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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 name of set with a number of elements which cannot be counted?
6
1
An infinite set.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
2. What is the 'Range' of a function?
1:sqrt3:2
90
The set of output values for a function.
An expression with just one term (-6x - 2a^2)
3. What is the formula for compounded interest?
... the square of the ratios of the corresponding sides.
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.
N! / (k!)(n-k)!
1/2 times 7/3
4. 10<all primes<20
11 - 13 - 17 - 19
F(x-c)
...multiply by 100.
48
5. What is the sum of the angles of a triangle?
180 degrees
7 / 1000
28. n = 8 - k = 2. n! / k!(n-k)!
41 - 43 - 47
6. What percent of 40 is 22?
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.
55%
x^(6-3) = x^3
The two xes after factoring.
7. a^2 - 2ab + b^2
An angle which is supplementary to an interior angle.
2.592 kg
The direction of the inequality is reversed.
(a - b)^2
8. Evaluate (4^3)^2
The set of output values for a function.
(b + c)
No - only like radicals can be added.
4096
9. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
The overlapping sections.
1
II
An isosceles right triangle.
10. To convert a decimal to a percent...
...multiply by 100.
2.592 kg
180
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)
11. What is the slope of a horizontal line?
0
1 & 37/132
The objects within a set.
Lies opposite the greater angle
12. What is a set with no members called?
From northeast - counterclockwise. I - II - III - IV
A = I (1 + rt)
1.0843 X 10^11
The empty set - denoted by a circle with a diagonal through it.
13. Can the output value of a function have more than one input value?
31 - 37
5 OR -5
The set of elements found in both A and B.
Yes. [i.e. f(x) = x^2 - 1
14. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Move the decimal point to the right x places
The shortest arc between points A and B on a circle'S diameter.
Cd
Part = Percent X Whole
15. What are the members or elements of a set?
The objects within a set.
C = 2(pi)r
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
16. a^0 =
5 OR -5
27^(-4)
1
The point of intersection of the systems.
17. What are the real numbers?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Two angles whose sum is 90.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
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)
18. What are congruent triangles?
13
10
Triangles with same measure and same side lengths.
62.5%
19. 30< all primes<40
The curve opens upward and the vertex is the minimal point on the graph.
Indeterminable.
3sqrt4
31 - 37
20. Length of an arc of a circle?
A chord is a line segment joining two points on a circle.
The steeper the slope.
1/(x^y)
Angle/360 x 2(pi)r
21. How to find the area of a sector?
7 / 1000
Angle/360 x (pi)r^2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The second graph is less steep.
22. 7/8 in percent?
1 & 37/132
27^(-4)
87.5%
413.03 / 10^4 (move the decimal point 4 places to the left)
23. Write 10 -843 X 10^7 in scientific notation
I
(a - b)(a + b)
62.5%
1.0843 X 10^11
24. 5x^2 - 35x -55 = 0
12.5%
55%
500
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
25. What is the 'domain' of a function?
N! / (n-k)!
F(x-c)
The set of input values for a function.
0
26. 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?
7 / 1000
2.592 kg
The longest arc between points A and B on a circle'S diameter.
The point of intersection of the systems.
27. Legs 6 - 8. Hypotenuse?
Angle/360 x 2(pi)r
10
16.6666%
A circle centered on the origin with radius 8.
28. a^2 - b^2 =
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
(a - b)(a + b)
1.7
29. 40 < all primes<50
5
Undefined
41 - 43 - 47
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
30. 2sqrt4 + sqrt4 =
Sqrt 12
The set of elements found in both A and B.
3/2 - 5/3
3sqrt4
31. Describe the relationship between the graphs of x^2 and (1/2)x^2
1 & 37/132
The second graph is less steep.
9 & 6/7
11 - 13 - 17 - 19
32. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
The shortest arc between points A and B on a circle'S diameter.
Even
The curve opens downward and the vertex is the maximum point on the graph.
33. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4096
2sqrt6
(b + c)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
34. 0^0
1
Undefined
6
...multiply by 100.
35. 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?
10! / (10-3)! = 720
9 : 25
180 degrees
Yes - like radicals can be added/subtracted.
36. (a^-1)/a^5
1/a^6
N! / (n-k)!
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The two xes after factoring.
37. Max and Min lengths for a side of a triangle?
The third side is greater than the difference and less than the sum.
When the function is not defined for all real numbers -; only a subset of the real numbers.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Two angles whose sum is 180.
38. 5/6 in percent?
A reflection about the origin.
55%
No - only like radicals can be added.
83.333%
39. Define an 'expression'.
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
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)
Divide by 100.
413.03 / 10^4 (move the decimal point 4 places to the left)
40. What is the area of a regular hexagon with side 6?
6 : 1 : 2
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
(amount of increase/original price) x 100%
41. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
1/a^6
Lies opposite the greater angle
All numbers multiples of 1.
A reflection about the axis.
42. (12sqrt15) / (2sqrt5) =
Triangles with same measure and same side lengths.
27^(-4)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The union of A and B.
43. The larger the absolute value of the slope...
(a - b)^2
130pi
37.5%
The steeper the slope.
44. Formula for the area of a sector of a circle?
1:1:sqrt2
90 degrees
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Sector area = (n/360) X (pi)r^2
45. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
130pi
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
90
46. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
A circle centered at -2 - -2 with radius 3.
The sum of its digits is divisible by 3.
...multiply by 100.
47. Which is greater? 200x^295 or 10x^294?
37.5%
Relationship cannot be determined (what if x is negative?)
1
288 (8 9 4)
48. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
All numbers multiples of 1.
Angle/360 x 2(pi)r
75:11
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
49. How many multiples does a given number have?
Move the decimal point to the right x places
(amount of decrease/original price) x 100%
Infinite.
71 - 73 - 79
50. Simplify 9^(1/2) X 4^3 X 2^(-6)?
The curve opens upward and the vertex is the minimal point on the graph.
Undefined
11 - 13 - 17 - 19
3