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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 sum of the measures of the four angles in a quadrilateral?
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted up 2 units.
360°
Set y = 0 - and solve.

2. What are the important properties of a 45-45 - 90 triangle?
Avg = sum of n numbers/n
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.

3. In a circle of radius r - what is the formula for the area?
For any number b: b = -b if and only if b = 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = pr^2
B^m/b^n = b^m-n

4. Properties of zero 5
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
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

5. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
Arc = (x°/360)(2pr) where x is the central angle.
Corresponding sides of similar triangles are in proportion.
C = p2r

6. How do you find a percent of a number?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Write the percent as a decimal - and multiply.
A = [(s^2*v3)/4]
A = pr^2

7. What are the median and the mode of a set of data?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Is a right triangle with a ratio of sides x:xv3:2x.
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.
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.

8. What is the formula for the surface area of a cube?
Write the percent as a decimal - and multiply.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
No matter how many angles there are - the sum around the point is 360°.
A = 6(l^2)

9. What is a composite number?
Then the quotient y/x is a constant.
A = pr^2
V = lwh
An integer greater than one that is not prime.

10. What is an even and an odd number?
Area = (x°/360)(pr^2) where x is the central angle.
Write the percent over 100 and reduce.
Even numbers are divisible by 2 and odd numbers are not.
Set x = 0 - and solve.

11. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Their sum is 180°.
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

12. How do you find the slope of a line?
(x + y)(x - y) = x^2 - y^2
A = 6(l^2)
M = (y2 - y1)/(x2 - x1)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

13. Law of exponents 5
B^m/b^n = b^m-n
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.
A^m/b^m = (a/b)^m
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

14. How do you find the y-intercept of a graph?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Set x = 0 - and solve.
(n - 2)(180°)
Shifted up 2 units.

15. Properties of zero 3
0 is a multiple of every integer.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.
Area = (x°/360)(pr^2) where x is the central angle.

16. How do we write the equation of a line?
A fraction whose denominator is 100 i.e. 17% = 17/100
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent over 100 and reduce.
An angle formed by extending the side of the polygon.

17. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
(n - 2)(180°)
V = pr^2h
A = 6(l^2)

18. Properties of zero 1
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An equation that states that two ratios are equivalent. 4/6 = 10/15
0 is the only number that is neither positive nor negative.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

19. What is the triangle inequality?
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.
A^m/b^m = (a/b)^m
Divide - then multiply by 100.
All positive and negative whole numbers - and zero.

20. What is an exterior angle of a triangle?
(x + y)(x - y) = x^2 - y^2
For any right triangle - a^2 + b^2 = c^2.
C = p2r
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

21. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
B^m*b^n = b^m+n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
At least one of the factors is 0.

22. Properties of one 1
Write the percent over 100 and reduce.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any number a: a * 1 = a and a / 1 = a.
A = (1/2)bh.

23. What is the formula for the area of a parallelogram?
[(x1 + x2)/2] -[(y1 + y2)/2]
(Circumference/diameter) of a circle - or approximately 3.14.
A = bh
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

24. What is true about the slopes of perpendicular lines?
1 is a divisor (or factor) of every integer.
For any number b: b = -b if and only if b = 0.
A = 6(l^2)
The product of their slopes is -1 (negative reciprocal).

25. What is the volume of a cube?
V = l^3
A = s^2 or A =d^2/2 where d is the diagonal
B^m*b^n = b^m+n
An integer greater than one that is not prime.

26. What are the quotient and the remainder?

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27. Law of exponents 3
Is a right triangle with a ratio of sides x:xv3:2x.
[(x1 + x2)/2] -[(y1 + y2)/2]
(b^m)^n = b^mn
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.

28. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
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.
Shifted right 2 units.
Area = (x°/360)(pr^2) where x is the central angle.

29. For what values of a function is the function undefined?
Then the quotient y/x is a constant.
Write the percent as a decimal - and multiply.
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 the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

30. What is p?
For any right triangle - a^2 + b^2 = c^2.
(Circumference/diameter) of a circle - or approximately 3.14.
0 is a multiple of every integer.
A^m/b^m = (a/b)^m

31. What is a multiple of an integer?
Write the percent as a decimal - and multiply.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.

32. What is true about the slopes of parallel lines?
Equal slopes.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = lwh

33. Properties of zero 2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).
How steep the line is. Horizontal line = 0 - vertical has no slope.
If a is negative and b is positive - then a < 0 < b.

34. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A fraction whose denominator is 100 i.e. 17% = 17/100
If a is negative and b is positive - then a < 0 < b.
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°.
Arc = (x°/360)(2pr) where x is the central angle.

35. In a circle of radius r - what is the formula for the diameter?
C = p2r
Avg = sum of n numbers/n
All positive and negative whole numbers - and zero.
D = 2r

36. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted up 2 units.
Their sum is 180°.
360°

37. Law of exponents 4
V = lwh
B^m/b^n = b^m-n
Equal slopes.
A^m*b^m = (ab)^m

38. If the product of two or more numbers is 0 - what do you know about the numbers?
(Circumference/diameter) of a circle - or approximately 3.14.
A = 2(lw + lh + hw)
At least one of the factors is 0.
360°

39. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
A^m/b^m = (a/b)^m
Area = (x°/360)(pr^2) where x is the central angle.
An equation that states that two ratios are equivalent. 4/6 = 10/15

40. What is the formula for the volume of a rectangular solid?
(b^m)^n = b^mn
V = lwh
Write the percent as a decimal - and multiply.
How steep the line is. Horizontal line = 0 - vertical has no slope.

41. How do you convert a percent to a fraction or a decimal?
If a is negative and b is positive - then a < 0 < b.
Write the percent over 100 and reduce.
Arc = (x°/360)(2pr) where x is the central angle.
For any integer n: 1^n = 1.

42. What is a prime number?
Their sum is 180°.
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any number b: b = -b if and only if b = 0.

43. Important binomial 1
(x + y)(x - y) = x^2 - y^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = lw

44. What is a percent?
A^m*b^m = (ab)^m
A fraction whose denominator is 100 i.e. 17% = 17/100
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
360°

45. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Their sum is 90°.
An integer greater than one that is not prime.
All positive and negative whole numbers - and zero.

46. How do you calculate percent increases and decreases?
A = pr^2
Divide - then multiply by 100.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
How steep the line is. Horizontal line = 0 - vertical has no slope.

47. What is a negative exponent?
Shifted down 2 units.
Set y = 0 - and solve.
1 is the smallest positive odd integer.
For any number n: x^-n means 1/x^n.

48. What is an exterior angle of a polygon?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(b^m)^n = b^mn
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
An angle formed by extending the side of the polygon.

49. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
0 is the only number that is neither positive nor negative.
1 is a divisor (or factor) of every integer.
A = (1/2)bh.

50. What is the distributive law?
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.
(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.
Area = (x°/360)(pr^2) where x is the central angle.