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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. Describe the relationship between 3x^2 and 3(x - 1)^2
$11 -448
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
31 - 37
(n-2) x 180
2. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
10! / 3!(10-3)! = 120
28. n = 8 - k = 2. n! / k!(n-k)!
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
True
3. How to determine percent decrease?
4725
(amount of decrease/original price) x 100%
28. n = 8 - k = 2. n! / k!(n-k)!
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
4. What are complementary angles?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
A subset.
The set of elements which can be found in either A or B.
Two angles whose sum is 90.
5. In a regular polygon with n sides - the formula for the sum of interior angles
(n-2) x 180
1
The set of input values for a function.
The curve opens downward and the vertex is the maximum point on the graph.
6. 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?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
N! / (k!)(n-k)!
3 - -3
75:11
7. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
Part = Percent X Whole
$11 -448
500
x^(4+7) = x^11
8. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
I
y = 2x^2 - 3
True
Cd
9. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
16.6666%
4725
67 - 71 - 73
6
10. 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?
A reflection about the origin.
6 : 1 : 2
$3 -500 in the 9% and $2 -500 in the 7%.
10
11. Define an 'expression'.
4:5
II
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)
5 OR -5
12. (-1)^2 =
13pi / 2
12.5%
1
C = (pi)d
13. 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)?
62.5%
y = (x + 5)/2
180 degrees
7 / 1000
14. 60 < all primes <70
61 - 67
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
12sqrt2
(a - b)(a + b)
15. 70 < all primes< 80
71 - 73 - 79
Even
x^(4+7) = x^11
53 - 59
16. What is the graph of f(x) shifted upward c units or spaces?
1/(x^y)
N! / (n-k)!
F(x) + c
Ax^2 + bx + c where a -b and c are constants and a /=0
17. What is the 'Solution' for a set of inequalities.
288 (8 9 4)
A reflection about the origin.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The overlapping sections.
18. What is the name for a grouping of the members within a set based on a shared characteristic?
Angle/360 x 2(pi)r
3 - -3
A subset.
90
19. 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?
9 : 25
The shortest arc between points A and B on a circle'S diameter.
The overlapping sections.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
20. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
10! / 3!(10-3)! = 120
6
13
The steeper the slope.
21. 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?
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 - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
2(pi)r^2 + 2(pi)rh
441000 = 1 10 10 10 21 * 21
22. What is the name of set with a number of elements which cannot be counted?
(a - b)(a + b)
An infinite set.
(amount of decrease/original price) x 100%
31 - 37
23. 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)]?
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)
True
A circle centered on the origin with radius 8.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
24. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
500
I
52
13pi / 2
25. 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?
y = 2x^2 - 3
The interesection of A and B.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The third side is greater than the difference and less than the sum.
26. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
A subset.
1
441000 = 1 10 10 10 21 * 21
The empty set - denoted by a circle with a diagonal through it.
27. What is an exterior angle?
An angle which is supplementary to an interior angle.
Factors are few - multiples are many.
... the square of the ratios of the corresponding sides.
Ax^2 + bx + c where a -b and c are constants and a /=0
28. To convert a decimal to a percent...
Undefined
Indeterminable.
...multiply by 100.
A reflection about the origin.
29. 6w^2 - w - 15 = 0
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Angle/360 x (pi)r^2
3/2 - 5/3
Triangles with same measure and same side lengths.
30. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
A tangent is a line that only touches one point on the circumference of a circle.
6
4a^2(b)
31. Volume for a cylinder?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
23 - 29
x^(4+7) = x^11
Area of the base X height = (pi)hr^2
32. How many 3-digit positive integers are even and do not contain the digit 4?
6
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)
The curve opens upward and the vertex is the minimal point on the graph.
288 (8 9 4)
33. A number is divisible by 6 if...
Its divisible by 2 and by 3.
1
The set of elements which can be found in either A or B.
A reflection about the axis.
34. Circumference of a circle?
1
Diameter(Pi)
... the square of the ratios of the corresponding sides.
An expression with just one term (-6x - 2a^2)
35. If the two sides of a triangle are unequal then the longer side...
$3 -500 in the 9% and $2 -500 in the 7%.
Lies opposite the greater angle
F(x + c)
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
36. 1/2 divided by 3/7 is the same as
1/2 times 7/3
The sum of its digits is divisible by 3.
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.
Infinite.
37. Which quadrant is the upper left hand?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The set of elements which can be found in either A or B.
5 OR -5
II
38. What is the maximum value for the function g(x) = (-2x^2) -1?
Move the decimal point to the right x places
9 & 6/7
1
F(x) + c
39. What is the slope of a vertical line?
40. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
...multiply by 100.
90
1
13pi / 2
41. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
The second graph is less steep.
2^9 / 2 = 256
... the square of the ratios of the corresponding sides.
A set with no members - denoted by a circle with a diagonal through it.
42. a^0 =
The union of A and B.
(b + c)
1
Two equal sides and two equal angles.
43. Simplify (a^2 + b)^2 - (a^2 - b)^2
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)
8
4a^2(b)
180
44. x^6 / x^3
6
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
An isosceles right triangle.
x^(6-3) = x^3
45. Formula for the area of a circle?
A = pi(r^2)
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)
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The set of output values for a function.
46. Which is greater? 27^(-4) or 9^(-8)
The greatest value minus the smallest.
3/2 - 5/3
27^(-4)
Area of the base X height = (pi)hr^2
47. What is the formula for computing simple interest?
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)
16.6666%
A = I (1 + rt)
1
48. Formula to calculate arc length?
The greatest value minus the smallest.
441000 = 1 10 10 10 21 * 21
Arc length = (n/360) x pi(2r) where n is the number of degrees.
0
49. 1/8 in percent?
1
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)
75:11
12.5%
50. What is the side length of an equilateral triangle with altitude 6?
The overlapping sections.
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...
y = 2x^2 - 3
(a + b)^2