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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 probability of an event that cannot occur? That must occur?
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Cannot is 0 - must is 1 - all others are in between.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

2. What is the volume of a cube?
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.
[(x1 + x2)/2] -[(y1 + y2)/2]
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.
V = l^3

3. What is the sum of the measures of the four angles in a quadrilateral?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
0 is the only number that is neither positive nor negative.
360°

4. What is the sum of the measures of the n angles of a polygon with n sides?
If a is negative and b is positive - then a < 0 < b.
(n - 2)(180°)
A fraction whose denominator is 100 i.e. 17% = 17/100
Write the percent over 100 and reduce.

5. What is true about the areas 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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Is a right triangle with a ratio of sides x:xv3:2x.
No matter how many angles there are - the sum around the point is 360°.

6. What is a function?
Avg = sum of n numbers/n
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.

7. Important binomial 3
A = 6(l^2)
Avg = sum of n numbers/n
An integer greater than one that is not prime.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

8. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
(Circumference/diameter) of a circle - or approximately 3.14.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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°.

9. If the product of two or more numbers is 0 - what do you know about the numbers?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The ratio of corresponding sides of similar triangles.
At least one of the factors is 0.
Set x = 0 - and solve.

10. What is the formula for the volume of a cylinder?
V = pr^2h
For any right triangle - a^2 + b^2 = c^2.
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m

11. What is an exterior angle of a polygon?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Set x = 0 - and solve.
An angle formed by extending the side of the polygon.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

12. What is a percent?
1 is a divisor (or factor) of every integer.
Shifted up 2 units.
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.
A fraction whose denominator is 100 i.e. 17% = 17/100

13. Properties of zero 2
Then the quotient y/x is a constant.
For any right triangle - a^2 + b^2 = c^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If a is negative and b is positive - then a < 0 < b.

14. In a circle of radius r - what is the formula for the circumference?
Area = (x°/360)(pr^2) where x is the central angle.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
C = p2r
They are both the same. A divisor or factor of an integer leaves no remainder.

15. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

16. What is the triangle inequality?
Shifted right 2 units.
Shifted up 2 units.
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.

17. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
A = 2(lw + lh + hw)
No matter how many angles there are - the sum around the point is 360°.
For any right triangle - a^2 + b^2 = c^2.

18. Properties of zero 5
For any number b: b = -b if and only if b = 0.
360°
0 is the only number that is neither positive nor negative.
Cannot is 0 - must is 1 - all others are in between.

19. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
For any right triangle - a^2 + b^2 = c^2.
A^m/b^m = (a/b)^m
Their sum is 180°.

20. Law of exponents 1
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
B^m*b^n = b^m+n
360°
Their sum is 180°.

21. What is a multiple of an integer?
All positive and negative whole numbers - and zero.
At least one of the factors is 0.
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.
Is a right triangle with a ratio of sides x:xv3:2x.

22. What is an even and an odd number?
A^m/b^m = (a/b)^m
B^m/b^n = b^m-n
Even numbers are divisible by 2 and odd numbers are not.
(Circumference/diameter) of a circle - or approximately 3.14.

23. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = pr^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

24. What is a composite number?
1 is a divisor (or factor) of every integer.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An integer greater than one that is not prime.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

25. Law of exponents 3
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.
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.
(b^m)^n = b^mn

26. What is a proportion?
Their sum is 90°.
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = bh

27. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Divide - then multiply by 100.
B^m/b^n = b^m-n
360°
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

28. Properties of square roots
360°
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(Circumference/diameter) of a circle - or approximately 3.14.

29. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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.

30. What is true about the measures of the four angles formed by two intersecting lines?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The two pairs of opposite angles formed are equal to each other.
(b^m)^n = b^mn
All positive and negative whole numbers - and zero.

31. What are the important properties of a 45-45 - 90 triangle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
How steep the line is. Horizontal line = 0 - vertical has no slope.
An angle formed by extending the side of the polygon.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

32. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
1 is a divisor (or factor) of every integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
360°
Shifted down 2 units.
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.

34. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
Set x = 0 - and solve.
Cannot is 0 - must is 1 - all others are in between.
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.

35. What is an exterior angle of a triangle?
[(x1 + x2)/2] -[(y1 + y2)/2]
A = [(s^2*v3)/4]
(n - 2)(180°)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

36. Properties of one 2
For any integer n: 1^n = 1.
Avg = sum of n numbers/n
Their sum is 90°.
V = pr^2h

37. What is an exponent?
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.
In the expression x^b - x is the base and b is the exponent.
Write the percent as a decimal - and multiply.
0 is the only number that is neither positive nor negative.

38. What is an integer?
All positive and negative whole numbers - and zero.
The two pairs of opposite angles formed are equal to each other.
360°
Set y = 0 - and solve.

39. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
At least one of the factors is 0.
Shifted left 2 units.
A = lw
If a is negative and b is positive - then a < 0 < b.

40. What is true about the measures of the two acute angles in a right triangle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The two pairs of opposite angles formed are equal to each other.
B^m*b^n = b^m+n
Their sum is 90°.

41. How do we write the equation of a line?
Set y = 0 - and solve.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

42. What is the formula for the area of a parallelogram?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number n: x^-n means 1/x^n.
A = bh

43. What formula is used for an average?
Then the quotient y/x is a constant.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
No matter how many angles there are - the sum around the point is 360°.
Avg = sum of n numbers/n

44. What are the important properties of 30-60-90 triangle?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any number a: a * 1 = a and a / 1 = a.
D = 2r
Is a right triangle with a ratio of sides x:xv3:2x.

45. What is a fractional exponent?
Corresponding sides of similar triangles are in proportion.
A = 2(lw + lh + hw)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

46. What is true about the slopes of perpendicular lines?
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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.
The product of their slopes is -1 (negative reciprocal).

47. How do you find the area of a sector of a circle?
Write the percent over 100 and reduce.
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.
Area = (x°/360)(pr^2) where x is the central angle.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

48. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is the only number that is neither positive nor negative.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
How steep the line is. Horizontal line = 0 - vertical has no slope.

49. What is the formula for the area of a triangle?
A = (1/2)bh.
360°
Cannot is 0 - must is 1 - all others are in between.
Shifted right 2 units.

50. Properties of zero 3
Shifted left 2 units.
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.
A = 2(lw + lh + hw)
0 is a multiple of every integer.