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. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
The sum of its digits is divisible by 3.
The set of elements which can be found in either A or B.
An isosceles right triangle.

2. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
A = I (1 + rt)
The interesection of A and B.
2sqrt6
Even

3. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
55%
441000 = 1 10 10 10 21 * 21
4096
62.5%

4. Max and Min lengths for a side of a triangle?
(b + c)
The greatest value minus the smallest.
The third side is greater than the difference and less than the sum.
The set of input values for a function.

5. What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
C = (pi)d
A central angle is an angle formed by 2 radii.
4096

6. What is the side length of an equilateral triangle with altitude 6?
A chord is a line segment joining two points on a circle.
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...
(p + q)/5
(a - b)^2

7. Length of an arc of a circle?
(a - b)^2
Two angles whose sum is 180.
Angle/360 x (pi)r^2
Angle/360 x 2(pi)r

8. (x^2)^4
10! / 3!(10-3)! = 120
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The set of output values for a function.
x^(2(4)) =x^8 = (x^4)^2

9. How to find the area of a sector?
180
Angle/360 x 2(pi)r
Angle/360 x (pi)r^2
II

10. Which is greater? 64^5 or 16^8
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Sqrt 12
180
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

11. Factor a^2 + 2ab + b^2
(a + b)^2
28. n = 8 - k = 2. n! / k!(n-k)!
4:5
1

12. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
(n-2) x 180
180
A set with a number of elements which can be counted.
48

13. a^0 =
6
1
55%
II

14. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
The set of elements which can be found in either A or B.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
(base*height) / 2
500

15. 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
(base*height) / 2
18
A reflection about the axis.
Relationship cannot be determined (what if x is negative?)

16. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
Relationship cannot be determined (what if x is negative?)
An isosceles right triangle.
61 - 67
3

17. What is the name of set with a number of elements which cannot be counted?
A = pi(r^2)
1
The sum of its digits is divisible by 3.
An infinite set.

18. 20<all primes<30
23 - 29
8
Diameter(Pi)
11 - 13 - 17 - 19

19. 7/8 in percent?
1.7
Pi is the ratio of a circle'S circumference to its diameter.
87.5%
Cd

20. a^2 - 2ab + b^2
Cd
6
9 : 25
(a - b)^2

21. Define a 'monomial'
The steeper the slope.
An expression with just one term (-6x - 2a^2)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
1/2 times 7/3

22. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Yes - like radicals can be added/subtracted.
12! / 5!7! = 792

23. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
The steeper the slope.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Angle/360 x 2(pi)r
1

24. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
...multiply by 100.
9 : 25
Triangles with same measure and same side lengths.
2.592 kg

25. (-1)^2 =
I
1
(a - b)(a + b)
3 - -3

26. Is 0 even or odd?
72
Even
The sum of digits is divisible by 9.
5 OR -5

27. Write 10 -843 X 10^7 in scientific notation
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...
90 degrees
The set of input values for a function.
1.0843 X 10^11

28. How to find the circumference of a circle which circumscribes a square?
130pi
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Ax^2 + bx + c where a -b and c are constants and a /=0
2sqrt6

29. 0^0
1/(x^y)
Two angles whose sum is 90.
Undefined
1:1:sqrt2

30. 6w^2 - w - 15 = 0
53 - 59
Area of the base X height = (pi)hr^2
1
3/2 - 5/3

31. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
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)
16.6666%
A 30-60-90 triangle.
x= (1.2)(.8)lw

32. What are the real numbers?
Angle/360 x (pi)r^2
4096
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
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)

33. Evaluate 3& 2/7 / 1/3
y = 2x^2 - 3
F(x) + c
9 & 6/7
A = I (1 + rt)

34. Which is greater? 27^(-4) or 9^(-8)
The direction of the inequality is reversed.
27^(-4)
Move the decimal point to the right x places
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.

35. x^4 + x^7 =
An isosceles right triangle.
13
x^(4+7) = x^11
The set of elements which can be found in either A or B.

36. Factor x^2 - xy + x.
48
A chord is a line segment joining two points on a circle.
A = pi(r^2)
x(x - y + 1)

37. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
Factors are few - multiples are many.
2(pi)r^2 + 2(pi)rh
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)

38. Evaluate 4/11 + 11/12
130pi
1 & 37/132
1
2 & 3/7

39. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
4:5
A subset.
The steeper the slope.
3

40. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
N! / (n-k)!
1/(x^y)
(a + b)^2

41. If the two sides of a triangle are unequal then the longer side...
6
Part = Percent X Whole
Lies opposite the greater angle
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

42. What are 'Supplementary angles?'
Two angles whose sum is 180.
13
The set of elements which can be found in either A or B.
An arc is a portion of a circumference of a circle.

43. 60 < all primes <70
53 - 59
All numbers multiples of 1.
Part = Percent X Whole
61 - 67

44. The objects in a set are called two names:
8
Members or elements
The longest arc between points A and B on a circle'S diameter.
72

45. What is the graph of f(x) shifted left c units or spaces?
4a^2(b)
5 OR -5
F(x + c)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

46. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
12! / 5!7! = 792
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
4725

47. How to determine percent increase?
Yes. [i.e. f(x) = x^2 - 1
6 : 1 : 2
A reflection about the origin.
(amount of increase/original price) x 100%

48. Simplify 9^(1/2) X 4^3 X 2^(-6)?
20.5
83.333%
A set with a number of elements which can be counted.
3

49. 4.809 X 10^7 =
Part = Percent X Whole
The set of output values for a function.
.0004809 X 10^11
41 - 43 - 47

50. 8.84 / 5.2
7 / 1000
1.7
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15