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GRE Math: All In One

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 congruent triangles?
The steeper the slope.
Triangles with same measure and same side lengths.
(distance)/(rate) d/r
180 degrees

2. 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.
A=½bh
1
F(x) + c

3. Write 10 -843 X 10^7 in scientific notation
The overlapping sections.
Lies opposite the greater angle
27
1.0843 X 10^11

4. What are the integers?
9 : 25
All numbers multiples of 1.
2.592 kg
Relationship cannot be determined (what if x is negative?)

5. The Denominator can never
V=side³
Be Zero!
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
Factors are few - multiples are many.

6. Solve the quadratic equation ax^2 + bx + c= 0
1:sqrt3:2
Factors are few - multiples are many.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The direction of the inequality is reversed.

7. 10<all primes<20
P=2(l+w)
11 - 13 - 17 - 19
x²-y²
Members or elements

8. Circumference of a circle
75:11
Infinite.
Pi(diameter)
4:5

9. Dividing by a number is the same as multiplying it by its
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
Smallest positive integer
7 / 1000
Reciprocal

10. A number is divisible by 4 is...
10! / 3!(10-3)! = 120
The set of elements which can be found in either A or B.
The overlapping sections.
Its last two digits are divisible by 4.

11. What number between 70 & 75 - inclusive - has the greatest number of factors?
A=pi*(r^2)
M
(distance)/(rate) d/r
72

12. Describe the relationship between 3x^2 and 3(x - 1)^2
360/n
Triangles with same measure and same side lengths.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
x²-y²

13. Factor x^2 - xy + x.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
x²-y²
3
x(x - y + 1)

14. a^2 - b^2 =
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)
Its last two digits are divisible by 4.
A subset.
(a - b)(a + b)

15. What are complementary angles?
Two angles whose sum is 90.
Add them. i.e. (5^7) * (5^3) = 5^10
23 - 29
90

16. 1/6 in percent?
16.6666%
52
87.5%
5

17. What is the maximum value for the function g(x) = (-2x^2) -1?
1
5 OR -5
F(x-c)
Cd

18. Volume of a rectangular box
V=Lwh
(a - b)(a + b)
90pi
(b + c)

19. What is the surface area of a cylinder with radius 5 and height 8?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
130pi
1/a^6
A=(base)(height)

20. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
75:11
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
55%
360°

21. b¹
Do not have slopes!
P=4s (s=side)
1
Add them. i.e. (5^7) * (5^3) = 5^10

22. Legs 5 - 12. Hypotenuse?
Subtract them. i.e (5^7)/(5^3)= 5^4
13
An angle which is supplementary to an interior angle.
A = length x width

23. What is a central angle?
(n-2) x 180
x(x - y + 1)
A central angle is an angle formed by 2 radii.
The interesection of A and B.

24. Formula for the area of a circle?
(a + b)^2
y/x is a constant
A = pi(r^2)
D/t (distance)/(time)

25. The sum of all angles around a point
360°
Negative
0
Ab-ac

26. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
2
x(x - y + 1)
10! / (10-3)! = 720
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

27. What is the graph of f(x) shifted right c units or spaces?
1 & 37/132
41 - 43 - 47
F(x-c)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

28. binomial product of (x+y)²
(x+y)(x+y)
360/n
1
Two equal sides and two equal angles.

29. Formula to calculate arc length?
F(x + c)
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.)
Arc length = (n/360) x pi(2r) where n is the number of degrees.
2 & 3/7

30. Evaluate 4/11 + 11/12
1/a^6
The set of output values for a function.
4a^2(b)
1 & 37/132

31. Formula for the area of a sector of a circle?
EVEN
2
6 : 1 : 2
Sector area = (n/360) X (pi)r^2

32. What is an arc of a circle?
An arc is a portion of a circumference of a circle.
13pi / 2
Ab+ac
Pi is the ratio of a circle'S circumference to its diameter.

33. The only number that is equal to its opposite
P=2(l+w)
X
Ø Ø=Ø
12sqrt2

34. Ø is
A multiple of every integer
C = 2(pi)r
(distance)/(rate) d/r
x²+2xy+y²

35. Probability of an Event
.0004809 X 10^11
P(E) = number of favorable outcomes/total number of possible outcomes
x - x(SR3) - 2x
Ø

36. A number is divisible by 9 if...
Null
The sum of digits is divisible by 9.
NOT A PRIME
(x+y)(x-y)

37. 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?
9 : 25
An angle which is supplementary to an interior angle.
90pi
10! / 3!(10-3)! = 120

38. 5x^2 - 35x -55 = 0
Right
23 - 29
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

39. How to find the circumference of a circle which circumscribes a square?
2(pi)r
No - only like radicals can be added.
1
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

40. What is the graph of f(x) shifted left c units or spaces?
True
26
F(x + c)
A subset.

41. The reciprocal of any non-zero number is
The sum of its digits is divisible by 3.
1/x
1
Sum of digits is a multiple of 3 and the last digit is even.

42. Number of degrees in a triangle
180
A = length x width
an angle that is less than 90°
Positive or Negative

43. How to recognize a # as a multiple of 3
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
1
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)
90

44. What are the irrational numbers?

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45. One is (a prime or not?)
An infinite set.
2^9 / 2 = 256
NOT A PRIME
1/x

46. (2²)³
All numbers multiples of 1.
(rate)(time) d=rt
26
An expression with just one term (-6x - 2a^2)

47. Consecutive integers
D/t (distance)/(time)
x - x+1 - x+2
3
A<-b

48. How many 3-digit positive integers are even and do not contain the digit 4?
52
288 (8 9 4)
M
The longest arc between points A and B on a circle'S diameter.

49. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
A set with no members - denoted by a circle with a diagonal through it.
N! / (n-k)!
Cd
Two angles whose sum is 180.

50. What is the side length of an equilateral triangle with altitude 6?
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...
F(x + c)
75:11
The sum of its digits is divisible by 3.

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GRE Math: All In One

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