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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. Max and Min lengths for a side of a triangle?
The third side is greater than the difference and less than the sum.
37.5%
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
4.25 - 6 - 22
2. 1/2 divided by 3/7 is the same as
31 - 37
1/2 times 7/3
Infinite.
The set of elements which can be found in either A or B.
3. How many sides does a hexagon have?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x(x - y + 1)
55%
6
4. (6sqrt3) x (2sqrt5) =
Yes. [i.e. f(x) = x^2 - 1
... the square of the ratios of the corresponding sides.
The set of elements which can be found in either A or B.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
5. What is the side length of an equilateral triangle with altitude 6?
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...
5 OR -5
(amount of decrease/original price) x 100%
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
6. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
52
13pi / 2
(amount of increase/original price) x 100%
1/(x^y)
7. When the 'a' in the parabola is negative...
9 : 25
The curve opens downward and the vertex is the maximum point on the graph.
... the square of the ratios of the corresponding sides.
413.03 / 10^4 (move the decimal point 4 places to the left)
8. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
70
The direction of the inequality is reversed.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The point of intersection of the systems.
9. Number of degrees in a triangle
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
1 & 37/132
Angle/360 x (pi)r^2
180
10. 70 < all primes< 80
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 30-60-90 triangle.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
71 - 73 - 79
11. Formula for the area of a sector of a circle?
2 & 3/7
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
Yes. [i.e. f(x) = x^2 - 1
Sector area = (n/360) X (pi)r^2
12. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
x^(6-3) = x^3
Factors are few - multiples are many.
4:5
13. What is a parabola?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The set of input values for a function.
3
Ax^2 + bx + c where a -b and c are constants and a /=0
14. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
A circle centered on the origin with radius 8.
The direction of the inequality is reversed.
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. What is the 'Solution' for a system of linear equations?
Yes - like radicals can be added/subtracted.
The point of intersection of the systems.
The objects within a set.
(p + q)/5
16. 8.84 / 5.2
1.7
(a - b)(a + b)
x(x - y + 1)
1
17. If an inequality is multiplied or divided by a negative number....
III
2 & 3/7
5
The direction of the inequality is reversed.
18. 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
67 - 71 - 73
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)
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.
19. Can you subtract 3sqrt4 from sqrt4?
(p + q)/5
Yes - like radicals can be added/subtracted.
3 - -3
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
20. (x^2)^4
x^(2(4)) =x^8 = (x^4)^2
11 - 13 - 17 - 19
Diameter(Pi)
4.25 - 6 - 22
21. Legs 6 - 8. Hypotenuse?
90pi
10
(a - b)(a + b)
31 - 37
22. What percent of 40 is 22?
$11 -448
A circle centered at -2 - -2 with radius 3.
3
55%
23. The slope of a line perpendicular to (a/b)?
48
Its negative reciprocal. (-b/a)
N! / (n-k)!
1
24. Simplify 9^(1/2) X 4^3 X 2^(-6)?
Infinite.
A tangent is a line that only touches one point on the circumference of a circle.
x^(6-3) = x^3
3
25. Simplify the expression (p^2 - q^2)/ -5(q - p)
The curve opens upward and the vertex is the minimal point on the graph.
(p + q)/5
4725
IV
26. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
0
0
A chord is a line segment joining two points on a circle.
90
27. What is an exterior angle?
87.5%
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Yes - like radicals can be added/subtracted.
An angle which is supplementary to an interior angle.
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?
71 - 73 - 79
Undefined
9 & 6/7
75:11
29. Surface area for a cylinder?
90pi
2(pi)r^2 + 2(pi)rh
4725
C = (pi)d
30. What is the empty set?
$11 -448
A set with no members - denoted by a circle with a diagonal through it.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
0
31. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
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)
A 30-60-90 triangle.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
32. What are the integers?
All numbers multiples of 1.
An arc is a portion of a circumference of a circle.
31 - 37
N! / (k!)(n-k)!
33. What is the name for a grouping of the members within a set based on a shared characteristic?
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.
Yes. [i.e. f(x) = x^2 - 1
6 : 1 : 2
A subset.
34. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
1
23 - 29
90
2.592 kg
35. a^2 - b^2 =
(n-2) x 180
(a - b)^2
(a - b)(a + b)
True
36. Circumference of a circle?
True
Diameter(Pi)
A central angle is an angle formed by 2 radii.
The point of intersection of the systems.
37. Can you add sqrt 3 and sqrt 5?
...multiply by 100.
No - only like radicals can be added.
1
A tangent is a line that only touches one point on the circumference of a circle.
38. a^2 - b^2
1/2 times 7/3
(a - b)(a + b)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
4725
39. 5/8 in percent?
From northeast - counterclockwise. I - II - III - IV
62.5%
III
71 - 73 - 79
40. Length of an arc of a circle?
2
2 & 3/7
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Angle/360 x 2(pi)r
41. Define an 'expression'.
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)
55%
A = I (1 + rt)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
42. 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)
4.25 - 6 - 22
20.5
1
Indeterminable.
43. 60 < all primes <70
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The set of input values for a function.
(b + c)
61 - 67
44. Evaluate (4^3)^2
4096
1
.0004809 X 10^11
All numbers multiples of 1.
45. What is a subset?
A = pi(r^2)
A = I (1 + rt)
Two angles whose sum is 180.
A grouping of the members within a set based on a shared characteristic.
46. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Two equal sides and two equal angles.
II
4:5
47. How to determine percent increase?
The union of A and B.
(amount of increase/original price) x 100%
180
Sector area = (n/360) X (pi)r^2
48. What is the 'Solution' for a set of inequalities.
71 - 73 - 79
The overlapping sections.
20.5
A 30-60-90 triangle.
49. What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
Two angles whose sum is 180.
x^(6-3) = x^3
I
50. Simplify the expression [(b^2 - c^2) / (b - c)]
Relationship cannot be determined (what if x is negative?)
9 : 25
3
(b + c)