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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. Which is greater? 27^(-4) or 9^(-8)
All numbers multiples of 1.
27^(-4)
Pi is the ratio of a circle'S circumference to its diameter.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
2. sqrt 2(sqrt 6)=
Sqrt 12
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
A grouping of the members within a set based on a shared characteristic.
From northeast - counterclockwise. I - II - III - IV
3. The slope of a line perpendicular to (a/b)?
(a + b)^2
C = (pi)d
All numbers multiples of 1.
Its negative reciprocal. (-b/a)
4. When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Infinite.
The shortest arc between points A and B on a circle'S diameter.
IV
5. 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?
Yes. [i.e. f(x) = x^2 - 1
The union of A and B.
10! / 3!(10-3)! = 120
288 (8 9 4)
6. 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?
The set of elements found in both A and B.
500
When the function is not defined for all real numbers -; only a subset of the real numbers.
G(x) = {x}
7. 1/2 divided by 3/7 is the same as
1/2 times 7/3
The shortest arc between points A and B on a circle'S diameter.
55%
True
8. Legs 5 - 12. Hypotenuse?
13
1/2 times 7/3
All numbers multiples of 1.
x= (1.2)(.8)lw
9. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
Undefined - because we can'T divide by 0.
23 - 29
5
0
10. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
2.592 kg
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
The interesection of A and B.
(b + c)
11. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
F(x-c)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Angle/360 x (pi)r^2
12. 40 < all primes<50
41 - 43 - 47
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
I
The objects within a set.
13. What is a central angle?
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 central angle is an angle formed by 2 radii.
The steeper the slope.
62.5%
14. What are the real numbers?
3 - -3
The two xes after factoring.
x^(4+7) = x^11
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)
15. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
The point of intersection of the systems.
Even
(a + b)^2
16. 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?
0
Angle/360 x 2(pi)r
9 : 25
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
17. What is the 'Solution' for a system of linear equations?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
13pi / 2
The point of intersection of the systems.
2sqrt6
18. What is the maximum value for the function g(x) = (-2x^2) -1?
The union of A and B.
7 / 1000
Indeterminable.
1
19. Simplify the expression [(b^2 - c^2) / (b - c)]
1:sqrt3:2
(b + c)
1:1:sqrt2
Sqrt 12
20. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
1 & 37/132
The curve opens downward and the vertex is the maximum point on the graph.
Factors are few - multiples are many.
21. The ratio of the areas of two similar polygons is ...
IV
Indeterminable.
0
... the square of the ratios of the corresponding sides.
22. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
$11 -448
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)
23. 10<all primes<20
3
(amount of decrease/original price) x 100%
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.
11 - 13 - 17 - 19
24. What is the percent formula?
2
Part = Percent X Whole
... the square of the ratios of the corresponding sides.
Undefined - because we can'T divide by 0.
25. Legs: 3 - 4. Hypotenuse?
2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Undefined - because we can'T divide by 0.
5
26. What is the measure of an exterior angle of a regular pentagon?
0
72
Its divisible by 2 and by 3.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
27. Factor x^2 - xy + x.
x(x - y + 1)
Sector area = (n/360) X (pi)r^2
9 : 25
An isosceles right triangle.
28. 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?
II
The steeper the slope.
75:11
x^(4+7) = x^11
29. What are complementary angles?
F(x) - c
12! / 5!7! = 792
Part = Percent X Whole
Two angles whose sum is 90.
30. 1/6 in percent?
16.6666%
The set of elements found in both A and B.
Infinite.
3
31. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
70
2(pi)r^2 + 2(pi)rh
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)
32. 5x^2 - 35x -55 = 0
Diameter(Pi)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
28. n = 8 - k = 2. n! / k!(n-k)!
33. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
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)
4:5
Sqrt 12
34. What is the graph of f(x) shifted downward c units or spaces?
N! / (k!)(n-k)!
F(x) - c
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The set of output values for a function.
35. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
(amount of increase/original price) x 100%
1:sqrt3:2
y = (x + 5)/2
36. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
The greatest value minus the smallest.
288 (8 9 4)
(n-2) x 180
37. 25^(1/2) or sqrt. 25 =
1
Cd
5 OR -5
Angle/360 x (pi)r^2
38. Write 10 -843 X 10^7 in scientific notation
Triangles with same measure and same side lengths.
10! / (10-3)! = 720
Ax^2 + bx + c where a -b and c are constants and a /=0
1.0843 X 10^11
39. Evaluate 3& 2/7 / 1/3
0
9 & 6/7
N! / (n-k)!
18
40. A number is divisible by 6 if...
12.5%
(a + b)^2
20.5
Its divisible by 2 and by 3.
41. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
Relationship cannot be determined (what if x is negative?)
4096
4:5
A circle centered on the origin with radius 8.
42. What is a chord of a circle?
An infinite set.
2.592 kg
A chord is a line segment joining two points on a circle.
A tangent is a line that only touches one point on the circumference of a circle.
43. What are the integers?
All numbers multiples of 1.
2.592 kg
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
12.5%
44. 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)]?
1/a^6
71 - 73 - 79
True
10
45. What is a minor arc?
46. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
Indeterminable.
A reflection about the axis.
The shortest arc between points A and B on a circle'S diameter.
9 & 6/7
47. The objects in a set are called two names:
7 / 1000
72
A central angle is an angle formed by 2 radii.
Members or elements
48. Convert 0.7% to a fraction.
(a + b)^2
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...
7 / 1000
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
49. What is the surface area of a cylinder with radius 5 and height 8?
Area of the base X height = (pi)hr^2
130pi
An isosceles right triangle.
1
50. What are the rational numbers?
The overlapping sections.
180
83.333%
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)