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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 the sum of the angles of a triangle?
180 degrees
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
11 - 13 - 17 - 19
N! / (k!)(n-k)!
2. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
18
90
4725
3. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
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
9 & 6/7
90
4. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
(n-2) x 180
1/a^6
$3 -500 in the 9% and $2 -500 in the 7%.
5. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
The set of elements found in both A and B.
All numbers multiples of 1.
F(x + c)
28. n = 8 - k = 2. n! / k!(n-k)!
6. What is a finite set?
75:11
The union of A and B.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
A set with a number of elements which can be counted.
7. Describe the relationship between 3x^2 and 3(x - 1)^2
The third side is greater than the difference and less than the sum.
130pi
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A = I (1 + rt)
8. Formula for the area of a sector of a circle?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Sector area = (n/360) X (pi)r^2
1
Its divisible by 2 and by 3.
9. 30< all primes<40
The set of input values for a function.
Two equal sides and two equal angles.
A set with a number of elements which can be counted.
31 - 37
10. Solve the quadratic equation ax^2 + bx + c= 0
Pi is the ratio of a circle'S circumference to its diameter.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
1
(a - b)^2
11. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The direction of the inequality is reversed.
A grouping of the members within a set based on a shared characteristic.
12. 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?
Undefined - because we can'T divide by 0.
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
The set of elements which can be found in either A or B.
Even
13. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
A grouping of the members within a set based on a shared characteristic.
C = 2(pi)r
The set of output values for a function.
14. Define an 'expression'.
288 (8 9 4)
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)
Ax^2 + bx + c where a -b and c are constants and a /=0
15. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
2^9 / 2 = 256
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
... the square of the ratios of the corresponding sides.
16. (x^2)^4
x^(2(4)) =x^8 = (x^4)^2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The overlapping sections.
17. The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
C = (pi)d
(a - b)(a + b)
Two angles whose sum is 180.
18. 1/8 in percent?
0
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
12.5%
x^(6-3) = x^3
19. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
I
2 & 3/7
An angle which is supplementary to an interior angle.
87.5%
20. 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
7 / 1000
x^(2(4)) =x^8 = (x^4)^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)
21. a^2 - 2ab + b^2
All numbers multiples of 1.
(a - b)^2
The longest arc between points A and B on a circle'S diameter.
The set of elements found in both A and B.
22. The objects in a set are called two names:
28. n = 8 - k = 2. n! / k!(n-k)!
Members or elements
2^9 / 2 = 256
6
23. How many sides does a hexagon have?
4a^2(b)
90
6
1:sqrt3:2
24. Factor a^2 + 2ab + b^2
(a + b)^2
A central angle is an angle formed by 2 radii.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
288 (8 9 4)
25. A number is divisible by 9 if...
The sum of digits is divisible by 9.
The set of elements which can be found in either A or B.
A = I (1 + rt)
18
26. 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?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1
8
75:11
27. What is the 'Restricted domain of a function'?
All numbers multiples of 1.
(a + b)^2
When the function is not defined for all real numbers -; only a subset of the real numbers.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
28. When the 'a' in the parabola is negative...
Angle/360 x 2(pi)r
Its negative reciprocal. (-b/a)
Angle/360 x (pi)r^2
The curve opens downward and the vertex is the maximum point on the graph.
29. What are the integers?
N! / (n-k)!
All numbers multiples of 1.
2.592 kg
6 : 1 : 2
30. The slope of a line perpendicular to (a/b)?
(b + c)
1
A circle centered on the origin with radius 8.
Its negative reciprocal. (-b/a)
31. Evaluate 4/11 + 11/12
y = 2x^2 - 3
1 & 37/132
Area of the base X height = (pi)hr^2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
32. A number is divisible by 4 is...
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A chord is a line segment joining two points on a circle.
Its last two digits are divisible by 4.
Infinite.
33. Simplify the expression [(b^2 - c^2) / (b - c)]
1/a^6
Members or elements
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(b + c)
34. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
(amount of decrease/original price) x 100%
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
75:11
35. The number of degrees in the largest angle of a triangle inscribed in a circle - in which the diameter of the circle is one side of the triangle.
$11 -448
3 - -3
37.5%
90 degrees
36. 4.809 X 10^7 =
x(x - y + 1)
.0004809 X 10^11
No - the input value has exactly one output.
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)
37. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
3/2 - 5/3
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The point of intersection of the systems.
13pi / 2
38. Can you subtract 3sqrt4 from sqrt4?
130pi
Two angles whose sum is 180.
Yes - like radicals can be added/subtracted.
71 - 73 - 79
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)]?
The set of elements which can be found in either A or B.
52
12.5%
True
40. Which is greater? 64^5 or 16^8
The empty set - denoted by a circle with a diagonal through it.
Even
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
41. Surface area for a cylinder?
2(pi)r^2 + 2(pi)rh
180 degrees
A reflection about the axis.
1/2 times 7/3
42. a^2 - b^2
Factors are few - multiples are many.
(a - b)(a + b)
A tangent is a line that only touches one point on the circumference of a circle.
Area of the base X height = (pi)hr^2
43. x^6 / x^3
x^(6-3) = x^3
The sum of digits is divisible by 9.
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)
6 : 1 : 2
44. What is the order of operations?
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)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
6
45. Number of degrees in a triangle
180
Cd
1/(x^y)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
46. Formula to find a circle'S circumference from its diameter?
Move the decimal point to the right x places
C = (pi)d
1.7
The sum of its digits is divisible by 3.
47. How to find the area of a sector?
Angle/360 x (pi)r^2
A grouping of the members within a set based on a shared characteristic.
Indeterminable.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
48. How to find the diagonal of a rectangular solid?
C = (pi)d
(a - b)(a + b)
7 / 1000
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
49. If the two sides of a triangle are unequal then the longer side...
6
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Lies opposite the greater angle
Factors are few - multiples are many.
50. Formula of rectangle where l increases by 20% and w decreases by 20%
x^(4+7) = x^11
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...
x= (1.2)(.8)lw
When the function is not defined for all real numbers -; only a subset of the real numbers.