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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 maximum value for the function g(x) = (-2x^2) -1?
1/2 times 7/3
12sqrt2
1
Two angles whose sum is 180.
2. What is the side length of an equilateral triangle with altitude 6?
71 - 73 - 79
4a^2(b)
18
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...
3. What is the absolute value function?
The sum of digits is divisible by 9.
G(x) = {x}
27^(-4)
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
4. What is the name for a grouping of the members within a set based on a shared characteristic?
Undefined - because we can'T divide by 0.
72
Factors are few - multiples are many.
A subset.
5. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
.0004809 X 10^11
10
2
2(pi)r^2 + 2(pi)rh
6. 0^0
16.6666%
The sum of its digits is divisible by 3.
75:11
Undefined
7. What are the roots of the quadrinomial x^2 + 2x + 1?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Divide by 100.
$3 -500 in the 9% and $2 -500 in the 7%.
The two xes after factoring.
8. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
(a - b)^2
2^9 / 2 = 256
18
Factors are few - multiples are many.
9. What is the surface area of a cylinder with radius 5 and height 8?
130pi
16.6666%
Its last two digits are divisible by 4.
41 - 43 - 47
10. Define a 'Term' -
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)
71 - 73 - 79
Diameter(Pi)
F(x-c)
11. Number of degrees in a triangle
From northeast - counterclockwise. I - II - III - IV
180
A = pi(r^2)
83.333%
12. 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?
9 & 6/7
10! / (10-3)! = 720
Divide by 100.
2(pi)r^2 + 2(pi)rh
13. When does a function automatically have a restricted domain (2)?
52
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Sector area = (n/360) X (pi)r^2
413.03 / 10^4 (move the decimal point 4 places to the left)
14. Area of a triangle?
When the function is not defined for all real numbers -; only a subset of the real numbers.
(base*height) / 2
Relationship cannot be determined (what if x is negative?)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
15. Can the output value of a function have more than one input value?
2.592 kg
Yes. [i.e. f(x) = x^2 - 1
180 degrees
2sqrt6
16. Formula for the area of a circle?
11 - 13 - 17 - 19
20.5
A = pi(r^2)
Lies opposite the greater angle
17. Simplify 9^(1/2) X 4^3 X 2^(-6)?
An infinite set.
441000 = 1 10 10 10 21 * 21
3
13pi / 2
18. Circumference of a circle?
Diameter(Pi)
No - only like radicals can be added.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
(a - b)(a + b)
19. What is a parabola?
2sqrt6
Part = Percent X Whole
Ax^2 + bx + c where a -b and c are constants and a /=0
1
20. A number is divisible by 4 is...
Its last two digits are divisible by 4.
2.592 kg
12sqrt2
87.5%
21. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
A chord is a line segment joining two points on a circle.
12sqrt2
An arc is a portion of a circumference of a circle.
22. 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)
Triangles with same measure and same side lengths.
4.25 - 6 - 22
20.5
7 / 1000
23. a^2 - b^2 =
(a - b)(a + b)
1
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
III
24. Which quadrant is the upper right hand?
1
True
I
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
25. 1/8 in percent?
18
Its last two digits are divisible by 4.
All numbers multiples of 1.
12.5%
26. The larger the absolute value of the slope...
The steeper the slope.
413.03 / 10^4 (move the decimal point 4 places to the left)
The curve opens downward and the vertex is the maximum point on the graph.
Cd
27. (-1)^3 =
Area of the base X height = (pi)hr^2
1
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 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)
28. What is the percent formula?
Part = Percent X Whole
An infinite set.
Triangles with same measure and same side lengths.
Its divisible by 2 and by 3.
29. What is the 'Restricted domain of a function'?
55%
1.7
Sector area = (n/360) X (pi)r^2
When the function is not defined for all real numbers -; only a subset of the real numbers.
30. (6sqrt3) x (2sqrt5) =
11 - 13 - 17 - 19
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
True
75:11
31. a^0 =
7 / 1000
6
1
.0004809 X 10^11
32. What is the ratio of the sides of an isosceles right triangle?
$3 -500 in the 9% and $2 -500 in the 7%.
F(x + c)
1:1:sqrt2
4096
33. a^2 + 2ab + b^2
Triangles with same measure and same side lengths.
(a + b)^2
The sum of digits is divisible by 9.
90 degrees
34. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
1:1:sqrt2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
From northeast - counterclockwise. I - II - III - IV
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
35. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
Cd
500
An expression with just one term (-6x - 2a^2)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
36. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
A grouping of the members within a set based on a shared characteristic.
10
0
37. 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?
A grouping of the members within a set based on a shared characteristic.
... the square of the ratios of the corresponding sides.
41 - 43 - 47
N! / (n-k)!
38. What is a chord of a circle?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A chord is a line segment joining two points on a circle.
The greatest value minus the smallest.
An expression with just one term (-6x - 2a^2)
39. x^(-y)=
x^(6-3) = x^3
A circle centered on the origin with radius 8.
72
1/(x^y)
40. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
441000 = 1 10 10 10 21 * 21
An arc is a portion of a circumference of a circle.
1.0843 X 10^11
Ax^2 + bx + c where a -b and c are constants and a /=0
41. How to determine percent decrease?
3sqrt4
(amount of decrease/original price) x 100%
An angle which is supplementary to an interior angle.
I
42. 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.
An expression with just one term (-6x - 2a^2)
48
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)
43. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
1/a^6
The set of input values for a function.
90
28. n = 8 - k = 2. n! / k!(n-k)!
44. Legs 6 - 8. Hypotenuse?
x(x - y + 1)
A set with no members - denoted by a circle with a diagonal through it.
10
7 / 1000
45. 2sqrt4 + sqrt4 =
8
Move the decimal point to the right x places
2^9 / 2 = 256
3sqrt4
46. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
The curve opens upward and the vertex is the minimal point on the graph.
F(x) - c
A reflection about the axis.
IV
47. Evaluate 4/11 + 11/12
1 & 37/132
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
4a^2(b)
1
48. What number between 70 & 75 - inclusive - has the greatest number of factors?
Divide by 100.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
3
72
49. 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?
Relationship cannot be determined (what if x is negative?)
75:11
Triangles with same measure and same side lengths.
10! / (10-3)! = 720
50. 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.
90 degrees
Diameter(Pi)
The third side is greater than the difference and less than the sum.
53 - 59