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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 quadrant is the upper left hand?
II
441000 = 1 10 10 10 21 * 21
Relationship cannot be determined (what if x is negative?)
1:1:sqrt2
2. x^6 / x^3
$11 -448
x^(6-3) = x^3
Angle/360 x (pi)r^2
All numbers multiples of 1.
3. Solve the quadratic equation ax^2 + bx + c= 0
The set of elements found in both A and B.
13pi / 2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
4. How to determine percent increase?
(amount of increase/original price) x 100%
No - the input value has exactly one output.
Members or elements
G(x) = {x}
5. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4096
Area of the base X height = (pi)hr^2
4:5
The set of output values for a function.
6. The ratio of the areas of two similar polygons is ...
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.
F(x + c)
Indeterminable.
... the square of the ratios of the corresponding sides.
7. What is the measure of an exterior angle of a regular pentagon?
72
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
10! / 3!(10-3)! = 120
48
8. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
1.7
441000 = 1 10 10 10 21 * 21
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
9. (x^2)^4
A set with a number of elements which can be counted.
The set of elements which can be found in either A or B.
x^(2(4)) =x^8 = (x^4)^2
Even
10. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
180
The curve opens upward and the vertex is the minimal point on the graph.
87.5%
11. Evaluate 3& 2/7 / 1/3
2
7 / 1000
The overlapping sections.
9 & 6/7
12. Simplify the expression [(b^2 - c^2) / (b - c)]
Lies opposite the greater angle
A reflection about the axis.
True
(b + c)
13. Factor x^2 - xy + x.
Sector area = (n/360) X (pi)r^2
The curve opens downward and the vertex is the maximum point on the graph.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
x(x - y + 1)
14. Define a 'Term' -
413.03 / 10^4 (move the decimal point 4 places to the left)
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)
A reflection about the axis.
72
15. 7/8 in percent?
Infinite.
The direction of the inequality is reversed.
87.5%
The curve opens upward and the vertex is the minimal point on the graph.
16. The larger the absolute value of the slope...
52
The objects within a set.
A set with no members - denoted by a circle with a diagonal through it.
The steeper the slope.
17. Area of a triangle?
The set of output values for a function.
8
A tangent is a line that only touches one point on the circumference of a circle.
(base*height) / 2
18. What is the graph of f(x) shifted left c units or spaces?
A reflection about the axis.
F(x + c)
Even
180 degrees
19. 10<all primes<20
Two angles whose sum is 180.
Divide by 100.
11 - 13 - 17 - 19
The greatest value minus the smallest.
20. 10^6 has how many zeroes?
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...
The objects within a set.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
21. What is an arc of a circle?
Sector area = (n/360) X (pi)r^2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1/(x^y)
An arc is a portion of a circumference of a circle.
22. a^2 + 2ab + b^2
A subset.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
1:sqrt3:2
(a + b)^2
23. The objects in a set are called two names:
4.25 - 6 - 22
Members or elements
Pi is the ratio of a circle'S circumference to its diameter.
10
24. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
2sqrt6
1
25. Circumference of a circle?
130pi
Diameter(Pi)
When the function is not defined for all real numbers -; only a subset of the real numbers.
3sqrt4
26. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
Its last two digits are divisible by 4.
An isosceles right triangle.
4:5
27. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A grouping of the members within a set based on a shared characteristic.
2
28. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
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.
8
2^9 / 2 = 256
29. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
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)
48
A set with a number of elements which can be counted.
Even
30. What is the ratio of the sides of an isosceles right triangle?
288 (8 9 4)
1:1:sqrt2
1 & 37/132
12! / 5!7! = 792
31. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
Cd
$3 -500 in the 9% and $2 -500 in the 7%.
The set of output values for a function.
Angle/360 x (pi)r^2
32. What are the smallest three prime numbers greater than 65?
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)
Sector area = (n/360) X (pi)r^2
The empty set - denoted by a circle with a diagonal through it.
67 - 71 - 73
33. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
6
The sum of digits is divisible by 9.
18
34. Which is greater? 64^5 or 16^8
The set of input values for a function.
5 OR -5
The empty set - denoted by a circle with a diagonal through it.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
35. 60 < all primes <70
The third side is greater than the difference and less than the sum.
61 - 67
The shortest arc between points A and B on a circle'S diameter.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
36. Which quadrant is the upper right hand?
x= (1.2)(.8)lw
The shortest arc between points A and B on a circle'S diameter.
(amount of increase/original price) x 100%
I
37. 1/8 in percent?
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...
12.5%
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.
70
38. What are 'Supplementary angles?'
Two angles whose sum is 180.
C = 2(pi)r
Move the decimal point to the right x places
11 - 13 - 17 - 19
39. a^2 - b^2 =
67 - 71 - 73
(a - b)(a + b)
Yes - like radicals can be added/subtracted.
A grouping of the members within a set based on a shared characteristic.
40. A number is divisible by 6 if...
61 - 67
Its divisible by 2 and by 3.
1.7
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.
41. What is a chord of a circle?
Pi is the ratio of a circle'S circumference to its diameter.
A chord is a line segment joining two points on a circle.
I
A grouping of the members within a set based on a shared characteristic.
42. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
Factors are few - multiples are many.
4096
1 & 37/132
43. What is the formula for computing simple interest?
Ax^2 + bx + c where a -b and c are constants and a /=0
2sqrt6
1.0843 X 10^11
A = I (1 + rt)
44. What number between 70 & 75 - inclusive - has the greatest number of factors?
Two angles whose sum is 180.
The sum of digits is divisible by 9.
72
67 - 71 - 73
45. a^0 =
The shortest arc between points A and B on a circle'S diameter.
2 & 3/7
6
1
46. 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?
55%
The longest arc between points A and B on a circle'S diameter.
10! / (10-3)! = 720
F(x) + c
47. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
18
x= (1.2)(.8)lw
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)
48. What is the intersection of A and B?
x^(6-3) = x^3
Members or elements
The set of elements found in both A and B.
...multiply by 100.
49. 70 < all primes< 80
8
62.5%
3
71 - 73 - 79
50. What is a major arc?
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