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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. 70 < all primes< 80
x(x - y + 1)
Angle/360 x (pi)r^2
(a - b)(a + b)
71 - 73 - 79
2. Define an 'expression'.
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
52
Its negative reciprocal. (-b/a)
3. What are complementary angles?
(a - b)(a + b)
x^(2(4)) =x^8 = (x^4)^2
The third side is greater than the difference and less than the sum.
Two angles whose sum is 90.
4. Solve the quadratic equation ax^2 + bx + c= 0
The set of output values for a function.
1
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
5. If an inequality is multiplied or divided by a negative number....
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The direction of the inequality is reversed.
Ax^2 + bx + c where a -b and c are constants and a /=0
16.6666%
6. Factor a^2 + 2ab + b^2
(a + b)^2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
...multiply by 100.
41 - 43 - 47
7. What is the 'union' of A and B?
The curve opens downward and the vertex is the maximum point on the graph.
4a^2(b)
7 / 1000
The set of elements which can be found in either A or B.
8. What are the members or elements of a set?
The objects within a set.
Its divisible by 2 and by 3.
Lies opposite the greater angle
Infinite.
9. Which quadrant is the upper left hand?
II
7 / 1000
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)
Pi is the ratio of a circle'S circumference to its diameter.
10. What is an exterior angle?
11 - 13 - 17 - 19
No - only like radicals can be added.
An angle which is supplementary to an interior angle.
72
11. What is a central angle?
A central angle is an angle formed by 2 radii.
Area of the base X height = (pi)hr^2
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
No - the input value has exactly one output.
12. What is a set with no members called?
(a - b)(a + b)
IV
67 - 71 - 73
The empty set - denoted by a circle with a diagonal through it.
13. What does the graph x^2 + y^2 = 64 look like?
A circle centered on the origin with radius 8.
F(x) - c
The curve opens downward and the vertex is the maximum point on the graph.
C = (pi)d
14. Simplify the expression [(b^2 - c^2) / (b - c)]
(a - b)^2
A circle centered on the origin with radius 8.
Ax^2 + bx + c where a -b and c are constants and a /=0
(b + c)
15. 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
The curve opens upward and the vertex is the minimal point on the graph.
Even
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
16. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
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
0
(n-2) x 180
87.5%
17. What is the 'domain' of a function?
(a - b)(a + b)
2^9 / 2 = 256
The set of input values for a function.
.0004809 X 10^11
18. How to determine percent decrease?
A circle centered on the origin with radius 8.
An expression with just one term (-6x - 2a^2)
5
(amount of decrease/original price) x 100%
19. Factor x^2 - xy + x.
4.25 - 6 - 22
x(x - y + 1)
Yes - like radicals can be added/subtracted.
41 - 43 - 47
20. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
No - the input value has exactly one output.
x^(4+7) = x^11
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)
21. 1/6 in percent?
16.6666%
The direction of the inequality is reversed.
3 - -3
x^(2(4)) =x^8 = (x^4)^2
22. Which quadrant is the lower left hand?
III
Members or elements
An infinite set.
Its negative reciprocal. (-b/a)
23. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
130pi
Cd
2.592 kg
27^(-4)
24. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
y = 2x^2 - 3
An infinite set.
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)
25. Area of a triangle?
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
(base*height) / 2
An expression with just one term (-6x - 2a^2)
500
26. What are the roots of the quadrinomial x^2 + 2x + 1?
A grouping of the members within a set based on a shared characteristic.
A subset.
The interesection of A and B.
The two xes after factoring.
27. Legs: 3 - 4. Hypotenuse?
4a^2(b)
All numbers multiples of 1.
5
4096
28. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
I
2sqrt6
y = (x + 5)/2
29. What is the graph of f(x) shifted upward c units or spaces?
A central angle is an angle formed by 2 radii.
F(x) + c
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)
3 - -3
30. 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?
1
9 : 25
83.333%
An arc is a portion of a circumference of a circle.
31. Find the surface area of a cylinder with radius 3 and height 12.
90pi
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
3/2 - 5/3
2^9 / 2 = 256
32. Simplify (a^2 + b)^2 - (a^2 - b)^2
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
An isosceles right triangle.
4a^2(b)
83.333%
33. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
x(x - y + 1)
(base*height) / 2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
An isosceles right triangle.
34. 10<all primes<20
27^(-4)
1
4:5
11 - 13 - 17 - 19
35. 4.809 X 10^7 =
F(x + c)
75:11
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
.0004809 X 10^11
36. 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)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(amount of decrease/original price) x 100%
y = (x + 5)/2
F(x) - c
37. Order of quadrants:
2
IV
An arc is a portion of a circumference of a circle.
From northeast - counterclockwise. I - II - III - IV
38. When the 'a' in a parabola is positive....
The curve opens upward and the vertex is the minimal point on the graph.
0
IV
9 : 25
39. Evaluate (4^3)^2
The shortest arc between points A and B on a circle'S diameter.
71 - 73 - 79
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
4096
40. 25^(1/2) or sqrt. 25 =
5 OR -5
x^(4+7) = x^11
Yes. [i.e. f(x) = x^2 - 1
The third side is greater than the difference and less than the sum.
41. How many sides does a hexagon have?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
37.5%
6
Part = Percent X Whole
42. Evaluate 4/11 + 11/12
Its last two digits are divisible by 4.
13pi / 2
1 & 37/132
A circle centered on the origin with radius 8.
43. 20<all primes<30
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
23 - 29
90
(a + b)^2
44. A number is divisible by 9 if...
The sum of digits is divisible by 9.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
A grouping of the members within a set based on a shared characteristic.
3 - -3
45. 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)]?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
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)
72
True
46. Which is greater? 27^(-4) or 9^(-8)
All numbers multiples of 1.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The objects within a set.
27^(-4)
47. 1/2 divided by 3/7 is the same as
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.
1/2 times 7/3
Undefined - because we can'T divide by 0.
3
48. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
5
An angle which is supplementary to an interior angle.
90
7 / 1000
49. Formula for the area of a circle?
(amount of increase/original price) x 100%
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)
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)
50. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
G(x) = {x}
I
III