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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. Whats the difference between factors and multiples?
288 (8 9 4)
Factors are few - multiples are many.
55%
No - the input value has exactly one output.
2. 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
An angle which is supplementary to an interior angle.
No - the input value has exactly one output.
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)
3. 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)]?
Two angles whose sum is 90.
The longest arc between points A and B on a circle'S diameter.
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
True
4. 6w^2 - w - 15 = 0
13
23 - 29
Area of the base X height = (pi)hr^2
3/2 - 5/3
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)
x= (1.2)(.8)lw
... the square of the ratios of the corresponding sides.
Part = Percent X Whole
4.25 - 6 - 22
6. Max and Min lengths for a side of a triangle?
10
90 degrees
The third side is greater than the difference and less than the sum.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
7. Area of a triangle?
4725
The objects within a set.
37.5%
(base*height) / 2
8. What number between 70 & 75 - inclusive - has the greatest number of factors?
A subset.
Two angles whose sum is 180.
72
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
9. 5x^2 - 35x -55 = 0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Two angles whose sum is 180.
An angle which is supplementary to an interior angle.
G(x) = {x}
10. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
The second graph is less steep.
62.5%
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
53 - 59
11. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
A 30-60-90 triangle.
52
61 - 67
2^9 / 2 = 256
12. The objects in a set are called two names:
x(x - y + 1)
Members or elements
2sqrt6
The empty set - denoted by a circle with a diagonal through it.
13. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A reflection about the origin.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
70
From northeast - counterclockwise. I - II - III - IV
14. How to determine percent increase?
(amount of increase/original price) x 100%
Two angles whose sum is 180.
2
Its negative reciprocal. (-b/a)
15. 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 -500 in the 9% and $2 -500 in the 7%.
Lies opposite the greater angle
Indeterminable.
Yes. [i.e. f(x) = x^2 - 1
16. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
N! / (k!)(n-k)!
288 (8 9 4)
90 degrees
G(x) = {x}
17. Which quandrant is the lower right hand?
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 30-60-90 triangle.
Yes. [i.e. f(x) = x^2 - 1
IV
18. 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.
A = I (1 + rt)
(a - b)(a + b)
10
90 degrees
19. (6sqrt3) x (2sqrt5) =
6
No - the input value has exactly one output.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Angle/360 x (pi)r^2
20. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
4725
Its divisible by 2 and by 3.
A reflection about the axis.
An isosceles right triangle.
21. (-1)^3 =
1
41 - 43 - 47
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
A circle centered at -2 - -2 with radius 3.
22. When does a function automatically have a restricted domain (2)?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
11 - 13 - 17 - 19
5
23. What are complementary angles?
55%
Two angles whose sum is 90.
1:1:sqrt2
The longest arc between points A and B on a circle'S diameter.
24. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
61 - 67
$11 -448
1/a^6
3/2 - 5/3
25. 1/8 in percent?
The overlapping sections.
Sector area = (n/360) X (pi)r^2
12.5%
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
26. The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
(amount of increase/original price) x 100%
83.333%
27. What is the set of elements which can be found in either A or B?
9 & 6/7
Part = Percent X Whole
The union of A and B.
II
28. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
Its negative reciprocal. (-b/a)
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)
An infinite set.
29. A number is divisible by 6 if...
The point of intersection of the systems.
Its divisible by 2 and by 3.
23 - 29
13pi / 2
30. 2sqrt4 + sqrt4 =
Yes. [i.e. f(x) = x^2 - 1
The set of elements which can be found in either A or B.
A chord is a line segment joining two points on a circle.
3sqrt4
31. Legs 5 - 12. Hypotenuse?
13
The greatest value minus the smallest.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
72
32. 70 < all primes< 80
37.5%
71 - 73 - 79
1 & 37/132
48
33. Evaluate (4^3)^2
F(x) - c
4096
0
From northeast - counterclockwise. I - II - III - IV
34. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
2
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
The shortest arc between points A and B on a circle'S diameter.
35. Define a 'Term' -
180
20.5
A set with a number of elements which can be counted.
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)
36. x^6 / x^3
55%
2 & 3/7
No - only like radicals can be added.
x^(6-3) = x^3
37. Evaluate 4/11 + 11/12
1 & 37/132
The greatest value minus the smallest.
288 (8 9 4)
1
38. 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?
13
y = 2x^2 - 3
3sqrt4
10! / (10-3)! = 720
39. How to find the diagonal of a rectangular solid?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1.7
A 30-60-90 triangle.
(a - b)(a + b)
40. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
10! / 3!(10-3)! = 120
71 - 73 - 79
N! / (k!)(n-k)!
41. (-1)^2 =
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)
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
6
1
42. Factor a^2 + 2ab + b^2
4096
(a + b)^2
10! / (10-3)! = 720
27^(-4)
43. a^2 - b^2 =
10
83.333%
(a - b)(a + b)
II
44. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
Angle/360 x (pi)r^2
90
0
45. How many multiples does a given number have?
Infinite.
(a + b)^2
The third side is greater than the difference and less than the sum.
23 - 29
46. What is the side length of an equilateral triangle with altitude 6?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Pi is the ratio of a circle'S circumference to its diameter.
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...
The greatest value minus the smallest.
47. 40 < all primes<50
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
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)
1:sqrt3:2
41 - 43 - 47
48. What is the set of elements found in both A and B?
An arc is a portion of a circumference of a circle.
N! / (k!)(n-k)!
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The interesection of A and B.
49. What is the slope of a horizontal line?
0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(amount of decrease/original price) x 100%
... the square of the ratios of the corresponding sides.
50. What is the order of operations?
72
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The sum of digits is divisible by 9.
A = pi(r^2)