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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. The larger the absolute value of the slope...
N! / (n-k)!
62.5%
The steeper the slope.
13

2. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
413.03 / 10^4 (move the decimal point 4 places to the left)
61 - 67
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)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

3. Legs: 3 - 4. Hypotenuse?
5
2.592 kg
N! / (k!)(n-k)!
Members or elements

4. Describe the relationship between the graphs of x^2 and (1/2)x^2
1
The interesection of A and B.
3sqrt4
The second graph is less steep.

5. What is the 'domain' of a function?
True
The set of input values for a function.
90
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

6. What is a minor arc?

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7. When the 'a' in the parabola is negative...
Ax^2 + bx + c where a -b and c are constants and a /=0
A subset.
The curve opens downward and the vertex is the maximum point on the graph.
An isosceles right triangle.

8. x^4 + x^7 =
4.25 - 6 - 22
52
x^(4+7) = x^11
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

9. Evaluate (4^3)^2
4096
(a + b)^2
6
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

10. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
III
1
Angle/360 x (pi)r^2
130pi

11. What is the graph of f(x) shifted left c units or spaces?
Sector area = (n/360) X (pi)r^2
0
Part = Percent X Whole
F(x + c)

12. What is the 'Range' of a series of numbers?
Diameter(Pi)
Angle/360 x 2(pi)r
The greatest value minus the smallest.
72

13. The objects in a set are called two names:
Members or elements
3/2 - 5/3
N! / (k!)(n-k)!
The greatest value minus the smallest.

14. The slope of a line perpendicular to (a/b)?
87.5%
(amount of decrease/original price) x 100%
Its negative reciprocal. (-b/a)
1

15. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
1
x^(4+7) = x^11
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

16. The ratio of the areas of two similar polygons is ...
2(pi)r^2 + 2(pi)rh
... the square of the ratios of the corresponding sides.
61 - 67
6

17. 4.809 X 10^7 =
.0004809 X 10^11
20.5
Undefined - because we can'T divide by 0.
10

18. 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...
The sum of its digits is divisible by 3.
6
288 (8 9 4)

19. How to find the diagonal of a rectangular solid?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
61 - 67
Sector area = (n/360) X (pi)r^2
x= (1.2)(.8)lw

20. (-1)^3 =
1
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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)
87.5%

21. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
4:5
9 : 25
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

22. What is the empty set?
3sqrt4
Angle/360 x 2(pi)r
2.592 kg
A set with no members - denoted by a circle with a diagonal through it.

23. 10<all primes<20
An expression with just one term (-6x - 2a^2)
1.7
11 - 13 - 17 - 19
Part = Percent X Whole

24. The number of degrees in the largest angle of a triangle inscribed in a circle - in which the diameter of the circle is one side of the triangle.
The union of A and B.
130pi
13pi / 2
90 degrees

25. (-1)^2 =
48
x^(2(4)) =x^8 = (x^4)^2
C = (pi)d
1

26. 40 < all primes<50
41 - 43 - 47
1:sqrt3:2
Diameter(Pi)
90 degrees

27. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
A set with a number of elements which can be counted.
(p + q)/5
A reflection about the axis.

28. a^2 - 2ab + b^2
The set of elements which can be found in either A or B.
(a + b)^2
(a - b)^2
F(x) + c

29. Which is greater? 64^5 or 16^8
IV
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
500
67 - 71 - 73

30. What is the measure of an exterior angle of a regular pentagon?
Angle/360 x 2(pi)r
20.5
72
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

31. How to find the area of a sector?
28. n = 8 - k = 2. n! / k!(n-k)!
Angle/360 x (pi)r^2
N! / (n-k)!
6 : 1 : 2

32. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
71 - 73 - 79
1.0843 X 10^11
3

33. To multiply a number by 10^x
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
4a^2(b)
Move the decimal point to the right x places
Sector area = (n/360) X (pi)r^2

34. 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)?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
2sqrt6
y = (x + 5)/2
Diameter(Pi)

35. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
G(x) = {x}
2^9 / 2 = 256
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
48

36. Convert 0.7% to a fraction.
An isosceles right triangle.
1/(x^y)
7 / 1000
(p + q)/5

37. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
(p + q)/5
Undefined
Triangles with same measure and same side lengths.
2 & 3/7

38. What are the members or elements of a set?
y = (x + 5)/2
All numbers multiples of 1.
The objects within a set.
13

39. Can you simplify sqrt72?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Undefined - because we can'T divide by 0.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The sum of digits is divisible by 9.

40. What is the formula for compounded interest?
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.
13pi / 2
Members or elements
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

41. Formula for the area of a sector of a circle?
71 - 73 - 79
III
Sector area = (n/360) X (pi)r^2
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

42. 5/8 in percent?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
3
62.5%

43. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Area of the base X height = (pi)hr^2
9 & 6/7
Cd
A tangent is a line that only touches one point on the circumference of a circle.

44. What is an exterior angle?
An angle which is supplementary to an interior angle.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
A grouping of the members within a set based on a shared characteristic.
31 - 37

45. a^0 =
III
(b + c)
1
F(x-c)

46. What are the irrational numbers?

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47. A number is divisible by 4 is...
Its last two digits are divisible by 4.
(b + c)
C = (pi)d
The set of elements which can be found in either A or B.

48. Simplify 9^(1/2) X 4^3 X 2^(-6)?
1
Infinite.
3
Triangles with same measure and same side lengths.

49. What is the order of operations?
The curve opens downward and the vertex is the maximum point on the graph.
y = 2x^2 - 3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
F(x) - c

50. Define a 'Term' -
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)
The curve opens upward and the vertex is the minimal point on the graph.
2(pi)r^2 + 2(pi)rh
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)