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Test your basic knowledge |
GRE Math: Common Errors
Start Test
Study First
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)