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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. 10^6 has how many zeroes?
83.333%
$11 -448
6
An angle which is supplementary to an interior angle.
2. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
y = 2x^2 - 3
$3 -500 in the 9% and $2 -500 in the 7%.
Part = Percent X Whole
3. x^6 / x^3
4725
288 (8 9 4)
180 degrees
x^(6-3) = x^3
4. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
6
27^(-4)
6
5. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
A reflection about the origin.
Diameter(Pi)
9 : 25
6 : 1 : 2
6. If the two sides of a triangle are unequal then the longer side...
1
Lies opposite the greater angle
(a - b)(a + b)
The sum of its digits is divisible by 3.
7. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Yes. [i.e. f(x) = x^2 - 1
8. What is a finite set?
Undefined
Cd
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
A set with a number of elements which can be counted.
9. If an inequality is multiplied or divided by a negative number....
The direction of the inequality is reversed.
The set of input values for a function.
1.0843 X 10^11
12! / 5!7! = 792
10. A number is divisible by 6 if...
Its divisible by 2 and by 3.
1.7
31 - 37
4725
11. 413.03 x 10^(-4) =
The set of output values for a function.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1 & 37/132
413.03 / 10^4 (move the decimal point 4 places to the left)
12. When the 'a' in a parabola is positive....
The curve opens upward and the vertex is the minimal point on the graph.
2
1/(x^y)
130pi
13. 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?
Part = Percent X Whole
C = 2(pi)r
55%
10! / (10-3)! = 720
14. What is the graph of f(x) shifted right c units or spaces?
90
Two equal sides and two equal angles.
F(x-c)
(a + b)^2
15. a^0 =
The direction of the inequality is reversed.
A set with a number of elements which can be counted.
1
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.
16. 6w^2 - w - 15 = 0
A central angle is an angle formed by 2 radii.
13pi / 2
A chord is a line segment joining two points on a circle.
3/2 - 5/3
17. Which is greater? 27^(-4) or 9^(-8)
From northeast - counterclockwise. I - II - III - IV
(n-2) x 180
27^(-4)
The sum of digits is divisible by 9.
18. 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)
53 - 59
The set of output values for a function.
.0004809 X 10^11
19. 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?
III
N! / (k!)(n-k)!
Divide by 100.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
20. 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?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
The greatest value minus the smallest.
10! / 3!(10-3)! = 120
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.
21. Which quadrant is the upper right hand?
x^(6-3) = x^3
I
$11 -448
The second graph is less steep.
22. What are the real numbers?
2.592 kg
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 reflection about the axis.
Factors are few - multiples are many.
23. What is the name for a grouping of the members within a set based on a shared characteristic?
62.5%
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
A subset.
The set of elements which can be found in either A or B.
24. 0^0
180
(a - b)(a + b)
Undefined
$3 -500 in the 9% and $2 -500 in the 7%.
25. Define an 'expression'.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
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)
Move the decimal point to the right x places
31 - 37
26. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
All numbers multiples of 1.
28. n = 8 - k = 2. n! / k!(n-k)!
Cd
The direction of the inequality is reversed.
27. What is the formula for computing simple interest?
87.5%
A = I (1 + rt)
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...
No - the input value has exactly one output.
28. What is the 'Solution' for a set of inequalities.
1
The overlapping sections.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
29. What is an exterior angle?
37.5%
An angle which is supplementary to an interior angle.
6
Ax^2 + bx + c where a -b and c are constants and a /=0
30. What are complementary angles?
Two angles whose sum is 90.
x^(6-3) = x^3
A 30-60-90 triangle.
The set of input values for a function.
31. Can the input value of a function have more than one output value (i.e. x: y - y1)?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
(a + b)^2
0
No - the input value has exactly one output.
32. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
28. n = 8 - k = 2. n! / k!(n-k)!
13
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
The shortest arc between points A and B on a circle'S diameter.
33. What is the set of elements found in both A and B?
The interesection of A and B.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
y = 2x^2 - 3
x^(4+7) = x^11
34. What is the side length of an equilateral triangle with altitude 6?
Triangles with same measure and same side lengths.
413.03 / 10^4 (move the decimal point 4 places to the left)
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 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)
35. What is the absolute value function?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
G(x) = {x}
72
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)
36. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Lies opposite the greater angle
83.333%
2^9 / 2 = 256
A set with a number of elements which can be counted.
37. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
...multiply by 100.
1
Sector area = (n/360) X (pi)r^2
2 & 3/7
38. 5/8 in percent?
90pi
62.5%
The direction of the inequality is reversed.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
39. Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
2^9 / 2 = 256
The longest arc between points A and B on a circle'S diameter.
The second graph is less steep.
40. What is the formula for compounded interest?
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.
IV
x^(6-3) = x^3
A = I (1 + rt)
41. 40 < all primes<50
1
F(x) - c
23 - 29
41 - 43 - 47
42. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
I
x^(6-3) = x^3
2 & 3/7
43. Legs: 3 - 4. Hypotenuse?
Lies opposite the greater angle
5
10! / (10-3)! = 720
The interesection of A and B.
44. A number is divisible by 4 is...
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
y = 2x^2 - 3
Its last two digits are divisible by 4.
Angle/360 x 2(pi)r
45. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
61 - 67
(b + c)
46. Formula of rectangle where l increases by 20% and w decreases by 20%
x= (1.2)(.8)lw
The curve opens downward and the vertex is the maximum point on the graph.
The greatest value minus the smallest.
The set of elements which can be found in either A or B.
47. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
The second graph is less steep.
A reflection about the axis.
Its last two digits are divisible by 4.
48. 20<all primes<30
4a^2(b)
5 OR -5
x^(4+7) = x^11
23 - 29
49. What is the 'Restricted domain of a function'?
441000 = 1 10 10 10 21 * 21
When the function is not defined for all real numbers -; only a subset of the real numbers.
Cd
An expression with just one term (-6x - 2a^2)
50. a^2 - b^2 =
90 degrees
(a - b)^2
C = (pi)d
(a - b)(a + b)