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GRE Math: Facts

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. How do you find the length of an arc of a circle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Arc = (x°/360)(2pr) where x is the central angle.
C = p2r
The set of all ordered pairs (x -y) such that y = f(x).

2. What is a Venn diagram?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A^m*b^m = (ab)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

3. What is the area of a square?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = s^2 or A =d^2/2 where d is the diagonal
A = 6(l^2)
C = p2r

4. What is the ratio of similitude?
They are both the same. A divisor or factor of an integer leaves no remainder.
The ratio of corresponding sides of similar triangles.
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

5. What is a multiple of an integer?
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.
C = p2r
The set of all ordered pairs (x -y) such that y = f(x).
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

6. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any right triangle - a^2 + b^2 = c^2.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(x + y)(x - y) = x^2 - y^2

7. What is true about the slopes of parallel lines?
Equal slopes.
The product of their slopes is -1 (negative reciprocal).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The ratio of corresponding sides of similar triangles.

8. In a circle of radius r - what is the formula for the area?
A = pr^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The product of their slopes is -1 (negative reciprocal).

9. What is an integer?
All positive and negative whole numbers - and zero.
A = pr^2
For any number b: b = -b if and only if b = 0.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

10. Properties of one 3
360°
1 is a divisor (or factor) of every integer.
Set y = 0 - and solve.
A = s^2 or A =d^2/2 where d is the diagonal

11. How do we write the equation of a line?
V = lwh
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

12. Law of exponents 4
Divide - then multiply by 100.
A^m*b^m = (ab)^m
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

13. Law of exponents 1
All positive and negative whole numbers - and zero.
For any integer n: 1^n = 1.
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.

14. What does it mean if y is inversely proportional to x?
A = pr^2
A^m/b^m = (a/b)^m
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Then the product xy is a constant.

15. What are the properties of a parallelogram?
(x + y)(x - y) = x^2 - y^2
The set of all ordered pairs (x -y) such that y = f(x).
Avg = sum of n numbers/n
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

16. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Avg = sum of n numbers/n
Corresponding sides of similar triangles are in proportion.
(x + y)(x - y) = x^2 - y^2

17. How do you find a percent of a number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Write the percent as a decimal - and multiply.
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

18. If you were given the graph of y = f(x) - what does f(a) represent?
Even numbers are divisible by 2 and odd numbers are not.
Divide - then multiply by 100.
Their sum is 180°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

19. For what values of a function is the function undefined?
For any number b: b = -b if and only if b = 0.
A^m/b^m = (a/b)^m
An integer greater than one that is not prime.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

20. What is the probability of an event that cannot occur? That must occur?
A = s^2 or A =d^2/2 where d is the diagonal
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Cannot is 0 - must is 1 - all others are in between.
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.

21. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.
B^m/b^n = b^m-n
No matter how many angles there are - the sum around the point is 360°.

22. Properties of zero 1
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.
Shifted down 2 units.
0 is the only number that is neither positive nor negative.

23. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
360°
Shifted down 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

24. What is the midpoint formula?
B^m/b^n = b^m-n
A = lw
[(x1 + x2)/2] -[(y1 + y2)/2]
A = 2(lw + lh + hw)

25. What is the distributive law?
Then the quotient y/x is a constant.
Divide - then multiply by 100.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Write the percent as a decimal - and multiply.

26. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Even numbers are divisible by 2 and odd numbers are not.
The ratio of corresponding sides of similar triangles.
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.

27. What is a composite number?
V = l^3
An integer greater than one that is not prime.
The product of their slopes is -1 (negative reciprocal).
For any right triangle - a^2 + b^2 = c^2.

28. What do we mean by the slope of the line?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
How steep the line is. Horizontal line = 0 - vertical has no slope.
Their sum is 180°.

29. Properties of zero 4
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
0 is a multiple of every integer.
(n - 2)(180°)

30. What is the measure of a straight angle?
Their sum is 180°.
180°. If two or more angles form a straight angle - their sum is 180°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Is a right triangle with a ratio of sides x:xv3:2x.

31. What is special formula for the area of an equilateral triangle?
V = l^3
A = [(s^2*v3)/4]
All positive and negative whole numbers - and zero.
(b^m)^n = b^mn

32. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Then the quotient y/x is a constant.
Cannot is 0 - must is 1 - all others are in between.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

33. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
At least one of the factors is 0.
Shifted left 2 units.

34. What is a fractional exponent?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An integer greater than one that is not prime.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

35. Properties of one 1
At least one of the factors is 0.
Write the percent over 100 and reduce.
In the expression x^b - x is the base and b is the exponent.
For any number a: a * 1 = a and a / 1 = a.

36. What is a divisor and a factor of an integer?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted right 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
They are both the same. A divisor or factor of an integer leaves no remainder.

37. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Their sum is 180°.
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(n - 2)(180°)

38. What is the sum of the measures of all angles around a point?
Set x = 0 - and solve.
No matter how many angles there are - the sum around the point is 360°.
180°. If two or more angles form a straight angle - their sum is 180°.
C = p2r

39. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Shifted up 2 units.
Then the product xy is a constant.

40. What is true about the measures of the two acute angles in a right triangle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Their sum is 90°.
A = lw

41. What is the formula for the area of a parallelogram?
V = l^3
For any number n: x^-n means 1/x^n.
Shifted right 2 units.
A = bh

42. What is the volume of a cube?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
V = l^3
A = [(s^2*v3)/4]

43. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
1 is a divisor (or factor) of every integer.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

44. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
The set of all ordered pairs (x -y) such that y = f(x).
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
How steep the line is. Horizontal line = 0 - vertical has no slope.

45. Law of exponents 5
A^m/b^m = (a/b)^m
Cannot is 0 - must is 1 - all others are in between.
For any number b: b = -b if and only if b = 0.
A = lw

46. What is the formula for the area of a rectangle?
A = lw
Shifted right 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

47. What is true about the areas of similar triangles?
All positive and negative whole numbers - and zero.
If a is negative and b is positive - then a < 0 < b.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

48. In a circle of radius r - what is the formula for the diameter?
A^m/b^m = (a/b)^m
For any right triangle - a^2 + b^2 = c^2.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
D = 2r

49. What are the sum - difference - products - and quotient of two numbers?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
All positive and negative whole numbers - and zero.
Even numbers are divisible by 2 and odd numbers are not.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

50. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
1 is a divisor (or factor) of every integer.