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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. Properties of zero 3
For any right triangle - a^2 + b^2 = c^2.
For any integer n: 1^n = 1.
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.

2. For what values of a function is the function undefined?
Even numbers are divisible by 2 and odd numbers are not.
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 the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
0 is the only number that is neither positive nor negative.

3. How do you find a percent of a number?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Write the percent as a decimal - and multiply.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

4. If you were given the graph of y = f(x) - what does f(a) represent?
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.
0 is the only number that is neither positive nor negative.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

5. What does it mean if y is inversely proportional to x?
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.
In the expression x^b - x is the base and b is the exponent.
Then the product xy is a constant.
Then the quotient y/x is a constant.

6. What is the triangle inequality?
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.
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.

7. What is the formula for the area of a parallelogram?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(x + y)(x - y) = x^2 - y^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = bh

8. Important binomial 1
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.
(x + y)(x - y) = x^2 - y^2
Is a right triangle with a ratio of sides x:xv3:2x.

9. Properties of square roots
For any number a: a * 1 = a and a / 1 = a.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Their sum is 90°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

10. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
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.
[(x1 + x2)/2] -[(y1 + y2)/2]
360°

11. What is the distance formula?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(b^m)^n = b^mn
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
No matter how many angles there are - the sum around the point is 360°.

12. What formula is used for an average?
Avg = sum of n numbers/n
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.
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

13. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
An integer greater than one that is not prime.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Set y = 0 - and solve.

14. Law of exponents 3
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.
(b^m)^n = b^mn
The product of their slopes is -1 (negative reciprocal).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

15. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
For any integer n: 1^n = 1.
(b^m)^n = b^mn
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

16. What is an exponent?
B^m/b^n = b^m-n
A = bh
The ratio of corresponding sides of similar triangles.
In the expression x^b - x is the base and b is the exponent.

17. Properties of zero 1
The product of their slopes is -1 (negative reciprocal).
Cannot is 0 - must is 1 - all others are in between.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
0 is the only number that is neither positive nor negative.

18. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = 6(l^2)
Arc = (x°/360)(2pr) where x is the central angle.
All positive and negative whole numbers - and zero.

19. Law of exponents 4
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.
Set y = 0 - and solve.
A^m*b^m = (ab)^m
Cannot is 0 - must is 1 - all others are in between.

20. What is the volume of a cube?
Their sum is 180°.
V = l^3
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Equal slopes.

21. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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^m/b^m = (a/b)^m
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.

22. What is a multiple of an integer?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

23. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
At least one of the factors is 0.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.

24. What is the sum of the measures of the n angles of a polygon with n sides?
A = (1/2)bh.
M = (y2 - y1)/(x2 - x1)
(n - 2)(180°)
Write the percent as a decimal - and multiply.

25. What is the formula for the volume of a rectangular solid?
How steep the line is. Horizontal line = 0 - vertical has no slope.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Corresponding sides of similar triangles are in proportion.
V = lwh

26. What is the formula for the surface area of a rectangular solid?
Shifted up 2 units.
A = 2(lw + lh + hw)
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.
An integer greater than one that is not prime.

27. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
An integer greater than one that is not prime.

28. What is an exterior angle of a polygon?
Shifted up 2 units.
An angle formed by extending the side of the polygon.
A^m*b^m = (ab)^m
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

29. What is the area of a square?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = s^2 or A =d^2/2 where d is the diagonal
For any number n: x^-n means 1/x^n.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

30. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
360°
Shifted right 2 units.

31. Properties of one 4
Then the quotient y/x is a constant.
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.
The set of all ordered pairs (x -y) such that y = f(x).

32. What is the sum of the measures of the four angles in a quadrilateral?
360°
No matter how many angles there are - the sum around the point is 360°.
Shifted down 2 units.
The set of all ordered pairs (x -y) such that y = f(x).

33. What is the formula for the area of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = lw
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = lwh

34. What are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The product of their slopes is -1 (negative reciprocal).
180°. If two or more angles form a straight angle - their sum is 180°.

35. Properties of zero 2
At least one of the factors is 0.
Their sum is 90°.
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.

36. 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.
B^m*b^n = b^m+n
The set of all ordered pairs (x -y) such that y = f(x).
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

37. What is the formula for the volume of a cylinder?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = pr^2h
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.

38. 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 a multiple of every integer.
Cannot is 0 - must is 1 - all others are in between.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

39. What is the graph of a function?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The two pairs of opposite angles formed are equal to each other.
If a is negative and b is positive - then a < 0 < b.
The set of all ordered pairs (x -y) such that y = f(x).

40. How do you find the slope of a line?
An integer greater than one that is not prime.
M = (y2 - y1)/(x2 - x1)
A fraction whose denominator is 100 i.e. 17% = 17/100
The two pairs of opposite angles formed are equal to each other.

41. What is a Venn diagram?
Shifted down 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
In the expression x^b - x is the base and b is the exponent.
360°

42. In a circle of radius r - what is the formula for the area?
A = 6(l^2)
A = pr^2
An integer greater than one that is not prime.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

43. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
An integer greater than one that is not prime.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Write the percent over 100 and reduce.

44. What is true about the measures of the two acute angles in a right triangle?
Then the quotient y/x is a constant.
Shifted right 2 units.
Their sum is 90°.
D = 2r

45. What is the Pythagorean theorem?
How steep the line is. Horizontal line = 0 - vertical has no slope.
An integer greater than one that is not prime.
For any right triangle - a^2 + b^2 = c^2.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

46. In a circle of radius r - what is the formula for the circumference?
C = p2r
Write the percent as a decimal - and multiply.
The ratio of corresponding sides of similar triangles.
Shifted up 2 units.

47. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted right 2 units.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
In the expression x^b - x is the base and b is the exponent.

48. How do you find the length of an arc of a circle?
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.
The product of their slopes is -1 (negative reciprocal).
Arc = (x°/360)(2pr) where x is the central angle.
A = 2(lw + lh + hw)

49. What is true about the slopes of parallel lines?
Equal slopes.
(x + y)(x - y) = x^2 - y^2
Divide - then multiply by 100.
A^m*b^m = (ab)^m

50. How do you calculate a weighted average?
(b^m)^n = b^mn
For any number b: b = -b if and only if b = 0.
A = s^2 or A =d^2/2 where d is the diagonal
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.