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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. Formula to calculate arc length?
The union of A and B.
3/2 - 5/3
Arc length = (n/360) x pi(2r) where n is the number of degrees.
20.5
2. What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
A circle centered on the origin with radius 8.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
II
3. What is the set of elements which can be found in either A or B?
500
The union of A and B.
1
Angle/360 x (pi)r^2
4. Simplify 9^(1/2) X 4^3 X 2^(-6)?
2^9 / 2 = 256
C = 2(pi)r
3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
5. x^2 = 9. What is the value of x?
3 - -3
12! / 5!7! = 792
12.5%
4096
6. A number is divisible by 4 is...
Its last two digits are divisible by 4.
F(x-c)
180
A chord is a line segment joining two points on a circle.
7. Which quandrant is the lower right hand?
IV
Sector area = (n/360) X (pi)r^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)
Arc length = (n/360) x pi(2r) where n is the number of degrees.
8. 25^(1/2) or sqrt. 25 =
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
5 OR -5
23 - 29
Its last two digits are divisible by 4.
9. What is a major arc?
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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?
The direction of the inequality is reversed.
A grouping of the members within a set based on a shared characteristic.
Ax^2 + bx + c where a -b and c are constants and a /=0
$3 -500 in the 9% and $2 -500 in the 7%.
11. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
4096
500
0
18
12. What is the measure of an exterior angle of a regular pentagon?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
23 - 29
72
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
13. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
The third side is greater than the difference and less than the sum.
23 - 29
x= (1.2)(.8)lw
14. 4.809 X 10^7 =
Cd
The interesection of A and B.
.0004809 X 10^11
9 & 6/7
15. Order of quadrants:
0
2(pi)r^2 + 2(pi)rh
From northeast - counterclockwise. I - II - III - IV
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)
16. 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?
Move the decimal point to the right x places
5 OR -5
75:11
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
17. What is a central angle?
N! / (n-k)!
A central angle is an angle formed by 2 radii.
The union of A and B.
IV
18. Can you simplify sqrt72?
The direction of the inequality is reversed.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
8
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
19. 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 empty set - denoted by a circle with a diagonal through it.
441000 = 1 10 10 10 21 * 21
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(amount of decrease/original price) x 100%
20. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
A subset.
16.6666%
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
21. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
3sqrt4
... the square of the ratios of the corresponding sides.
87.5%
22. Max and Min lengths for a side of a triangle?
83.333%
1.7
The third side is greater than the difference and less than the sum.
18
23. What are the rational numbers?
$11 -448
The curve opens upward and the vertex is the minimal point on the graph.
2sqrt6
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
24. Which is greater? 64^5 or 16^8
G(x) = {x}
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
7 / 1000
11 - 13 - 17 - 19
25. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
N! / (n-k)!
61 - 67
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
26. 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
130pi
Area of the base X height = (pi)hr^2
83.333%
27. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
441000 = 1 10 10 10 21 * 21
90pi
$3 -500 in the 9% and $2 -500 in the 7%.
28. Area of a triangle?
Factors are few - multiples are many.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
1:sqrt3:2
(base*height) / 2
29. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
F(x) + c
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 set of output values for a function.
500
30. 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?
1/(x^y)
The interesection of A and B.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
y = 2x^2 - 3
31. What is the slope of a vertical line?
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32. Which quadrant is the upper right hand?
Two angles whose sum is 180.
Undefined
Arc length = (n/360) x pi(2r) where n is the number of degrees.
I
33. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
3sqrt4
Two equal sides and two equal angles.
The second graph is less steep.
34. What is a parabola?
4096
The shortest arc between points A and B on a circle'S diameter.
Ax^2 + bx + c where a -b and c are constants and a /=0
Yes. [i.e. f(x) = x^2 - 1
35. Can you subtract 3sqrt4 from sqrt4?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The two xes after factoring.
Yes - like radicals can be added/subtracted.
1/2 times 7/3
36. What are the integers?
67 - 71 - 73
48
All numbers multiples of 1.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
37. What is the 'union' of A and B?
A reflection about the origin.
(a - b)(a + b)
2^9 / 2 = 256
The set of elements which can be found in either A or B.
38. What are complementary angles?
Two angles whose sum is 90.
3sqrt4
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Move the decimal point to the right x places
39. When the 'a' in a parabola is positive....
61 - 67
.0004809 X 10^11
The curve opens upward and the vertex is the minimal point on the graph.
75:11
40. What is an exterior angle?
Its divisible by 2 and by 3.
An angle which is supplementary to an interior angle.
Members or elements
A subset.
41. Number of degrees in a triangle
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)
A grouping of the members within a set based on a shared characteristic.
180
42. Evaluate (4^3)^2
4096
4a^2(b)
$3 -500 in the 9% and $2 -500 in the 7%.
67 - 71 - 73
43. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A set with a number of elements which can be counted.
...multiply by 100.
A circle centered at -2 - -2 with radius 3.
The overlapping sections.
44. If the two sides of a triangle are unequal then the longer side...
12! / 5!7! = 792
F(x) - c
True
Lies opposite the greater angle
45. Factor x^2 - xy + x.
10! / 3!(10-3)! = 120
x(x - y + 1)
23 - 29
9 : 25
46. a^2 - b^2
An isosceles right triangle.
F(x-c)
(a - b)(a + b)
62.5%
47. Which quadrant is the lower left hand?
37.5%
The set of input values for a function.
III
1:sqrt3:2
48. What is an arc of a circle?
6
7 / 1000
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
An arc is a portion of a circumference of a circle.
49. What is the graph of f(x) shifted right c units or spaces?
1/2 times 7/3
F(x-c)
The sum of its digits is divisible by 3.
All numbers multiples of 1.
50. a^2 + 2ab + b^2
3
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The sum of its digits is divisible by 3.
(a + b)^2