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GRE Math: All In One

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. Which is greater? 64^5 or 16^8
3
An expression with just one term (-6x - 2a^2)
13
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16

2. 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)?
y = (x + 5)/2
F(x) - c
5
A chord is a line segment joining two points on a circle.

3. 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?
P(E) = 1/1 = 1
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
48
(x+y)(x-y)

4. Can you simplify sqrt72?
The shortest arc between points A and B on a circle'S diameter.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
x(x - y + 1)
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

5. 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?
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
(b + c)
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...
9

6. What is the intersection of A and B?
The set of elements found in both A and B.
90
The objects within a set.
True

7. The product of any number x and its reciprocal
The empty set - denoted by a circle with a diagonal through it.
90°
D/t (distance)/(time)
1

8. How to recognize if a # is a multiple of 12
28
The interesection of A and 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.)
Its divisible by 2 and by 3.

9. 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)]?
x²+2xy+y²
x²-y²
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
True

10. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
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.)
2(pi)r
62.5%

11. Slope given 2 points
M= (Y1-Y2)/(X1-X2)
20.5
Pi(diameter)
An angle which is supplementary to an interior angle.

12. If a is inversely porportional to b - what does it equal?
The interesection of A and B.
A subset.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Ab=k (k is a constant)

13. X is the opposite of
X
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The sum of its digits is divisible by 3.
2²

14. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
1 & 37/132
Distance=rate×time or d=rt
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
M= (Y1-Y2)/(X1-X2)

15. factored binomial product of (x+y)²
A subset.
x²+2xy+y²
12sqrt2
P=4s (s=side)

16. a<b then a - b is positive or negative?
A+c<b+c
A-b is negative
Every number
11 - 13 - 17 - 19

17. binomial product of (x+y)(x-y)
An arc is a portion of a circumference of a circle.
A set with no members - denoted by a circle with a diagonal through it.
x²-y²
130pi

18. How many multiples does a given number have?
Undefined - because we can'T divide by 0.
A+c<b+c
Infinite.
Every number

19. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
90°
Pi is the ratio of a circle'S circumference to its diameter.
3
2sqrt6

20. Rate
(2x7)³
A tangent is a line that only touches one point on the circumference of a circle.
y/x is a constant
D/t (distance)/(time)

21. 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?
x(x - y + 1)
2.592 kg
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
3x - 4x - 5x

22. How to recognize a multiple of 6
The set of output values for a function.
13pi / 2
1/a^6
Sum of digits is a multiple of 3 and the last digit is even.

23. Find distance when given time and rate
D=rt so r= d/t and t=d/r
61 - 67
x²+2xy+y²
1

24. a(b+c)
Ab+ac
... the square of the ratios of the corresponding sides.
P=4s (s=side)
Lies opposite the greater angle

25. If a product of two numbers is Ø - one number must be
D=rt so r= d/t and t=d/r
P= 2L + 2w
F(x-c)
Ø

26. 30 60 90
12! / 5!7! = 792
1
x - x(SR3) - 2x
6

27. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
ODD number
Ø=P(E)=1
$11 -448
F(x) + c

28. x^4 + x^7 =
9 : 25
48
F(x-c)
x^(4+7) = x^11

29. What is the maximum value for the function g(x) = (-2x^2) -1?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
2²
Ø
1

30. 2 is the only
67 - 71 - 73
Even prime number
F(x-c)
A=pi*(r^2)

31. Probability of Event all cases
An expression with just one term (-6x - 2a^2)
Ø=P(E)=1
52
ODD number

32. The reciprocal of any non-zero number is
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
6 : 1 : 2
41 - 43 - 47
1/x

33. When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Two equal sides and two equal angles.
31 - 37
180

34. The objects in a set are called two names:
V=l×w×h
x²-2xy+y²
Members or elements
C = (pi)d

35. factored binomial product of (x-y)²
2 & 3/7
The direction of the inequality is reversed.
x²-2xy+y²
1 - P(E)

36. Evaluate 3& 2/7 / 1/3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
3
Move the decimal point to the right x places
9 & 6/7

37. A prime number (or a prime)
A natural number greater than 1 that has no positive divisors other than 1 and itself
Its last two digits are divisible by 4.
D/t (distance)/(time)
An isosceles right triangle.

38. Acute Angle
A multiple of every integer
an angle that is less than 90°
31 - 37
A natural number greater than 1 that has no positive divisors other than 1 and itself

39. How to recognize a # as a multiple of 4
The set of output values for 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.)
Ab=k (k is a constant)
Two angles whose sum is 90.

40. -3²
9
P(E) = ø
V=Lwh
A=pi*(r^2)

41. Write 10 -843 X 10^7 in scientific notation
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1.0843 X 10^11
(base*height) / 2
130pi

42. The ratio of the areas of two similar polygons is ...
9
2sqrt6
12.5%
... the square of the ratios of the corresponding sides.

43. The larger the absolute value of the slope...
Do not have slopes!
The steeper the slope.
26
31 - 37

44. Ø²
52
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Ø
288 (8 9 4)

45. The Perimeter of a rectangle
P=2(l+w)
Ab+ac
y/x is a constant
A-b is negative

46. What is the ratio of the sides of an isosceles right triangle?
1
1:1:sqrt2
10
70

47. What are the members or elements of a set?
Diameter(Pi)
x^(4+7) = x^11
Be Zero!
The objects within a set.

48. 25^(1/2) or sqrt. 25 =
x²-2xy+y²
Members or elements
5 OR -5
1/x

49. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A grouping of the members within a set based on a shared characteristic.
A-b is positive
(amount of decrease/original price) x 100%

50. Factor a^2 + 2ab + b^2
Positive
5
Add them. i.e. (5^7) * (5^3) = 5^10
(a + b)^2