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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?
Relationship cannot be determined (what if x is negative?)
Yes - like radicals can be added/subtracted.
71 - 73 - 79
The third side is greater than the difference and less than the sum.
2. Can the output value of a function have more than one input value?
$11 -448
F(x) - c
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
3. If the two sides of a triangle are unequal then the longer side...
Lies opposite the greater angle
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.
x= (1.2)(.8)lw
No - the input value has exactly one output.
4. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
...multiply by 100.
x= (1.2)(.8)lw
A reflection about the axis.
0
5. The number of degrees in the largest angle of a triangle inscribed in a circle - in which the diameter of the circle is one side of the triangle.
An infinite set.
90 degrees
x= (1.2)(.8)lw
The sum of its digits is divisible by 3.
6. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
The sum of its digits is divisible by 3.
The sum of digits is divisible by 9.
2 & 3/7
288 (8 9 4)
7. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
6
Two angles whose sum is 90.
3sqrt4
8. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
(a - b)(a + b)
12! / 5!7! = 792
12sqrt2
0
9. Surface area for a cylinder?
2(pi)r^2 + 2(pi)rh
An isosceles right triangle.
The set of input values for a function.
Pi is the ratio of a circle'S circumference to its diameter.
10. What is a major arc?
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11. Describe the relationship between the graphs of x^2 and (1/2)x^2
The steeper the slope.
Lies opposite the greater angle
1
The second graph is less steep.
12. What is the 'Solution' for a set of inequalities.
(a + b)^2
y = 2x^2 - 3
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The overlapping sections.
13. A number is divisible by 6 if...
Its divisible by 2 and by 3.
41 - 43 - 47
The curve opens upward and the vertex is the minimal point on the graph.
31 - 37
14. What is the sum of the angles of a triangle?
180 degrees
A reflection about the axis.
(n-2) x 180
F(x + c)
15. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
4725
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)
2^9 / 2 = 256
5
16. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
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 + b)^2
48
x= (1.2)(.8)lw
17. Formula of rectangle where l increases by 20% and w decreases by 20%
A chord is a line segment joining two points on a circle.
x= (1.2)(.8)lw
The interesection of A and B.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
18. 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)]?
True
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
3
Yes - like radicals can be added/subtracted.
19. a^2 + 2ab + b^2
An angle which is supplementary to an interior angle.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
(a + b)^2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
20. What is a tangent?
52
4.25 - 6 - 22
1/2 times 7/3
A tangent is a line that only touches one point on the circumference of a circle.
21. What is the graph of f(x) shifted left c units or spaces?
Cd
A = pi(r^2)
F(x + c)
The overlapping sections.
22. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
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
0
A central angle is an angle formed by 2 radii.
13pi / 2
23. To convert a decimal to a percent...
...multiply by 100.
37.5%
(amount of decrease/original price) x 100%
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
24. 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?
N! / (k!)(n-k)!
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
(a - b)(a + b)
x^(6-3) = x^3
25. Length of an arc of a circle?
413.03 / 10^4 (move the decimal point 4 places to the left)
1
Angle/360 x 2(pi)r
23 - 29
26. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
The two xes after factoring.
87.5%
288 (8 9 4)
27. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
x= (1.2)(.8)lw
No - the input value has exactly one output.
70
288 (8 9 4)
28. In a regular polygon with n sides - the formula for the sum of interior angles
10! / 3!(10-3)! = 120
(a + b)^2
3sqrt4
(n-2) x 180
29. To convert a percent to a fraction....
Its negative reciprocal. (-b/a)
Divide by 100.
2^9 / 2 = 256
90pi
30. a^2 - b^2
The union of A and B.
53 - 59
... the square of the ratios of the corresponding sides.
(a - b)(a + b)
31. 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.
I
Area of the base X height = (pi)hr^2
.0004809 X 10^11
32. Which quadrant is the upper left hand?
Even
A chord is a line segment joining two points on a circle.
II
180 degrees
33. A number is divisible by 9 if...
Infinite.
1
The sum of digits is divisible by 9.
x= (1.2)(.8)lw
34. Which is greater? 64^5 or 16^8
6
61 - 67
Undefined - because we can'T divide by 0.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
35. What are congruent triangles?
Triangles with same measure and same side lengths.
All numbers multiples of 1.
A subset.
4725
36. How to find the area of a sector?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Angle/360 x (pi)r^2
An infinite set.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
37. 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?
10! / (10-3)! = 720
(b + c)
A = I (1 + rt)
9 : 25
38. What are the integers?
All numbers multiples of 1.
1
x= (1.2)(.8)lw
An isosceles right triangle.
39. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
A grouping of the members within a set based on a shared characteristic.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
2.592 kg
90
40. (12sqrt15) / (2sqrt5) =
N! / (k!)(n-k)!
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
(base*height) / 2
$11 -448
41. The larger the absolute value of the slope...
An angle which is supplementary to an interior angle.
The steeper the slope.
The longest arc between points A and B on a circle'S diameter.
2 & 3/7
42. 3/8 in percent?
37.5%
Yes - like radicals can be added/subtracted.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Part = Percent X Whole
43. How many sides does a hexagon have?
6
Sector area = (n/360) X (pi)r^2
x= (1.2)(.8)lw
1
44. a^0 =
F(x) - c
2^9 / 2 = 256
1
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
45. x^(-y)=
N! / (n-k)!
1/(x^y)
180 degrees
90pi
46. 1/6 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...
16.6666%
An angle which is supplementary to an interior angle.
8
47. How many multiples does a given number have?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
1/a^6
90 degrees
Infinite.
48. What are the irrational numbers?
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49. 1/2 divided by 3/7 is the same as
The third side is greater than the difference and less than the sum.
4:5
1/2 times 7/3
F(x + c)
50. 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.
I
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
2.592 kg
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