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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. How to find the area of a sector?
x^(4+7) = x^11
The set of elements found in both A and B.
Angle/360 x (pi)r^2
0
2. The slope of a line perpendicular to (a/b)?
Two equal sides and two equal angles.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Its negative reciprocal. (-b/a)
52
3. 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.
28. n = 8 - k = 2. n! / k!(n-k)!
90
y = (x + 5)/2
4. What is the 'Solution' for a set of inequalities.
The overlapping sections.
The curve opens downward and the vertex is the maximum point on the graph.
Factors are few - multiples are many.
Two angles whose sum is 90.
5. When the 'a' in a parabola is positive....
F(x + c)
18
The curve opens upward and the vertex is the minimal point on the graph.
28. n = 8 - k = 2. n! / k!(n-k)!
6. What is the measure of an exterior angle of a regular pentagon?
A grouping of the members within a set based on a shared characteristic.
72
The sum of its digits is divisible by 3.
G(x) = {x}
7. How to determine percent increase?
A = I (1 + rt)
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
(amount of increase/original price) x 100%
Sector area = (n/360) X (pi)r^2
8. Volume for a cylinder?
18
The sum of digits is divisible by 9.
Area of the base X height = (pi)hr^2
A grouping of the members within a set based on a shared characteristic.
9. What is the area of a regular hexagon with side 6?
The point of intersection of the systems.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
1
3/2 - 5/3
10. Legs 6 - 8. Hypotenuse?
1:1:sqrt2
10
A grouping of the members within a set based on a shared characteristic.
4a^2(b)
11. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
1
12. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A circle centered at -2 - -2 with radius 3.
10! / (10-3)! = 720
(b + c)
(amount of decrease/original price) x 100%
13. Surface area for a cylinder?
Two angles whose sum is 180.
The sum of digits is divisible by 9.
2(pi)r^2 + 2(pi)rh
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
14. What is the 'union' of A and B?
1 & 37/132
A = pi(r^2)
10! / 3!(10-3)! = 120
The set of elements which can be found in either A or B.
15. Can the input value of a function have more than one output value (i.e. x: y - y1)?
A reflection about the axis.
61 - 67
No - the input value has exactly one output.
An infinite set.
16. Which quadrant is the upper left hand?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(amount of decrease/original price) x 100%
II
$3 -500 in the 9% and $2 -500 in the 7%.
17. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
2.592 kg
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
20.5
18. How many sides does a hexagon have?
...multiply by 100.
53 - 59
72
6
19. What is the graph of f(x) shifted downward c units or spaces?
The longest arc between points A and B on a circle'S diameter.
18
F(x) - c
9 & 6/7
20. x^2 = 9. What is the value of x?
13
3 - -3
413.03 / 10^4 (move the decimal point 4 places to the left)
An expression with just one term (-6x - 2a^2)
21. What is an arc of a circle?
180 degrees
An arc is a portion of a circumference of a circle.
The greatest value minus the smallest.
...multiply by 100.
22. a^2 - b^2 =
The union of A and B.
(a - b)(a + b)
A = I (1 + rt)
Yes. [i.e. f(x) = x^2 - 1
23. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
Lies opposite the greater angle
3 - -3
Two equal sides and two equal angles.
24. 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?
27^(-4)
48
Its negative reciprocal. (-b/a)
A set with no members - denoted by a circle with a diagonal through it.
25. Define a 'monomial'
Angle/360 x (pi)r^2
An expression with just one term (-6x - 2a^2)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
26. 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?
13
N! / (k!)(n-k)!
41 - 43 - 47
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)
27. What is the name for a grouping of the members within a set based on a shared characteristic?
x^(4+7) = x^11
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
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
A subset.
28. What is the slope of a vertical line?
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183
29. Can you simplify sqrt72?
Its divisible by 2 and by 3.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
I
1.0843 X 10^11
30. Formula to find a circle'S circumference from its diameter?
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
$3 -500 in the 9% and $2 -500 in the 7%.
C = (pi)d
Yes. [i.e. f(x) = x^2 - 1
31. 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?
75:11
An isosceles right triangle.
23 - 29
Two angles whose sum is 180.
32. What is the set of elements found in both A and B?
130pi
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The interesection of A and B.
1
33. Area of a triangle?
Its last two digits are divisible by 4.
The interesection of A and B.
(p + q)/5
(base*height) / 2
34. In a regular polygon with n sides - the formula for the sum of interior angles
1
11 - 13 - 17 - 19
(n-2) x 180
A reflection about the origin.
35. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
12sqrt2
2 & 3/7
Cd
Undefined - because we can'T divide by 0.
36. 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?
288 (8 9 4)
(amount of increase/original price) x 100%
1
9 : 25
37. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
F(x-c)
Factors are few - multiples are many.
2 & 3/7
5 OR -5
38. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
F(x) - c
The set of output values for a function.
18
39. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x= (1.2)(.8)lw
x(x - y + 1)
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.
Two angles whose sum is 180.
6
1:sqrt3:2
41. a^2 + 2ab + b^2
Undefined
(a + b)^2
4.25 - 6 - 22
1.7
42. Describe the relationship between the graphs of x^2 and (1/2)x^2
3sqrt4
The set of output values for a function.
The second graph is less steep.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
43. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
90pi
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
3
44. Formula for the area of a sector of a circle?
(a + b)^2
Sector area = (n/360) X (pi)r^2
9 & 6/7
... the square of the ratios of the corresponding sides.
45. 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?
The shortest arc between points A and B on a circle'S diameter.
441000 = 1 10 10 10 21 * 21
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
The objects within a set.
46. What is an isoceles triangle?
1/2 times 7/3
4725
A reflection about the axis.
Two equal sides and two equal angles.
47. 10^6 has how many zeroes?
6
(b + c)
75:11
IV
48. 1/2 divided by 3/7 is the same as
The point of intersection of the systems.
An expression with just one term (-6x - 2a^2)
C = 2(pi)r
1/2 times 7/3
49. a^0 =
13pi / 2
x(x - y + 1)
Undefined - because we can'T divide by 0.
1
50. Reduce: 4.8 : 0.8 : 1.6
2^9 / 2 = 256
F(x) + c
6 : 1 : 2
130pi