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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 are complementary angles?
Two angles whose sum is 90.
The overlapping sections.
Angle/360 x 2(pi)r
C = (pi)d
2. 6w^2 - w - 15 = 0
1
3/2 - 5/3
27^(-4)
4725
3. Legs 6 - 8. Hypotenuse?
10
$3 -500 in the 9% and $2 -500 in the 7%.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
1/(x^y)
4. Formula for the area of a circle?
Divide by 100.
A = pi(r^2)
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
413.03 / 10^4 (move the decimal point 4 places to the left)
5. What is the intersection of A and B?
7 / 1000
48
The set of elements found in both A and B.
(amount of increase/original price) x 100%
6. x^2 = 9. What is the value of x?
3 - -3
The curve opens upward and the vertex is the minimal point on the graph.
Area of the base X height = (pi)hr^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
7. Formula to find a circle'S circumference from its diameter?
4725
The third side is greater than the difference and less than the sum.
C = (pi)d
When the function is not defined for all real numbers -; only a subset of the real numbers.
8. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
An arc is a portion of a circumference of a circle.
4:5
The steeper the slope.
9. Formula for the area of a sector of a circle?
Diameter(Pi)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Sector area = (n/360) X (pi)r^2
The second graph is less steep.
10. 2sqrt4 + sqrt4 =
Sector area = (n/360) X (pi)r^2
5 OR -5
3sqrt4
$3 -500 in the 9% and $2 -500 in the 7%.
11. When the 'a' in a parabola is positive....
The objects within a set.
1
The curve opens upward and the vertex is the minimal point on the graph.
The empty set - denoted by a circle with a diagonal through it.
12. Simplify (a^2 + b)^2 - (a^2 - b)^2
Factors are few - multiples are many.
3
4a^2(b)
61 - 67
13. (-1)^2 =
Yes - like radicals can be added/subtracted.
IV
1
3/2 - 5/3
14. What is a finite set?
A set with a number of elements which can be counted.
The sum of its digits is divisible by 3.
(amount of decrease/original price) x 100%
2^9 / 2 = 256
15. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
71 - 73 - 79
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
90 degrees
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?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
9 : 25
An arc is a portion of a circumference of a circle.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
17. x^(-y)=
1/(x^y)
No - the input value has exactly one output.
Area of the base X height = (pi)hr^2
True
18. What number between 70 & 75 - inclusive - has the greatest number of factors?
(amount of decrease/original price) x 100%
When the function is not defined for all real numbers -; only a subset of the real numbers.
4725
72
19. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
The longest arc between points A and B on a circle'S diameter.
28. n = 8 - k = 2. n! / k!(n-k)!
3
y = (x + 5)/2
20. 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?
Two angles whose sum is 180.
75:11
The longest arc between points A and B on a circle'S diameter.
4a^2(b)
21. What is the 'Solution' for a set of inequalities.
The overlapping sections.
75:11
0
20.5
22. Area of a triangle?
(base*height) / 2
y = 2x^2 - 3
Two angles whose sum is 90.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
23. What is the graph of f(x) shifted downward c units or spaces?
72
Sector area = (n/360) X (pi)r^2
F(x) - c
441000 = 1 10 10 10 21 * 21
24. Can the input value of a function have more than one output value (i.e. x: y - y1)?
No - the input value has exactly one output.
9 : 25
2sqrt6
x^(6-3) = x^3
25. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
52
20.5
12.5%
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
26. What is the graph of f(x) shifted left c units or spaces?
The greatest value minus the smallest.
83.333%
2 & 3/7
F(x + c)
27. How many 3-digit positive integers are even and do not contain the digit 4?
F(x + c)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
288 (8 9 4)
Undefined - because we can'T divide by 0.
28. 40 < all primes<50
41 - 43 - 47
3/2 - 5/3
F(x) + c
5
29. What is an exterior angle?
10! / 3!(10-3)! = 120
An angle which is supplementary to an interior angle.
The overlapping sections.
A circle centered at -2 - -2 with radius 3.
30. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
x= (1.2)(.8)lw
55%
3
31. What does scientific notation mean?
A set with a number of elements which can be counted.
II
The point of intersection of the systems.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
32. What are the rational numbers?
72
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
From northeast - counterclockwise. I - II - III - IV
11 - 13 - 17 - 19
33. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
70
The steeper the slope.
500
34. Simplify the expression [(b^2 - c^2) / (b - c)]
Sqrt 12
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
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
(b + c)
35. What is the formula for compounded interest?
$11 -448
$3 -500 in the 9% and $2 -500 in the 7%.
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.
288 (8 9 4)
36. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
A reflection about the axis.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
y = (x + 5)/2
Its last two digits are divisible by 4.
37. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
2(pi)r^2 + 2(pi)rh
Ax^2 + bx + c where a -b and c are constants and a /=0
31 - 37
38. What are congruent triangles?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
61 - 67
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
Triangles with same measure and same side lengths.
39. What is a set with no members called?
1
The empty set - denoted by a circle with a diagonal through it.
Two angles whose sum is 180.
An isosceles right triangle.
40. What is the area of a regular hexagon with side 6?
Cd
5 OR -5
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
41. 25^(1/2) or sqrt. 25 =
A circle centered on the origin with radius 8.
A = I (1 + rt)
Relationship cannot be determined (what if x is negative?)
5 OR -5
42. What is the surface area of a cylinder with radius 5 and height 8?
The curve opens downward and the vertex is the maximum point on the graph.
130pi
(amount of increase/original price) x 100%
Move the decimal point to the right x places
43. When the 'a' in the parabola is negative...
10! / (10-3)! = 720
The curve opens downward and the vertex is the maximum point on the graph.
10
72
44. 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
A set with no members - denoted by a circle with a diagonal through it.
52
13
45. Which quadrant is the upper right hand?
An expression with just one term (-6x - 2a^2)
I
A grouping of the members within a set based on a shared characteristic.
5
46. 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?
1
6 : 1 : 2
10! / 3!(10-3)! = 120
(amount of increase/original price) x 100%
47. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
6
Indeterminable.
48. a^2 - b^2 =
A grouping of the members within a set based on a shared characteristic.
Members or elements
(a - b)(a + b)
441000 = 1 10 10 10 21 * 21
49. Volume for a cylinder?
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
52
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Area of the base X height = (pi)hr^2
50. 1/8 in percent?
A subset.
A set with no members - denoted by a circle with a diagonal through it.
12.5%
Cd