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. When the 'a' in the parabola is negative...
The curve opens downward and the vertex is the maximum point on the graph.
12.5%
(amount of increase/original price) x 100%
48

2. The objects in a set are called two names:
Diameter(Pi)
Members or elements
The point of intersection of the systems.
A chord is a line segment joining two points on a circle.

3. What is a subset?
All numbers multiples of 1.
y = (x + 5)/2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
A grouping of the members within a set based on a shared characteristic.

4. 8.84 / 5.2
Part = Percent X Whole
1.7
13pi / 2
2(pi)r^2 + 2(pi)rh

5. 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)
A circle centered at -2 - -2 with radius 3.
53 - 59
288 (8 9 4)
4.25 - 6 - 22

6. How many sides does a hexagon have?
No - only like radicals can be added.
6
N! / (n-k)!
IV

7. What is the set of elements found in both A and B?
3
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
7 / 1000
The interesection of A and B.

8. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
The point of intersection of the systems.
1/a^6
4:5
1

9. If an inequality is multiplied or divided by a negative number....
A grouping of the members within a set based on a shared characteristic.
The sum of digits is divisible by 9.
61 - 67
The direction of the inequality is reversed.

10. (12sqrt15) / (2sqrt5) =
3
90
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
x^(2(4)) =x^8 = (x^4)^2

11. 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))?
20.5
When the function is not defined for all real numbers -; only a subset of the real numbers.
The overlapping sections.
Pi is the ratio of a circle'S circumference to its diameter.

12. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
Relationship cannot be determined (what if x is negative?)
12! / 5!7! = 792
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)
16.6666%

13. 1/6 in percent?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
16.6666%
When the function is not defined for all real numbers -; only a subset of the real numbers.
413.03 / 10^4 (move the decimal point 4 places to the left)

14. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
4725
True
The sum of its digits is divisible by 3.
90

15. Order of quadrants:
When the function is not defined for all real numbers -; only a subset of the real numbers.
IV
A subset.
From northeast - counterclockwise. I - II - III - IV

16. 70 < all primes< 80
55%
y = (x + 5)/2
71 - 73 - 79
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

17. a^2 - b^2 =
(a - b)(a + b)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Divide by 100.
20.5

18. What is a parabola?
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Ax^2 + bx + c where a -b and c are constants and a /=0
An angle which is supplementary to an interior angle.
The shortest arc between points A and B on a circle'S diameter.

19. Can you simplify sqrt72?
2(pi)r^2 + 2(pi)rh
(base*height) / 2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

20. What is the side length of an equilateral triangle with altitude 6?
62.5%
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...
18
The union of A and B.

21. What is a piecewise equation?
Two equal sides and two equal angles.
Factors are few - multiples are many.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
90

22. What is an exterior angle?
1
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
28. n = 8 - k = 2. n! / k!(n-k)!
An angle which is supplementary to an interior angle.

23. What is the ratio of the sides of an isosceles right triangle?
Part = Percent X Whole
1:1:sqrt2
4725
5

24. What are the real numbers?
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)
41 - 43 - 47
4096
True

25. What is the name of set with a number of elements which cannot be counted?
An infinite set.
180 degrees
All numbers multiples of 1.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

26. What is the graph of f(x) shifted left c units or spaces?
F(x + c)
3
23 - 29
27^(-4)

27. sqrt 2(sqrt 6)=
Sqrt 12
A 30-60-90 triangle.
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...
A set with no members - denoted by a circle with a diagonal through it.

28. When does a function automatically have a restricted domain (2)?
71 - 73 - 79
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.
The objects within a set.

29. Which quandrant is the lower right hand?
An expression with just one term (-6x - 2a^2)
IV
441000 = 1 10 10 10 21 * 21
413.03 / 10^4 (move the decimal point 4 places to the left)

30. 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?
1
2.592 kg
413.03 / 10^4 (move the decimal point 4 places to the left)
2sqrt6

31. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
N! / (n-k)!
90pi
23 - 29
(a - b)(a + b)

32. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
An infinite set.
(a + b)^2
x^(2(4)) =x^8 = (x^4)^2

33. P and r are factors of 100. What is greater - pr or 100?
20.5
The sum of digits is divisible by 9.
Indeterminable.
(a + b)^2

34. The perimeter of a square is 48 inches. The length of its diagonal is:
3/2 - 5/3
12sqrt2
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...
Even

35. Can you subtract 3sqrt4 from sqrt4?
I
3 - -3
F(x) + c
Yes - like radicals can be added/subtracted.

36. (a^-1)/a^5
1.0843 X 10^11
A = I (1 + rt)
1.7
1/a^6

37. The larger the absolute value of the slope...
$11 -448
90
A grouping of the members within a set based on a shared characteristic.
The steeper the slope.

38. 10<all primes<20
Its divisible by 2 and by 3.
4a^2(b)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
11 - 13 - 17 - 19

39. 40 < all primes<50
Cd
Factors are few - multiples are many.
Area of the base X height = (pi)hr^2
41 - 43 - 47

40. What is the 'union' of A and B?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
5
The set of elements which can be found in either A or B.
52

41. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
Divide by 100.
An infinite set.
4a^2(b)

42. x^2 = 9. What is the value of x?
6
A chord is a line segment joining two points on a circle.
IV
3 - -3

43. Formula to calculate arc length?
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)
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
3/2 - 5/3

44. 30< all primes<40
Undefined - because we can'T divide by 0.
31 - 37
G(x) = {x}
A set with a number of elements which can be counted.

45. Which is greater? 64^5 or 16^8
48
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
The curve opens upward and the vertex is the minimal point on the graph.

46. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4.25 - 6 - 22
4725
2^9 / 2 = 256
(n-2) x 180

47. Which quadrant is the upper right hand?
I
12! / 5!7! = 792
Move the decimal point to the right x places
(b + c)

48. Length of an arc of a circle?
$11 -448
F(x + c)
Angle/360 x 2(pi)r
.0004809 X 10^11

49. What is the 'Range' of a function?
Two equal sides and two equal angles.
The set of output values for a function.
Cd
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

50. 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?
3
No - only like radicals can be added.
Yes - like radicals can be added/subtracted.
$3 -500 in the 9% and $2 -500 in the 7%.