Test your basic knowledge |

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 area of a regular hexagon with side 6?
C = 2(pi)r
The longest arc between points A and B on a circle'S diameter.
The sum of its digits is divisible by 3.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

2. Formula to find a circle'S circumference from its radius?
2(pi)r^2 + 2(pi)rh
C = 2(pi)r
2^9 / 2 = 256
Angle/360 x 2(pi)r

3. What is the measure of an exterior angle of a regular pentagon?
72
x^(4+7) = x^11
413.03 / 10^4 (move the decimal point 4 places to the left)
4:5

4. 60 < all primes <70
37.5%
(a - b)^2
(amount of decrease/original price) x 100%
61 - 67

5. a^0 =
The objects within a set.
90 degrees
1
Two equal sides and two equal angles.

6. A number is divisible by 6 if...
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Its divisible by 2 and by 3.
A set with no members - denoted by a circle with a diagonal through it.

7. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
Its negative reciprocal. (-b/a)
180
True

8. What is the slope of a vertical line?

9. sqrt 2(sqrt 6)=
Sqrt 12
The point of intersection of the systems.
41 - 43 - 47
61 - 67

10. The slope of a line perpendicular to (a/b)?
All numbers multiples of 1.
Its negative reciprocal. (-b/a)
3/2 - 5/3
6

11. What is the 'domain' of a function?
41 - 43 - 47
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
An angle which is supplementary to an interior angle.
The set of input values for a function.

12. 7/8 in percent?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
87.5%
180
441000 = 1 10 10 10 21 * 21

13. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
Two equal sides and two equal angles.
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
(a - b)(a + b)
0

14. (6sqrt3) x (2sqrt5) =
Members or elements
A subset.
The third side is greater than the difference and less than the sum.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

15. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
180 degrees
The curve opens downward and the vertex is the maximum point on the graph.
2sqrt6
Angle/360 x (pi)r^2

16. 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?
180 degrees
12! / 5!7! = 792
10! / (10-3)! = 720
53 - 59

17. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
70
No - the input value has exactly one output.
The point of intersection of the systems.
1

18. How many sides does a hexagon have?
6 : 1 : 2
37.5%
6
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.

19. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
13pi / 2
2
The empty set - denoted by a circle with a diagonal through it.
16.6666%

20. Factor x^2 - xy + x.
The interesection of A and B.
16.6666%
x(x - y + 1)
The sum of its digits is divisible by 3.

21. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
4.25 - 6 - 22
Its divisible by 2 and by 3.
An angle which is supplementary to an interior angle.

22. 20<all primes<30
90 degrees
23 - 29
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Lies opposite the greater angle

23. 0^0
The set of elements found in both A and B.
16.6666%
Undefined
A set with a number of elements which can be counted.

24. Which quadrant is the upper right hand?
The set of output values for a function.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
I
1

25. Which quadrant is the lower left hand?
The point of intersection of the systems.
The second graph is less steep.
III
10! / 3!(10-3)! = 120

26. What is a major arc?

27. A number is divisible by 9 if...
A chord is a line segment joining two points on a circle.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
10
The sum of digits is divisible by 9.

28. a^2 - 2ab + b^2
Indeterminable.
6 : 1 : 2
Relationship cannot be determined (what if x is negative?)
(a - b)^2

29. Order of quadrants:
A = pi(r^2)
From northeast - counterclockwise. I - II - III - IV
10! / (10-3)! = 720
The sum of digits is divisible by 9.

30. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
(amount of decrease/original price) x 100%
31 - 37
Cd

31. If a=-1 and b=3 - what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
18
1/a^6
20.5
Cd

32. Can the output value of a function have more than one input value?
83.333%
Yes. [i.e. f(x) = x^2 - 1
61 - 67
(b + c)

33. Length of an arc of a circle?
Angle/360 x (pi)r^2
70
Sector area = (n/360) X (pi)r^2
Angle/360 x 2(pi)r

34. What is a central angle?
G(x) = {x}
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A central angle is an angle formed by 2 radii.
(base*height) / 2

35. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
Divide by 100.
1
5
3

36. What is the 'Solution' for a system of linear equations?
Sector area = (n/360) X (pi)r^2
130pi
Undefined
The point of intersection of the systems.

37. What is the 'Solution' for a set of inequalities.
All numbers multiples of 1.
The overlapping sections.
75:11
A set with no members - denoted by a circle with a diagonal through it.

38. What is a minor arc?

39. What is the name for a grouping of the members within a set based on a shared characteristic?
The set of input values for a function.
A subset.
12.5%
1:sqrt3:2

40. What is a parabola?
Ax^2 + bx + c where a -b and c are constants and a /=0
An infinite set.
G(x) = {x}
Two equal sides and two equal angles.

41. What is the side length of an equilateral triangle with altitude 6?
No - only like radicals can be added.
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...
An arc is a portion of a circumference of a circle.
130pi

42. A number is divisible by 3 if ...
A = pi(r^2)
The sum of its digits is divisible by 3.
(a - b)(a + b)
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)

43. Formula for the area of a sector of a circle?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Sector area = (n/360) X (pi)r^2
3/2 - 5/3
The set of input values for a function.

44. Formula of rectangle where l increases by 20% and w decreases by 20%
An infinite set.
Lies opposite the greater angle
The interesection of A and B.
x= (1.2)(.8)lw

45. 1/6 in percent?
1/a^6
288 (8 9 4)
N! / (n-k)!
16.6666%

46. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
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)
A set with no members - denoted by a circle with a diagonal through it.
A 30-60-90 triangle.
The curve opens downward and the vertex is the maximum point on the graph.

47. (-1)^2 =
(a - b)^2
9 & 6/7
1
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

48. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
The overlapping sections.
A set with a number of elements which can be counted.
3sqrt4

49. Define an 'expression'.
II
(a - 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)
x(x - y + 1)

50. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
10! / 3!(10-3)! = 120
Members or elements
Undefined
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)