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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 are the properties of a square?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
0 is the only number that is neither positive nor negative.

2. What is a function?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 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.
Their sum is 90°.

3. What are the median and the mode of a set of data?
A^m*b^m = (ab)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.
0 is a multiple of every integer.
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.

4. How do you calculate a weighted average?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = l^3

5. 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.
V = lwh
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
0 is the only number that is neither positive nor negative.

6. What is an even and an odd number?
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.
Is a right triangle with a ratio of sides x:xv3:2x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Even numbers are divisible by 2 and odd numbers are not.

7. What is a negative exponent?
Write the percent over 100 and reduce.
1 is a divisor (or factor) of every integer.
For any integer n: 1^n = 1.
For any number n: x^-n means 1/x^n.

8. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
For any number a: a * 1 = a and a / 1 = a.
Area = (x°/360)(pr^2) where x is the central angle.
They are both the same. A divisor or factor of an integer leaves no remainder.
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. What is an exponent?
Corresponding sides of similar triangles are in proportion.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
In the expression x^b - x is the base and b is the exponent.
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.

10. What do we mean by the slope of the line?
(x + y)(x - y) = x^2 - y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = l^3
How steep the line is. Horizontal line = 0 - vertical has no slope.

11. What is a multiple of an integer?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
In the expression x^b - x is the base and b is the exponent.
(Circumference/diameter) of a circle - or approximately 3.14.

12. What is true about the measures of the two acute angles in a right triangle?
The ratio of corresponding sides of similar triangles.
Their sum is 90°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.

13. What is a percent?
A = pr^2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted right 2 units.

14. What is a proportion?
Their sum is 180°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = (1/2)bh.

15. What does it mean if y is directly proportional to x?
(b^m)^n = b^mn
A = (1/2)bh.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Then the quotient y/x is a constant.

16. What are the properties of a parallelogram?
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.
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

17. What is true about the slopes of parallel lines?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Area = (x°/360)(pr^2) where x is the central angle.
Equal slopes.

18. How do you convert a percent to a fraction or a decimal?
For any number a: a * 1 = a and a / 1 = a.
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.
Write the percent over 100 and reduce.

19. What is the formula for the area of a rectangle?
Area = (x°/360)(pr^2) where x is the central angle.
A = lw
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

20. Law of exponents 4
Avg = sum of n numbers/n
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^m*b^m = (ab)^m
Write the percent over 100 and reduce.

21. What is the formula for the area of a parallelogram?
Write the percent as a decimal - and multiply.
At least one of the factors is 0.
A = bh
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

22. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Then the quotient y/x is a constant.
(n - 2)(180°)
For any number b: b = -b if and only if b = 0.

23. What is the Pythagorean theorem?
Shifted right 2 units.
Set x = 0 - and solve.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any right triangle - a^2 + b^2 = c^2.

24. Law of exponents 2
B^m/b^n = b^m-n
A = lw
A^m/b^m = (a/b)^m
Divide - then multiply by 100.

25. Properties of one 2
A = (1/2)bh.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For any integer n: 1^n = 1.
180°. If two or more angles form a straight angle - their sum is 180°.

26. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
360°
No matter how many angles there are - the sum around the point is 360°.
At least one of the factors is 0.

27. What are the quotient and the remainder?

28. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.
A = pr^2
(n - 2)(180°)

29. What is the formula for the volume of a rectangular solid?
360°
V = lwh
An equation that states that two ratios are equivalent. 4/6 = 10/15
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

30. In a circle of radius r - what is the formula for the circumference?
(Circumference/diameter) of a circle - or approximately 3.14.
A = (1/2)bh.
Corresponding sides of similar triangles are in proportion.
C = p2r

31. Law of exponents 1
Shifted up 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
360°
B^m*b^n = b^m+n

32. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Arc = (x°/360)(2pr) where x is the central angle.
V = lwh

33. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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°.
They are both the same. A divisor or factor of an integer leaves no remainder.
A^m*b^m = (ab)^m

34. How do you find a percent of a number?
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°.
Write the percent as a decimal - and multiply.
Avg = sum of n numbers/n
An equation that states that two ratios are equivalent. 4/6 = 10/15

35. How do you find the x-intercept of a graph?
Cannot is 0 - must is 1 - all others are in between.
V = l^3
[(x1 + x2)/2] -[(y1 + y2)/2]
Set y = 0 - and solve.

36. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Area = (x°/360)(pr^2) where x is the central angle.
360°
A = 6(l^2)

37. What are the important properties of 30-60-90 triangle?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
B^m*b^n = b^m+n
Is a right triangle with a ratio of sides x:xv3:2x.

38. What is the distance formula?
V = pr^2h
For any integer n: 1^n = 1.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

39. What is p?
V = lwh
For any number a: a * 1 = a and a / 1 = a.
(Circumference/diameter) of a circle - or approximately 3.14.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

40. 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.
For any number n: x^-n means 1/x^n.
Is a right triangle with a ratio of sides x:xv3:2x.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

41. What does it mean if y is inversely proportional to x?
Area = (x°/360)(pr^2) where x is the central angle.
For any number n: x^-n means 1/x^n.
The product of their slopes is -1 (negative reciprocal).
Then the product xy is a constant.

42. What is the area of a square?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
A = s^2 or A =d^2/2 where d is the diagonal
Then the product xy is a constant.

43. Law of exponents 3
Then the product xy is a constant.
(b^m)^n = b^mn
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

44. What is the ratio of similitude?
(x + y)(x - y) = x^2 - y^2
The product of their slopes is -1 (negative reciprocal).
No matter how many angles there are - the sum around the point is 360°.
The ratio of corresponding sides of similar triangles.

45. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
C = p2r
Avg = sum of n numbers/n

46. What is true about the areas of similar triangles?
180°. If two or more angles form a straight angle - their sum is 180°.
Arc = (x°/360)(2pr) where x is the central angle.
[(x1 + x2)/2] -[(y1 + y2)/2]
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

47. What is true about the slopes of perpendicular lines?
Shifted down 2 units.
The product of their slopes is -1 (negative reciprocal).
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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 formula is used for an average?
Avg = sum of n numbers/n
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
360°
All positive and negative whole numbers - and zero.

49. What is the formula for the surface area of a cube?
V = l^3
A = bh
Shifted down 2 units.
A = 6(l^2)

50. What is the distributive law?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.