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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. What is the sum of the angles of a triangle?
180 degrees
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
11 - 13 - 17 - 19
N! / (k!)(n-k)!

2. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
18
90
4725

3. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
3
9 & 6/7
90

4. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
(n-2) x 180
1/a^6
$3 -500 in the 9% and $2 -500 in the 7%.

5. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
The set of elements found in both A and B.
All numbers multiples of 1.
F(x + c)
28. n = 8 - k = 2. n! / k!(n-k)!

6. What is a finite set?
75:11
The union of A and B.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
A set with a number of elements which can be counted.

7. Describe the relationship between 3x^2 and 3(x - 1)^2
The third side is greater than the difference and less than the sum.
130pi
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A = I (1 + rt)

8. Formula for the area of a sector of a circle?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Sector area = (n/360) X (pi)r^2
1
Its divisible by 2 and by 3.

9. 30< all primes<40
The set of input values for a function.
Two equal sides and two equal angles.
A set with a number of elements which can be counted.
31 - 37

10. Solve the quadratic equation ax^2 + bx + c= 0
Pi is the ratio of a circle'S circumference to its diameter.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
1
(a - b)^2

11. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The direction of the inequality is reversed.
A grouping of the members within a set based on a shared characteristic.

12. 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?
Undefined - because we can'T divide by 0.
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
The set of elements which can be found in either A or B.
Even

13. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
A grouping of the members within a set based on a shared characteristic.
C = 2(pi)r
The set of output values for a function.

14. Define an 'expression'.
288 (8 9 4)
F(x) - c
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)
Ax^2 + bx + c where a -b and c are constants and a /=0

15. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
2^9 / 2 = 256
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
... the square of the ratios of the corresponding sides.

16. (x^2)^4
x^(2(4)) =x^8 = (x^4)^2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The overlapping sections.

17. The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
C = (pi)d
(a - b)(a + b)
Two angles whose sum is 180.

18. 1/8 in percent?
0
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
12.5%
x^(6-3) = x^3

19. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
I
2 & 3/7
An angle which is supplementary to an interior angle.
87.5%

20. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
7 / 1000
x^(2(4)) =x^8 = (x^4)^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)

21. a^2 - 2ab + b^2
All numbers multiples of 1.
(a - b)^2
The longest arc between points A and B on a circle'S diameter.
The set of elements found in both A and B.

22. The objects in a set are called two names:
28. n = 8 - k = 2. n! / k!(n-k)!
Members or elements
2^9 / 2 = 256
6

23. How many sides does a hexagon have?
4a^2(b)
90
6
1:sqrt3:2

24. Factor a^2 + 2ab + b^2
(a + b)^2
A central angle is an angle formed by 2 radii.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
288 (8 9 4)

25. A number is divisible by 9 if...
The sum of digits is divisible by 9.
The set of elements which can be found in either A or B.
A = I (1 + rt)
18

26. 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?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1
8
75:11

27. What is the 'Restricted domain of a function'?
All numbers multiples of 1.
(a + b)^2
When the function is not defined for all real numbers -; only a subset of the real numbers.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

28. When the 'a' in the parabola is negative...
Angle/360 x 2(pi)r
Its negative reciprocal. (-b/a)
Angle/360 x (pi)r^2
The curve opens downward and the vertex is the maximum point on the graph.

29. What are the integers?
N! / (n-k)!
All numbers multiples of 1.
2.592 kg
6 : 1 : 2

30. The slope of a line perpendicular to (a/b)?
(b + c)
1
A circle centered on the origin with radius 8.
Its negative reciprocal. (-b/a)

31. Evaluate 4/11 + 11/12
y = 2x^2 - 3
1 & 37/132
Area of the base X height = (pi)hr^2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

32. A number is divisible by 4 is...
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A chord is a line segment joining two points on a circle.
Its last two digits are divisible by 4.
Infinite.

33. Simplify the expression [(b^2 - c^2) / (b - c)]
1/a^6
Members or elements
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(b + c)

34. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
(amount of decrease/original price) x 100%
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
75:11

35. 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.
$11 -448
3 - -3
37.5%
90 degrees

36. 4.809 X 10^7 =
x(x - y + 1)
.0004809 X 10^11
No - the input value has exactly one output.
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)

37. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
3/2 - 5/3
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The point of intersection of the systems.
13pi / 2

38. Can you subtract 3sqrt4 from sqrt4?
130pi
Two angles whose sum is 180.
Yes - like radicals can be added/subtracted.
71 - 73 - 79

39. 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)]?
The set of elements which can be found in either A or B.
52
12.5%
True

40. Which is greater? 64^5 or 16^8
The empty set - denoted by a circle with a diagonal through it.
Even
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

41. Surface area for a cylinder?
2(pi)r^2 + 2(pi)rh
180 degrees
A reflection about the axis.
1/2 times 7/3

42. a^2 - b^2
Factors are few - multiples are many.
(a - b)(a + b)
A tangent is a line that only touches one point on the circumference of a circle.
Area of the base X height = (pi)hr^2

43. x^6 / x^3
x^(6-3) = x^3
The sum of digits is divisible by 9.
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)
6 : 1 : 2

44. What is the order of operations?
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)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
6

45. Number of degrees in a triangle
180
Cd
1/(x^y)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

46. Formula to find a circle'S circumference from its diameter?
Move the decimal point to the right x places
C = (pi)d
1.7
The sum of its digits is divisible by 3.

47. How to find the area of a sector?
Angle/360 x (pi)r^2
A grouping of the members within a set based on a shared characteristic.
Indeterminable.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

48. How to find the diagonal of a rectangular solid?
C = (pi)d
(a - b)(a + b)
7 / 1000
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

49. If the two sides of a triangle are unequal then the longer side...
6
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Lies opposite the greater angle
Factors are few - multiples are many.

50. Formula of rectangle where l increases by 20% and w decreases by 20%
x^(4+7) = x^11
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...
x= (1.2)(.8)lw
When the function is not defined for all real numbers -; only a subset of the real numbers.