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GRE Math: Common Errors

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 is a major arc?

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2. What is a central angle?
37.5%
The second graph is less steep.
A central angle is an angle formed by 2 radii.
Divide by 100.

3. When does a function automatically have a restricted domain (2)?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The point of intersection of the systems.
The longest arc between points A and B on a circle'S diameter.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

4. What are the members or elements of a set?
12sqrt2
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The objects within a set.
2^9 / 2 = 256

5. Evaluate (4^3)^2
180
10! / 3!(10-3)! = 120
4096
The two xes after factoring.

6. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
(amount of increase/original price) x 100%
6
The curve opens downward and the vertex is the maximum point on the graph.
2sqrt6

7. 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?
87.5%
10! / 3!(10-3)! = 120
9 : 25
A = I (1 + rt)

8. 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?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Its last two digits are divisible by 4.
$3 -500 in the 9% and $2 -500 in the 7%.
The overlapping sections.

9. Which is greater? 27^(-4) or 9^(-8)
13pi / 2
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Cd
27^(-4)

10. 30< all primes<40
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...
31 - 37
Its last two digits are divisible by 4.
37.5%

11. Can you simplify sqrt72?
y = 2x^2 - 3
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
23 - 29
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

12. Describe the relationship between 3x^2 and 3(x - 1)^2
A set with a number of elements which can be counted.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
x^(4+7) = x^11
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

13. Area of a triangle?
I
(base*height) / 2
(n-2) x 180
Sqrt 12

14. 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
An infinite set.
The sum of digits is divisible by 9.
4096

15. Formula to find a circle'S circumference from its diameter?
The steeper the slope.
The sum of its digits is divisible by 3.
3 - -3
C = (pi)d

16. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
5 OR -5
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1.7

17. What is a chord of a circle?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
An isosceles right triangle.
A chord is a line segment joining two points on a circle.
31 - 37

18. Length of an arc of a circle?
Angle/360 x 2(pi)r
The empty set - denoted by a circle with a diagonal through it.
(base*height) / 2
Cd

19. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
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)
1
28. n = 8 - k = 2. n! / k!(n-k)!
Diameter(Pi)

20. Formula for the area of a sector of a circle?
9 : 25
An angle which is supplementary to an interior angle.
(p + q)/5
Sector area = (n/360) X (pi)r^2

21. What is the 'Solution' for a system of linear equations?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
2.592 kg
The point of intersection of the systems.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

22. Simplify (a^2 + b)^2 - (a^2 - b)^2
F(x) - c
4a^2(b)
The greatest value minus the smallest.
(a - b)^2

23. Which quandrant is the lower right hand?
2.592 kg
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
IV
Angle/360 x 2(pi)r

24. What is the measure of an exterior angle of a regular pentagon?
...multiply by 100.
The sum of digits is divisible by 9.
Its negative reciprocal. (-b/a)
72

25. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
(amount of decrease/original price) x 100%
Its negative reciprocal. (-b/a)
13pi / 2

26. Pi is a ratio of what to what?

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27. What does the graph x^2 + y^2 = 64 look like?
41 - 43 - 47
A circle centered on the origin with radius 8.
413.03 / 10^4 (move the decimal point 4 places to the left)
A = pi(r^2)

28. Formula for the area of a circle?
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)
500
A = pi(r^2)
x^(6-3) = x^3

29. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
20.5
A 30-60-90 triangle.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
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)

30. 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...
413.03 / 10^4 (move the decimal point 4 places to the left)
Triangles with same measure and same side lengths.
83.333%

31. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
The union of A and B.
12! / 5!7! = 792
The curve opens upward and the vertex is the minimal point on the graph.
$11 -448

32. What are the roots of the quadrinomial x^2 + 2x + 1?
(amount of increase/original price) x 100%
The two xes after factoring.
3/2 - 5/3
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

33. What are the rational numbers?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
9 : 25
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Move the decimal point to the right x places

34. Convert 0.7% to a fraction.
The steeper the slope.
C = (pi)d
7 / 1000
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...

35. How many sides does a hexagon have?
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...
1
(a - b)(a + b)
6

36. Find the surface area of a cylinder with radius 3 and height 12.
(a - b)^2
90pi
Area of the base X height = (pi)hr^2
Triangles with same measure and same side lengths.

37. What is the formula for compounded interest?
90
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
18
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.

38. Which quadrant is the upper right hand?
I
.0004809 X 10^11
x(x - y + 1)
Its negative reciprocal. (-b/a)

39. 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)]?
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
(amount of decrease/original price) x 100%
True
10! / (10-3)! = 720

40. What is the 'Solution' for a set of inequalities.
288 (8 9 4)
The overlapping sections.
Infinite.
... the square of the ratios of the corresponding sides.

41. (12sqrt15) / (2sqrt5) =
Yes. [i.e. f(x) = x^2 - 1
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
11 - 13 - 17 - 19
x^(4+7) = x^11

42. Can the input value of a function have more than one output value (i.e. x: y - y1)?
3sqrt4
72
48
No - the input value has exactly one output.

43. How to determine percent decrease?
(amount of decrease/original price) x 100%
3
71 - 73 - 79
4:5

44. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
G(x) = {x}
A subset.
An expression with just one term (-6x - 2a^2)

45. What are complementary angles?
Two angles whose sum is 90.
y = (x + 5)/2
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
Sector area = (n/360) X (pi)r^2

46. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
The shortest arc between points A and B on a circle'S diameter.
The curve opens upward and the vertex is the minimal point on the graph.
72

47. 6w^2 - w - 15 = 0
12! / 5!7! = 792
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
3/2 - 5/3
62.5%

48. x^2 = 9. What is the value of x?
A chord is a line segment joining two points on a circle.
Members or elements
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
3 - -3

49. a^2 - b^2 =
(a - b)(a + b)
The union of A and B.
The two xes after factoring.
37.5%

50. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
16.6666%
An expression with just one term (-6x - 2a^2)