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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. What is a major arc?
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183
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)