slope.
11. a>b then a - b is positive or negative?
A-b is positive
A tangent is a line that only touches one point on the circumference of a circle.
(distance)/(rate) d/r
x²+2xy+y²
12. The only number that is equal to its opposite
Ab+ac
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
Ø Ø=Ø
y/x is a constant
13. 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?
Even
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
10! / 3!(10-3)! = 120
Ab-ac
14. 30 60 90
6
20.5
3
5 - 12 - 13
15. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
M
Relationship cannot be determined (what if x is negative?)
A reflection about the axis.
Ø
16. A prime number (or a prime)
Sector area = (n/360) X (pi)r^2
The greatest value minus the smallest.
A natural number greater than 1 that has no positive divisors other than 1 and itself
An isosceles right triangle.
17. Area of a rectangle
F(x) - c
A = length x width
x^(2(4)) =x^8 = (x^4)^2
67 - 71 - 73
18. 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?
An expression with just one term (-6x - 2a^2)
The sum of its digits is divisible by 3.
The interesection of A and B.
48
19. What is a percent?
31 - 37
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
A percent is a fraction whose denominator is 100.
3 - -3
20. binomial product of (x-y)²
A percent is a fraction whose denominator is 100.
(x+y)(x-y)
1
27^(-4)
21. Area of a triangle?
x²-y²
8
A = length x width
(base*height) / 2
22. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
angle that is greater than 90° but less than 180°
(a - b)^2
Positive or Negative
2sqrt6
23. Circumference of a Circle
A=pi*(r^2)
C=2 x pi x r OR pi x D
3x - 4x - 5x
Be Zero!
24. One is (a prime or not?)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Ø
... the square of the ratios of the corresponding sides.
NOT A PRIME
25. Convert 0.7% to a fraction.
7 / 1000
360°
angle that is greater than 90° but less than 180°
Null
26. P and r are factors of 100. What is greater - pr or 100?
75:11
Indeterminable.
71 - 73 - 79
The union of A and B.
27. In any polygon - all external angles equal up to
360°
6 : 1 : 2
The objects within a set.
(length)(width)(height)
28. Find distance when given time and rate
A 30-60-90 triangle.
D=rt so r= d/t and t=d/r
(base*height) / 2
1:1:sqrt2
29. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Infinite.
C = 2(pi)r
2(pi)r
Cd
30. Ø is
All numbers multiples of 1.
Even
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(pi)r²
31. 5/6 in percent?
83.333%
9
x²-y²
5 - 12 - 13
32. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
360°
Ø
y = 2x^2 - 3
2
33. Pi is a ratio of what to what?
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34. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
75:11
4:5
A subset.
No - only like radicals can be added.
35. Which is greater? 200x^295 or 10x^294?
(n-2) x 180
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
72
Relationship cannot be determined (what if x is negative?)
36. Factor a^2 + 2ab + b^2
1
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
P(E) = 1/1 = 1
(a + b)^2
37. What is the 'Solution' for a set of inequalities.
An isosceles right triangle.
The point of intersection of the systems.
The overlapping sections.
3/2 - 5/3
38. x^4 + x^7 =
P=4s (s=side)
11 - 13 - 17 - 19
x^(4+7) = x^11
The sum of the digits is a multiple of 9.
39. 10^6 has how many zeroes?
A 30-60-90 triangle.
6
F(x + c)
A chord is a line segment joining two points on a circle.
40. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
1
x²-y²
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
2^9 / 2 = 256
41. What is the set of elements found in both A and B?
The interesection of A and B.
Factors are few - multiples are many.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
42. What is the area of a regular hexagon with side 6?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
(x+y)(x-y)
Indeterminable.
43. What is the graph of f(x) shifted upward c units or spaces?
A tangent is a line that only touches one point on the circumference of a circle.
F(x) + c
P=2(l+w)
The point of intersection of the systems.
44. How to recognize if a # is a multiple of 12
M
Ø=P(E)=1
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)
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.)
45. What is a minor arc?
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46. (x-y)²
x²-2xy+y²
x²+2xy+y²
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.)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
47. 8.84 / 5.2
x²-y²
1.7
360°
Positive
48. 7/8 in percent?
Null
The two xes after factoring.
87.5%
(length)(width)(height)
49. What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
8
an angle that is less than 90°
1 - P(E)
50. What is a finite set?
Ø
A set with a number of elements which can be counted.
70
3 - -3