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GRE Math: Common Errors

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. 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)?
(a + b)^2
...multiply by 100.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
y = (x + 5)/2

2. Formula of rectangle where l increases by 20% and w decreases by 20%
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
0
x= (1.2)(.8)lw
The point of intersection of the systems.

3. What is the maximum value for the function g(x) = (-2x^2) -1?
Diameter(Pi)
Lies opposite the greater angle
1
x^(4+7) = x^11

4. 1/2 divided by 3/7 is the same as
1/2 times 7/3
Pi is the ratio of a circle'S circumference to its diameter.
16.6666%
x(x - y + 1)

5. What is the 'domain' of a function?
An arc is a portion of a circumference of a circle.
87.5%
(a - b)(a + b)
The set of input values for a function.

6. What is the set of elements which can be found in either A or B?
The union of A and B.
Indeterminable.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
41 - 43 - 47

7. Which quadrant is the upper right hand?
I
IV
31 - 37
13pi / 2

8. What is the slope of a horizontal line?
5
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...
0
The steeper the slope.

9. Length of an arc of a circle?
Its negative reciprocal. (-b/a)
Angle/360 x 2(pi)r
2 & 3/7
Yes - like radicals can be added/subtracted.

10. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
18
y = 2x^2 - 3
2^9 / 2 = 256
The objects within a set.

11. What are the integers?
An isosceles right triangle.
All numbers multiples of 1.
Triangles with same measure and same side lengths.
2^9 / 2 = 256

12. 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?
90
... the square of the ratios of the corresponding sides.
10! / (10-3)! = 720
F(x + c)

13. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
The sum of its digits is divisible by 3.
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
83.333%

14. What are the members or elements of a set?
The objects within a set.
90pi
A grouping of the members within a set based on a shared characteristic.
Sqrt 12

15. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
When the function is not defined for all real numbers -; only a subset of the real numbers.
x= (1.2)(.8)lw
Angle/360 x 2(pi)r

16. What is the side length of an equilateral triangle with altitude 6?
Divide by 100.
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...
6 : 1 : 2
27^(-4)

17. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
C = (pi)d
1:sqrt3:2
2^9 / 2 = 256
N! / (k!)(n-k)!

18. Which is greater? 27^(-4) or 9^(-8)
The overlapping sections.
The sum of digits is divisible by 9.
27^(-4)
(a - b)(a + b)

19. How many multiples does a given number have?
1 & 37/132
Infinite.
...multiply by 100.
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)

20. Number of degrees in a triangle
N! / (n-k)!
180
6 : 1 : 2
1

21. 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?
1
1/(x^y)
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
7 / 1000

22. When the 'a' in a parabola is positive....
1
The curve opens upward and the vertex is the minimal point on the graph.
37.5%
18

23. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
When the function is not defined for all real numbers -; only a subset of the real numbers.
Diameter(Pi)
10
2^9 / 2 = 256

24. Formula to find a circle'S circumference from its radius?
C = 2(pi)r
180 degrees
The sum of digits is divisible by 9.
Factors are few - multiples are many.

25. How to find the diagonal of a rectangular solid?
Pi is the ratio of a circle'S circumference to its diameter.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
(a - b)^2
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

26. 1/6 in percent?
A central angle is an angle formed by 2 radii.
37.5%
16.6666%
Its last two digits are divisible by 4.

27. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A reflection about the axis.
3
A central angle is an angle formed by 2 radii.
A 30-60-90 triangle.

28. What is the area of a regular hexagon with side 6?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
A tangent is a line that only touches one point on the circumference of a circle.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
A central angle is an angle formed by 2 radii.

29. Can the input value of a function have more than one output value (i.e. x: y - y1)?
90
67 - 71 - 73
No - the input value has exactly one output.
The second graph is less steep.

30. Factor a^2 + 2ab + b^2
3/2 - 5/3
13
(a + b)^2
61 - 67

31. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
The set of output values for a function.
2 & 3/7
The union of A and B.
II

32. 10<all primes<20
11 - 13 - 17 - 19
A = I (1 + rt)
N! / (k!)(n-k)!
C = (pi)d

33. 20<all primes<30
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
The curve opens downward and the vertex is the maximum point on the graph.
...multiply by 100.
23 - 29

34. How to determine percent decrease?
(amount of decrease/original price) x 100%
A set with a number of elements which can be counted.
500
(a - b)^2

35. What is the 'Restricted domain of a function'?
Even
When the function is not defined for all real numbers -; only a subset of the real numbers.
F(x-c)
2.592 kg

36. What are the smallest three prime numbers greater than 65?
13
67 - 71 - 73
3
27^(-4)

37. What is the order of operations?
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)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
(a - b)^2

38. Legs 5 - 12. Hypotenuse?
13
23 - 29
A= I (1 + (r/c))^tC - where I is the investment - C is the number of times compounded annually - and t is the number of years.
1:1:sqrt2

39. 0^0
Undefined
Its last two digits are divisible by 4.
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)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

40. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
Yes. [i.e. f(x) = x^2 - 1
12! / 5!7! = 792
3/2 - 5/3
31 - 37

41. What is the ratio of the sides of a 30-60-90 triangle?
The shortest arc between points A and B on a circle'S diameter.
1:sqrt3:2
A chord is a line segment joining two points on a circle.
The point of intersection of the systems.

42. Is 0 even or odd?
Even
Area of the base X height = (pi)hr^2
(base*height) / 2
1

43. Which quadrant is the upper left hand?
II
0
An infinite set.
37.5%

44. 6w^2 - w - 15 = 0
3/2 - 5/3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
When the function is not defined for all real numbers -; only a subset of the real numbers.
(amount of decrease/original price) x 100%

45. What is the sum of the angles of a triangle?
(a - b)(a + b)
The two xes after factoring.
(a + b)^2
180 degrees

46. What is the formula for compounded interest?
2sqrt6
A= I (1 + (r/c))^tC - where I is the investment - C is the number of times compounded annually - and t is the number of years.
1
x= (1.2)(.8)lw

47. To multiply a number by 10^x
41 - 43 - 47
Move the decimal point to the right x places
A central angle is an angle formed by 2 radii.
27^(-4)

48. To convert a percent to a fraction....
23 - 29
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Divide by 100.
70

49. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
Sector area = (n/360) X (pi)r^2
x^(2(4)) =x^8 = (x^4)^2
1
A set with a number of elements which can be counted.

50. Pi is a ratio of what to what?

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