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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 a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
(Circumference/diameter) of a circle - or approximately 3.14.
A^m*b^m = (ab)^m
0 is the only number that is neither positive nor negative.

2. What is the graph of a function?
Set x = 0 - and solve.
The set of all ordered pairs (x -y) such that y = f(x).
Equal slopes.
The ratio of corresponding sides of similar triangles.

3. What is the formula for the volume of a rectangular solid?
At least one of the factors is 0.
V = lwh
Shifted left 2 units.
(b^m)^n = b^mn

4. What is a percent?
Their sum is 180°.
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 fraction whose denominator is 100 i.e. 17% = 17/100
Shifted up 2 units.

5. Important binomial 3
For any number n: x^-n means 1/x^n.
(b^m)^n = b^mn
For any integer n: 1^n = 1.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

6. What is the sum of the measures of the four angles in a quadrilateral?
360°
If a is negative and b is positive - then a < 0 < b.
Then the product xy is a constant.
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.

7. Law of exponents 4
A^m*b^m = (ab)^m
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The ratio of corresponding sides of similar triangles.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

8. 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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A^m*b^m = (ab)^m
Area = (x°/360)(pr^2) where x is the central angle.

9. What are the properties of a square?
Even numbers are divisible by 2 and odd numbers are not.
If a is negative and b is positive - then a < 0 < b.
A = pr^2
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.

10. What is the sum of the measures of the n angles of a polygon with n sides?
A = bh
No matter how many angles there are - the sum around the point is 360°.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(n - 2)(180°)

11. Properties of one 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.
Divide - then multiply by 100.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For any integer n: 1^n = 1.

12. Properties of zero 4
V = l^3
1 is a divisor (or factor) of every integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

13. How do you find the slope of a line?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.
M = (y2 - y1)/(x2 - x1)
A = s^2 or A =d^2/2 where d is the diagonal

14. What are the sum - difference - products - and quotient of two numbers?
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A^m/b^m = (a/b)^m
For any right triangle - a^2 + b^2 = c^2.

15. What is the formula for the volume of a cylinder?
For any integer n: 1^n = 1.
For any number b: b = -b if and only if b = 0.
Shifted left 2 units.
V = pr^2h

16. What does it mean if y is inversely proportional to x?
D = 2r
Then the product xy is a constant.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = (1/2)bh.

17. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Is a right triangle with a ratio of sides x:xv3:2x.

18. What is special formula for the area of an equilateral triangle?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = [(s^2*v3)/4]
A = lw
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

19. What is true about the measures of the three angles in a triangle?
Shifted down 2 units.
Write the percent over 100 and reduce.
In the expression x^b - x is the base and b is the exponent.
Their sum is 180°.

20. What is the formula for the surface area of a rectangular solid?
An integer greater than one that is not prime.
If a is negative and b is positive - then a < 0 < b.
V = pr^2h
A = 2(lw + lh + hw)

21. How do we write the equation of a line?
V = l^3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Arc = (x°/360)(2pr) where x is the central angle.

22. What are the median and the mode of a set of data?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.
C = p2r
Set x = 0 - and solve.

23. Properties of square roots
Cannot is 0 - must is 1 - all others are in between.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Is a right triangle with a ratio of sides x:xv3:2x.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

24. What is a multiple of an integer?
Area = (x°/360)(pr^2) where x is the central angle.
A = s^2 or A =d^2/2 where d is the diagonal
The product of their slopes is -1 (negative reciprocal).
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.

25. What is the formula for the area of a parallelogram?
Shifted up 2 units.
A = s^2 or A =d^2/2 where d is the diagonal
A = bh
Their sum is 180°.

26. What important property do similar triangles have?
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.
Corresponding sides of similar triangles are in proportion.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
C = p2r

27. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Their sum is 90°.
1 is the smallest positive odd integer.
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.

28. 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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(x + y)(x - y) = x^2 - y^2
Area = (x°/360)(pr^2) where x is the central angle.

29. How do you find the probability that an event will occur?
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.
Shifted down 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

30. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
An angle formed by extending the side of the polygon.

31. Law of exponents 1
P(e) = (# of favorable outcomes)/(# of possible outcomes)
An equation that states that two ratios are equivalent. 4/6 = 10/15
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
B^m*b^n = b^m+n

32. Law of exponents 3
(b^m)^n = b^mn
B^m*b^n = b^m+n
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

33. How you convert a fraction or a decimal to a percent?
B^m/b^n = b^m-n
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°.
360°
Divide - then multiply by 100.

34. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
Set x = 0 - and solve.
A = (1/2)bh.
Arc = (x°/360)(2pr) where x is the central angle.

35. Important binomial 1
Equal slopes.
(x + y)(x - y) = x^2 - y^2
Then the product xy is a constant.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

36. What is an exterior angle of a polygon?
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number a: a * 1 = a and a / 1 = a.
1 is a divisor (or factor) of every integer.
An angle formed by extending the side of the polygon.

37. How do you find the area of a sector of a circle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Area = (x°/360)(pr^2) where x is the central angle.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
0 is a multiple of every integer.

38. What is an integer?
All positive and negative whole numbers - and zero.
(n - 2)(180°)
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.

39. What is the formula for the surface area of a cube?
A = 6(l^2)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
360°
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

40. What is the distributive law?
No matter how many angles there are - the sum around the point is 360°.
An angle formed by extending the side of the polygon.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
They are both the same. A divisor or factor of an integer leaves no remainder.

41. What formula is used for an average?
Equal slopes.
A fraction whose denominator is 100 i.e. 17% = 17/100
No matter how many angles there are - the sum around the point is 360°.
Avg = sum of n numbers/n

42. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
360°
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Shifted down 2 units.

43. What is the formula for the area of a triangle?
A = (1/2)bh.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A^m/b^m = (a/b)^m
For any integer n: 1^n = 1.

44. In a circle of radius r - what is the formula for the diameter?
An angle formed by extending the side of the polygon.
Write the percent as a decimal - and multiply.
D = 2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

45. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = pr^2
Shifted up 2 units.
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°.
Corresponding sides of similar triangles are in proportion.

46. Law of exponents 2
B^m/b^n = b^m-n
0 is a multiple of every integer.
For any number b: b = -b if and only if b = 0.
The ratio of corresponding sides of similar triangles.

47. What are the properties of a rectangle?
B^m/b^n = b^m-n
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Even numbers are divisible by 2 and odd numbers are not.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

48. What is a fractional exponent?
Shifted left 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted down 2 units.

49. In a circle of radius r - what is the formula for the area?
V = l^3
The ratio of corresponding sides of similar triangles.
Area = (x°/360)(pr^2) where x is the central angle.
A = pr^2

50. What is the area of a square?
For any number n: x^-n means 1/x^n.
D = 2r
A = s^2 or A =d^2/2 where d is the diagonal
(b^m)^n = b^mn