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. Formula of rectangle where l increases by 20% and w decreases by 20%
x= (1.2)(.8)lw
G(x) = {x}
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
(base*height) / 2

2. A number is divisible by 6 if...
The greatest value minus the smallest.
Its divisible by 2 and by 3.
4096
The steeper the slope.

3. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
5
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)
F(x) + c
1

4. What is the order of operations?
4.25 - 6 - 22
Undefined
A chord is a line segment joining two points on a circle.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

5. Simplify (a^2 + b)^2 - (a^2 - b)^2
13
4a^2(b)
G(x) = {x}
A chord is a line segment joining two points on a circle.

6. Factor x^2 - xy + x.
3/2 - 5/3
x(x - y + 1)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
1/a^6

7. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
(a - b)(a + b)
A reflection about the axis.
4725
A chord is a line segment joining two points on a circle.

8. 70 < all primes< 80
(a + b)^2
(base*height) / 2
71 - 73 - 79
Diameter(Pi)

9. How many multiples does a given number have?
Infinite.
48
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
No - only like radicals can be added.

10. A number is divisible by 9 if...
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Infinite.
The sum of digits is divisible by 9.
2^9 / 2 = 256

11. What is a subset?
1/(x^y)
A grouping of the members within a set based on a shared characteristic.
The union of A and B.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

12. What is the 'union' of A and B?
0
The union of A and B.
The set of elements which can be found in either A or B.
Sector area = (n/360) X (pi)r^2

13. What is the maximum value for the function g(x) = (-2x^2) -1?
1/(x^y)
.0004809 X 10^11
1
Members or elements

14. 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.
C = (pi)d
90 degrees
48
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

15. 20<all primes<30
7 / 1000
23 - 29
13pi / 2
62.5%

16. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
Sector area = (n/360) X (pi)r^2
Yes - like radicals can be added/subtracted.
Sqrt 12

17. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
180
1
G(x) = {x}

18. a^2 + 2ab + b^2
2 & 3/7
C = (pi)d
A central angle is an angle formed by 2 radii.
(a + b)^2

19. What is the side length of an equilateral triangle with altitude 6?
71 - 73 - 79
72
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 central angle is an angle formed by 2 radii.

20. 7/8 in percent?
10! / (10-3)! = 720
87.5%
90pi
The point of intersection of the systems.

21. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
0
The greatest value minus the smallest.
The direction of the inequality is reversed.

22. What is a finite set?
10
62.5%
The second graph is less steep.
A set with a number of elements which can be counted.

23. What are complementary angles?
413.03 / 10^4 (move the decimal point 4 places to the left)
10
(a - b)(a + b)
Two angles whose sum is 90.

24. Describe the relationship between the graphs of x^2 and (1/2)x^2
Ax^2 + bx + c where a -b and c are constants and a /=0
The second graph is less steep.
72
A tangent is a line that only touches one point on the circumference of a circle.

25. Define a 'Term' -
Yes. [i.e. f(x) = x^2 - 1
6 : 1 : 2
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)
1:sqrt3:2

26. 3/8 in percent?
An angle which is supplementary to an interior angle.
18
5
37.5%

27. Simplify the expression (p^2 - q^2)/ -5(q - p)
N! / (k!)(n-k)!
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
(p + q)/5
55%

28. What is a parabola?
Ax^2 + bx + c where a -b and c are constants and a /=0
All numbers multiples of 1.
1.0843 X 10^11
An infinite set.

29. Surface area for a cylinder?
48
A central angle is an angle formed by 2 radii.
Cd
2(pi)r^2 + 2(pi)rh

30. Is 0 even or odd?
An arc is a portion of a circumference of a circle.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
N! / (k!)(n-k)!
Even

31. What is the formula for computing simple interest?
A = I (1 + rt)
1/(x^y)
130pi
x^(4+7) = x^11

32. What is an exterior angle?
C = (pi)d
An angle which is supplementary to an interior angle.
F(x-c)
13pi / 2

33. 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.
90 degrees
y = 2x^2 - 3
N! / (k!)(n-k)!

34. The slope of a line perpendicular to (a/b)?
Yes. [i.e. f(x) = x^2 - 1
Its negative reciprocal. (-b/a)
(b + c)
When the function is not defined for all real numbers -; only a subset of the real numbers.

35. P and r are factors of 100. What is greater - pr or 100?
The direction of the inequality is reversed.
The steeper the slope.
x(x - y + 1)
Indeterminable.

36. How to find the area of a sector?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Angle/360 x (pi)r^2
Sector area = (n/360) X (pi)r^2
1

37. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
The steeper the slope.
1.7
288 (8 9 4)

38. Which quadrant is the upper right hand?
12! / 5!7! = 792
I
37.5%
4.25 - 6 - 22

39. Define an 'expression'.
(a - b)(a + b)
75:11
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)
The curve opens downward and the vertex is the maximum point on the graph.

40. 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
16.6666%
The sum of digits is divisible by 9.
Diameter(Pi)

41. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A set with no members - denoted by a circle with a diagonal through it.
The two xes after factoring.
F(x) + c

42. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
5 OR -5
75:11
4:5
The interesection of A and B.

43. Pi is a ratio of what to what?

44. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
413.03 / 10^4 (move the decimal point 4 places to the left)
500
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
8

45. What is the graph of f(x) shifted right c units or spaces?
Undefined
A reflection about the axis.
F(x-c)
31 - 37

46. A number is divisible by 3 if ...
A tangent is a line that only touches one point on the circumference of a circle.
The sum of its digits is divisible by 3.
4a^2(b)
The shortest arc between points A and B on a circle'S diameter.

47. a^2 - 2ab + b^2
4a^2(b)
12! / 5!7! = 792
(a - b)^2
1/2 times 7/3

48. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
6
IV
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
2^9 / 2 = 256

49. What is the slope of a horizontal line?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
0
(a + b)^2
(amount of increase/original price) x 100%

50. Factor a^2 + 2ab + b^2
The set of elements found in both A and B.
(a + b)^2
The curve opens downward and the vertex is the maximum point on the graph.
1