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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 formula for the area of a rectangle?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
V = lwh
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = lw

2. What is a Venn diagram?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
B^m/b^n = b^m-n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

3. Properties of one 3
Cannot is 0 - must is 1 - all others are in between.
The ratio of corresponding sides of similar triangles.
Then the product xy is a constant.
1 is a divisor (or factor) of every integer.

4. What does it mean if y is directly proportional to x?
In the expression x^b - x is the base and b is the exponent.
Write the percent as a decimal - and multiply.
Then the quotient y/x is a constant.
A = bh

5. What are similar triangles?
A = (1/2)bh.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(b^m)^n = b^mn

6. What is the triangle inequality?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

7. What is the sum of the measures of the four angles in a quadrilateral?
C = p2r
360°
An angle formed by extending the side of the polygon.
0 is the only number that is neither positive nor negative.

8. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
Set y = 0 - and solve.
(b^m)^n = b^mn
Shifted up 2 units.

9. What do we mean by the slope of the line?
M = (y2 - y1)/(x2 - x1)
How steep the line is. Horizontal line = 0 - vertical has no slope.
The set of all ordered pairs (x -y) such that y = f(x).
Set x = 0 - and solve.

10. What is the formula for the area of a triangle?
A = (1/2)bh.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = l^3

11. Law of exponents 3
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(b^m)^n = b^mn
Equal slopes.
Then the product xy is a constant.

12. In a circle of radius r - what is the formula for the area?
A = pr^2
The two pairs of opposite angles formed are equal to each other.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An integer greater than one that is not prime.

13. For what values of a function is the function undefined?
A = pr^2
Shifted down 2 units.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = bh

14. What are the properties of a square?
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
An integer greater than one that is not prime.
Shifted down 2 units.
A^m*b^m = (ab)^m

15. How do you calculate percent increases and decreases?
Then the quotient y/x is a constant.
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = lw

16. If you were given the graph of y = f(x) - what does f(a) represent?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
0 is the only number that is neither positive nor negative.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

17. What is the sum of the measures of all angles around a point?
B^m/b^n = b^m-n
No matter how many angles there are - the sum around the point is 360°.
An angle formed by extending the side of the polygon.
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.

18. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
How steep the line is. Horizontal line = 0 - vertical has no slope.
An integer greater than one that is not prime.
360°

19. What is the ratio of similitude?
In the expression x^b - x is the base and b is the exponent.
A = bh
The ratio of corresponding sides of similar triangles.
Set x = 0 - and solve.

20. How do you find the probability that an event will occur?
Then the product xy is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Even numbers are divisible by 2 and odd numbers are not.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

21. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
360°

22. Properties of zero 1
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
0 is the only number that is neither positive nor negative.
A = pr^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

23. What is the midpoint formula?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Even numbers are divisible by 2 and odd numbers are not.
[(x1 + x2)/2] -[(y1 + y2)/2]
A = 2(lw + lh + hw)

24. What is the formula for the surface area of a rectangular solid?
360°
(Circumference/diameter) of a circle - or approximately 3.14.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = 2(lw + lh + hw)

25. How do you convert a percent to a fraction or a decimal?
Shifted right 2 units.
Write the percent over 100 and reduce.
A = 2(lw + lh + hw)
Cannot is 0 - must is 1 - all others are in between.

26. In a circle of radius r - what is the formula for the diameter?
At least one of the factors is 0.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
D = 2r
(n - 2)(180°)

27. What is special formula for the area of an equilateral triangle?
An angle formed by extending the side of the polygon.
1 is the smallest positive odd integer.
(Circumference/diameter) of a circle - or approximately 3.14.
A = [(s^2*v3)/4]

28. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
V = pr^2h
For any number n: x^-n means 1/x^n.
180°. If two or more angles form a straight angle - their sum is 180°.

29. What is a function?
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If a is negative and b is positive - then a < 0 < b.

30. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

31. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
In the expression x^b - x is the base and b is the exponent.
0 is the only number that is neither positive nor negative.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

32. Important binomial 1
(x + y)(x - y) = x^2 - y^2
Divide - then multiply by 100.
Equal slopes.
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.

33. What is the area of a square?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = 2(lw + lh + hw)
(Circumference/diameter) of a circle - or approximately 3.14.
A = s^2 or A =d^2/2 where d is the diagonal

34. What is an exterior angle of a triangle?
Then the quotient y/x is a constant.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.

35. What is a divisor and a factor of an integer?
Then the product xy is a constant.
In the expression x^b - x is the base and b is the exponent.
B^m*b^n = b^m+n
They are both the same. A divisor or factor of an integer leaves no remainder.

36. How do we write the equation of a line?
Area = (x°/360)(pr^2) where x is the central angle.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Shifted up 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

37. What is an integer?
All positive and negative whole numbers - and zero.
The two pairs of opposite angles formed are equal to each other.
For any integer n: 1^n = 1.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

38. What formula is used for an average?
Avg = sum of n numbers/n
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any right triangle - a^2 + b^2 = c^2.

39. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Arc = (x°/360)(2pr) where x is the central angle.
V = l^3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted left 2 units.

40. Important binomial 3
[(x1 + x2)/2] -[(y1 + y2)/2]
A = 6(l^2)
M = (y2 - y1)/(x2 - x1)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

41. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Their sum is 90°.
No matter how many angles there are - the sum around the point is 360°.
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.

42. Properties of one 4
A = [(s^2*v3)/4]
Equal slopes.
1 is the smallest positive odd integer.
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.

43. In a circle of radius r - what is the formula for the circumference?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
1 is the smallest positive odd integer.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
C = p2r

44. How do you find the x-intercept of a graph?
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
Set x = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Set y = 0 - and solve.

45. What is an even and an odd number?
A fraction whose denominator is 100 i.e. 17% = 17/100
Then the quotient y/x is a constant.
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
Even numbers are divisible by 2 and odd numbers are not.

46. What is the graph of a function?
Arc = (x°/360)(2pr) where x is the central angle.
At least one of the factors is 0.
Shifted left 2 units.
The set of all ordered pairs (x -y) such that y = f(x).

47. Properties of zero 5
Even numbers are divisible by 2 and odd numbers are not.
For any number b: b = -b if and only if b = 0.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(b^m)^n = b^mn

48. What important property do similar triangles have?
Shifted up 2 units.
M = (y2 - y1)/(x2 - x1)
Corresponding sides of similar triangles are in proportion.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

49. What is the formula for the volume of a rectangular solid?
(b^m)^n = b^mn
V = lwh
For any number b: b = -b if and only if b = 0.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

50. How do you find the length of an arc of a circle?
Divide - then multiply by 100.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Arc = (x°/360)(2pr) where x is the central angle.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.