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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. What is true about the measures of the two acute angles in a right triangle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
They are both the same. A divisor or factor of an integer leaves no remainder.
Their sum is 90°.
No matter how many angles there are - the sum around the point is 360°.

2. How do you find the slope of a line?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Cannot is 0 - must is 1 - all others are in between.
M = (y2 - y1)/(x2 - x1)

3. What is the formula for the volume of a cylinder?
The product of their slopes is -1 (negative reciprocal).
A = [(s^2*v3)/4]
Shifted up 2 units.
V = pr^2h

4. What is the ratio of similitude?
Shifted up 2 units.
V = pr^2h
If a is negative and b is positive - then a < 0 < b.
The ratio of corresponding sides of similar triangles.

5. How do we write the equation of a line?
360°
M = (y2 - y1)/(x2 - x1)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

6. How do you find the y-intercept of a graph?
No matter how many angles there are - the sum around the point is 360°.
Set x = 0 - and solve.
V = l^3
Shifted up 2 units.

7. What is the graph of a function?
For any right triangle - a^2 + b^2 = c^2.
The set of all ordered pairs (x -y) such that y = f(x).
Avg = sum of n numbers/n
Corresponding sides of similar triangles are in proportion.

8. How do you calculate a weighted average?
A = lw
For any integer n: 1^n = 1.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

9. 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]
An angle formed by extending the side of the polygon.
A = pr^2
360°

10. What is a proportion?
Their sum is 90°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
1 is the smallest positive odd integer.
A^m*b^m = (ab)^m

11. What are similar triangles?
Their sum is 180°.
D = 2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
At least one of the factors is 0.

12. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Is a right triangle with a ratio of sides x:xv3:2x.
The product of their slopes is -1 (negative reciprocal).
Shifted right 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15

13. What is the formula for the volume of a rectangular solid?
V = lwh
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A^m*b^m = (ab)^m
C = p2r

14. Properties of zero 5
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
C = p2r
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.
For any number b: b = -b if and only if b = 0.

15. What is the midpoint formula?
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.
[(x1 + x2)/2] -[(y1 + y2)/2]

16. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = [(s^2*v3)/4]
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.

17. How do you calculate percent increases and decreases?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
B^m/b^n = b^m-n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Their sum is 180°.

18. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
For any right triangle - a^2 + b^2 = c^2.
A^m*b^m = (ab)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

19. What are the median and the mode of a set of data?
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.
Arc = (x°/360)(2pr) where x is the central angle.
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.
V = lwh

20. How do you convert a percent to a fraction or a decimal?
A = bh
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Write the percent over 100 and reduce.
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.

21. What are the properties of a rectangle?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.
Set y = 0 - and solve.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

22. Law of exponents 1
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
B^m*b^n = b^m+n
A = pr^2
V = l^3

23. What is a divisor and a factor of an integer?
Divide - then multiply by 100.
Shifted down 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
V = pr^2h

24. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Divide - then multiply by 100.
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.
180°. If two or more angles form a straight angle - their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.

25. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
No matter how many angles there are - the sum around the point is 360°.
A = pr^2
A = s^2 or A =d^2/2 where d is the diagonal

26. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
V = l^3
(x + y)(x - y) = x^2 - y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

27. In a circle of radius r - what is the formula for the circumference?
D = 2r
C = p2r
A = (1/2)bh.
(n - 2)(180°)

28. Properties of zero 3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.

29. What is the formula for the area of a triangle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
360°
A = (1/2)bh.
They are both the same. A divisor or factor of an integer leaves no remainder.

30. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = (1/2)bh.
Shifted right 2 units.
For any integer n: 1^n = 1.

31. Law of exponents 4
Set y = 0 - and solve.
A^m*b^m = (ab)^m
V = lwh
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

32. 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.
Shifted down 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
Divide - then multiply by 100.

33. What is an exterior angle of a polygon?
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.
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.
An angle formed by extending the side of the polygon.

34. What is the Pythagorean theorem?
Shifted left 2 units.
0 is the only number that is neither positive nor negative.
For any right triangle - a^2 + b^2 = c^2.
(n - 2)(180°)

35. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
A^m/b^m = (a/b)^m
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.

36. What is a composite number?
360°
(Circumference/diameter) of a circle - or approximately 3.14.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An integer greater than one that is not prime.

37. What is an even and an odd number?
A = bh
Even numbers are divisible by 2 and odd numbers are not.
(n - 2)(180°)
B^m*b^n = b^m+n

38. How do you find a percent of a number?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
Write the percent as a decimal - and multiply.

39. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
For any right triangle - a^2 + b^2 = c^2.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A^m*b^m = (ab)^m

40. What is the sum of the measures of all angles around a point?
Even numbers are divisible by 2 and odd numbers are not.
No matter how many angles there are - the sum around the point is 360°.
For any number n: x^-n means 1/x^n.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

41. How do you find the x-intercept of a graph?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(n - 2)(180°)
A^m/b^m = (a/b)^m
Set y = 0 - and solve.

42. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
0 is a multiple of every integer.
A = [(s^2*v3)/4]
A^m/b^m = (a/b)^m

43. What is special formula for the area of an equilateral triangle?
Corresponding sides of similar triangles are in proportion.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = [(s^2*v3)/4]
A = bh

44. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Corresponding sides of similar triangles are in proportion.
Shifted down 2 units.
Then the quotient y/x is a constant.

45. What is a prime number?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = pr^2
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.

46. What is the measure of a straight angle?
An angle formed by extending the side of the polygon.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the product xy is a constant.
180°. If two or more angles form a straight angle - their sum is 180°.

47. What is the triangle inequality?
They are both the same. A divisor or factor of an integer leaves no remainder.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

48. 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.
Shifted left 2 units.
B^m*b^n = b^m+n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

49. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number a: a * 1 = a and a / 1 = a.
They are both the same. A divisor or factor of an integer leaves no remainder.

50. What is the formula for the area of a rectangle?
1 is the smallest positive odd integer.
An integer greater than one that is not prime.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = lw