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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. Define a 'Term' -
No - only like radicals can be added.
75:11
1 & 37/132
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)
2. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
87.5%
2^9 / 2 = 256
Yes - like radicals can be added/subtracted.
12sqrt2
3. What is the order of operations?
1/2 times 7/3
1
x^(2(4)) =x^8 = (x^4)^2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
4. 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...
I
A tangent is a line that only touches one point on the circumference of a circle.
13
5. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
5 OR -5
(amount of increase/original price) x 100%
A reflection about the axis.
Lies opposite the greater angle
6. a^2 - b^2
4:5
(a - b)(a + b)
y = 2x^2 - 3
72
7. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
Undefined - because we can'T divide by 0.
72
y = (x + 5)/2
8. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
61 - 67
A set with no members - denoted by a circle with a diagonal through it.
Two angles whose sum is 90.
9. 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?
x= (1.2)(.8)lw
$3 -500 in the 9% and $2 -500 in the 7%.
(amount of decrease/original price) x 100%
180 degrees
10. How to determine percent increase?
(amount of increase/original price) x 100%
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
$3 -500 in the 9% and $2 -500 in the 7%.
II
11. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
Relationship cannot be determined (what if x is negative?)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
12. What is the graph of f(x) shifted right c units or spaces?
The direction of the inequality is reversed.
F(x-c)
The curve opens downward and the vertex is the maximum point on the graph.
Lies opposite the greater angle
13. x^(-y)=
1/(x^y)
6
(a + b)^2
53 - 59
14. What is a chord of a circle?
Area of the base X height = (pi)hr^2
Factors are few - multiples are many.
A chord is a line segment joining two points on a circle.
A 30-60-90 triangle.
15. How many sides does a hexagon have?
90 degrees
Relationship cannot be determined (what if x is negative?)
2sqrt6
6
16. What number between 70 & 75 - inclusive - has the greatest number of factors?
67 - 71 - 73
10! / (10-3)! = 720
1
72
17. P and r are factors of 100. What is greater - pr or 100?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Indeterminable.
1.0843 X 10^11
53 - 59
18. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
C = (pi)d
II
37.5%
19. Reduce: 4.8 : 0.8 : 1.6
Two angles whose sum is 90.
6 : 1 : 2
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.
Pi is the ratio of a circle'S circumference to its diameter.
20. x^4 + x^7 =
10
x^(4+7) = x^11
Lies opposite the greater angle
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
21. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
Cd
6 : 1 : 2
From northeast - counterclockwise. I - II - III - IV
22. 60 < all primes <70
1/a^6
61 - 67
N! / (n-k)!
Relationship cannot be determined (what if x is negative?)
23. Factor x^2 - xy + x.
N! / (k!)(n-k)!
x(x - y + 1)
441000 = 1 10 10 10 21 * 21
10! / (10-3)! = 720
24. How to find the area of a sector?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Angle/360 x (pi)r^2
4096
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
25. Volume for a cylinder?
Divide by 100.
Area of the base X height = (pi)hr^2
1:1:sqrt2
The steeper the slope.
26. What is the formula for computing simple interest?
A central angle is an angle formed by 2 radii.
A = I (1 + rt)
9 & 6/7
3
27. A number is divisible by 9 if...
Cd
The sum of digits is divisible by 9.
4a^2(b)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
28. 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)]?
y = (x + 5)/2
The set of elements found in both A and B.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
True
29. 6w^2 - w - 15 = 0
(a - b)(a + b)
3/2 - 5/3
Members or elements
Angle/360 x 2(pi)r
30. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The sum of digits is divisible by 9.
No - the input value has exactly one output.
2sqrt6
31. What is the set of elements found in both A and B?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
A subset.
The interesection of A and B.
48
32. 50 < all primes< 60
Area of the base X height = (pi)hr^2
(amount of increase/original price) x 100%
Relationship cannot be determined (what if x is negative?)
53 - 59
33. Can you simplify sqrt72?
Undefined
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
A reflection about the origin.
34. 70 < all primes< 80
x^(4+7) = x^11
130pi
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
71 - 73 - 79
35. Evaluate 4/11 + 11/12
An isosceles right triangle.
1 & 37/132
No - only like radicals can be added.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
36. The slope of a line perpendicular to (a/b)?
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 chord is a line segment joining two points on a circle.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Its negative reciprocal. (-b/a)
37. What is the maximum value for the function g(x) = (-2x^2) -1?
10! / (10-3)! = 720
1
71 - 73 - 79
Triangles with same measure and same side lengths.
38. Surface area for a cylinder?
(b + c)
12! / 5!7! = 792
2(pi)r^2 + 2(pi)rh
1
39. If a=-1 and b=3 - what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
20.5
500
(amount of increase/original price) x 100%
3
40. What is the slope of a horizontal line?
A = I (1 + rt)
0
3 - -3
The objects within a set.
41. Number of degrees in a triangle
500
180
The curve opens downward and the vertex is the maximum point on the graph.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
42. 10<all primes<20
11 - 13 - 17 - 19
F(x) - c
(b + c)
18
43. Which quadrant is the upper right hand?
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)
6
I
The greatest value minus the smallest.
44. 40 < all primes<50
1/2 times 7/3
41 - 43 - 47
288 (8 9 4)
Angle/360 x 2(pi)r
45. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
Cd
True
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
46. a^2 - b^2 =
8
(a - b)(a + b)
90pi
(n-2) x 180
47. What is the surface area of a cylinder with radius 5 and height 8?
An arc is a portion of a circumference of a circle.
130pi
4:5
441000 = 1 10 10 10 21 * 21
48. (x^2)^4
I
x^(2(4)) =x^8 = (x^4)^2
75:11
No - only like radicals can be added.
49. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(a - b)(a + b)
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)
50. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
True
Infinite.
y = 2x^2 - 3
55%