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 slope of a vertical line?

2. How to find the circumference of a circle which circumscribes a square?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
A reflection about the axis.
The interesection of A and B.

3. Length of an arc of a circle?
Angle/360 x 2(pi)r
4.25 - 6 - 22
The sum of digits is divisible by 9.
5 OR -5

4. Legs 6 - 8. Hypotenuse?
10
71 - 73 - 79
Infinite.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

5. Formula of rectangle where l increases by 20% and w decreases by 20%
Angle/360 x (pi)r^2
288 (8 9 4)
x= (1.2)(.8)lw
Two angles whose sum is 90.

6. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
7 / 1000
The set of output values for a function.
0
9 : 25

7. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Factors are few - multiples are many.
From northeast - counterclockwise. I - II - III - IV

8. What is a set with no members called?
52
3sqrt4
The empty set - denoted by a circle with a diagonal through it.
Yes. [i.e. f(x) = x^2 - 1

9. 6w^2 - w - 15 = 0
Part = Percent X Whole
18
The objects within a set.
3/2 - 5/3

10. What is the side length of an equilateral triangle with altitude 6?
Triangles with same measure and same side lengths.
67 - 71 - 73
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
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...

11. 1/2 divided by 3/7 is the same as
An angle which is supplementary to an interior angle.
1/2 times 7/3
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
1 & 37/132

12. Formula for the area of a circle?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(p + q)/5
A = pi(r^2)
Move the decimal point to the right x places

13. How many 3-digit positive integers are even and do not contain the digit 4?
7 / 1000
288 (8 9 4)
The union of A and B.
A central angle is an angle formed by 2 radii.

14. Which quandrant is the lower right hand?
130pi
1
IV
True

15. 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?
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
Infinite.
I
180 degrees

16. What are the roots of the quadrinomial x^2 + 2x + 1?
Cd
x= (1.2)(.8)lw
The two xes after factoring.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

17. 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?
10
500
F(x-c)
Even

18. What is a minor arc?

19. 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?
(amount of increase/original price) x 100%
5
10! / 3!(10-3)! = 120
(a + b)^2

20. What does the graph x^2 + y^2 = 64 look like?
The point of intersection of the systems.
3/2 - 5/3
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)
A circle centered on the origin with radius 8.

21. When the 'a' in a parabola is positive....
9 : 25
The curve opens upward and the vertex is the minimal point on the graph.
2 & 3/7
The set of elements found in both A and B.

22. Area of a triangle?
x(x - y + 1)
1
(base*height) / 2
Area of the base X height = (pi)hr^2

23. 25^(1/2) or sqrt. 25 =
52
Two equal sides and two equal angles.
5 OR -5
90pi

24. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Angle/360 x (pi)r^2
13pi / 2
2^9 / 2 = 256
Relationship cannot be determined (what if x is negative?)

25. 50 < all primes< 60
No - only like radicals can be added.
The two xes after factoring.
53 - 59
Part = Percent X Whole

26. What is a tangent?
16.6666%
1.0843 X 10^11
A tangent is a line that only touches one point on the circumference of a circle.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

27. What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
y = 2x^2 - 3
A grouping of the members within a set based on a shared characteristic.
The sum of digits is divisible by 9.

28. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
28. n = 8 - k = 2. n! / k!(n-k)!
$3 -500 in the 9% and $2 -500 in the 7%.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Undefined - because we can'T divide by 0.

29. What is a piecewise equation?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
6
8
(amount of decrease/original price) x 100%

30. P and r are factors of 100. What is greater - pr or 100?
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)
Indeterminable.
9 : 25
C = (pi)d

31. Formula to calculate arc length?
7 / 1000
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A circle centered on the origin with radius 8.
10! / (10-3)! = 720

32. x^(-y)=
4a^2(b)
A 30-60-90 triangle.
23 - 29
1/(x^y)

33. Find the surface area of a cylinder with radius 3 and height 12.
$11 -448
(amount of increase/original price) x 100%
90pi
83.333%

34. (a^-1)/a^5
2sqrt6
1:1:sqrt2
18
1/a^6

35. To convert a percent to a fraction....
5
A = I (1 + rt)
28. n = 8 - k = 2. n! / k!(n-k)!
Divide by 100.

36. Evaluate 4/11 + 11/12
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
1 & 37/132
(n-2) x 180
A tangent is a line that only touches one point on the circumference of a circle.

37. Define a 'Term' -
F(x) + c
Its divisible by 2 and by 3.
... the square of the ratios of the corresponding sides.
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. 5/6 in percent?
The interesection of A and B.
83.333%
x^(6-3) = x^3
The third side is greater than the difference and less than the sum.

39. In a regular polygon with n sides - the formula for the sum of interior angles
A reflection about the origin.
70
(n-2) x 180
(a - b)(a + b)

40. a^0 =
1
A set with a number of elements which can be counted.
III
Infinite.

41. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
No - only like radicals can be added.
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
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

42. Volume for a cylinder?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Area of the base X height = (pi)hr^2
61 - 67
The greatest value minus the smallest.

43. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(p + q)/5
0
x^(6-3) = x^3

44. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
II
2sqrt6
3/2 - 5/3
12sqrt2

45. The ratio of the areas of two similar polygons is ...
F(x-c)
The shortest arc between points A and B on a circle'S diameter.
441000 = 1 10 10 10 21 * 21
... the square of the ratios of the corresponding sides.

46. What is the 'domain' of a function?
The set of input values for a function.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Undefined
9 & 6/7

47. What is the graph of f(x) shifted downward c units or spaces?
90
The set of output values for a function.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
F(x) - c

48. The objects in a set are called two names:
4a^2(b)
Members or elements
When the function is not defined for all real numbers -; only a subset of the real numbers.
A 30-60-90 triangle.

49. 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)]?
A grouping of the members within a set based on a shared characteristic.
Divide by 100.
62.5%
True

50. What are the real numbers?
75:11
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)
(a + b)^2
413.03 / 10^4 (move the decimal point 4 places to the left)