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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 an exponent?
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.
0 is a multiple of every integer.
Shifted right 2 units.

2. What is the sum of the measures of the n angles of a polygon with n sides?
Even numbers are divisible by 2 and odd numbers are not.
(n - 2)(180°)
C = p2r
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

3. Properties of zero 5
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number b: b = -b if and only if b = 0.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

4. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
A = pr^2
360°
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Their sum is 180°.

5. What is the distance formula?
(x + y)(x - y) = x^2 - y^2
(b^m)^n = b^mn
For any number b: b = -b if and only if b = 0.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

6. How do you find the area of a sector of a circle?
A = lw
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Area = (x°/360)(pr^2) where x is the central angle.
A = (1/2)bh.

7. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A^m*b^m = (ab)^m
A = bh

8. What is true about the measures of the three angles in a triangle?
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.
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.
Their sum is 180°.

9. 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.
C = p2r
A = s^2 or A =d^2/2 where d is the diagonal
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

10. What is the distributive law?
Write the percent as a decimal - and multiply.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(b^m)^n = b^mn

11. What is the ratio of similitude?
(Circumference/diameter) of a circle - or approximately 3.14.
The ratio of corresponding sides of similar triangles.
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

12. How do you find the x-intercept of a graph?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Set y = 0 - and solve.
B^m*b^n = b^m+n
Then the quotient y/x is a constant.

13. What is the graph of a function?
An angle formed by extending the side of the polygon.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The set of all ordered pairs (x -y) such that y = f(x).
Area = (x°/360)(pr^2) where x is the central angle.

14. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
The product of their slopes is -1 (negative reciprocal).
The set of all ordered pairs (x -y) such that y = f(x).
A = (1/2)bh.

15. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted up 2 units.

16. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + 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°.

17. Properties of zero 2
They are both the same. A divisor or factor of an integer leaves no remainder.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Arc = (x°/360)(2pr) where x is the central angle.
If a is negative and b is positive - then a < 0 < b.

18. What is the formula for the area of a triangle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = (1/2)bh.
D = 2r

19. How do you find the length of an arc of a circle?
The product of their slopes is -1 (negative reciprocal).
Shifted down 2 units.
D = 2r
Arc = (x°/360)(2pr) where x is the central angle.

20. What is the sum of the measures of the four angles in a quadrilateral?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
The set of all ordered pairs (x -y) such that y = f(x).
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.

21. What is the formula for the surface area of a cube?
A = 6(l^2)
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°
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.

22. Important binomial 3
Write the percent over 100 and reduce.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = lwh
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.

23. Important binomial 1
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Area = (x°/360)(pr^2) where x is the central angle.
A = lw
(x + y)(x - y) = x^2 - y^2

24. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
A = lw
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
They are both the same. A divisor or factor of an integer leaves no remainder.

25. What important property do similar triangles have?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Corresponding sides of similar triangles are in proportion.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = [(s^2*v3)/4]

26. What is a proportion?
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]
An equation that states that two ratios are equivalent. 4/6 = 10/15
360°

27. What is a prime number?
Equal slopes.
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.
The product of their slopes is -1 (negative reciprocal).
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

28. What is a divisor and a factor of an integer?
Their sum is 180°.
The two pairs of opposite angles formed are equal to each other.
They are both the same. A divisor or factor of an integer leaves no remainder.
In the expression x^b - x is the base and b is the exponent.

29. Properties of one 2
Write the percent over 100 and reduce.
Shifted left 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°.
For any integer n: 1^n = 1.

30. What are the median and the mode of a set of data?
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any number n: x^-n means 1/x^n.
Shifted down 2 units.

31. If you were given the graph of y = f(x) - what does f(a) represent?
Area = (x°/360)(pr^2) where x is the central angle.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.

32. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
V = pr^2h
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°.

33. What is the formula for the volume of a rectangular solid?
V = lwh
For any number n: x^-n means 1/x^n.
A = 2(lw + lh + hw)
For any number b: b = -b if and only if b = 0.

34. What is a negative exponent?
1 is the smallest positive odd integer.
The set of all ordered pairs (x -y) such that y = f(x).
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any number n: x^-n means 1/x^n.

35. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.

36. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = lwh
M = (y2 - y1)/(x2 - x1)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

37. What is an exterior angle of a polygon?
No matter how many angles there are - the sum around the point is 360°.
[(x1 + x2)/2] -[(y1 + y2)/2]
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.
An angle formed by extending the side of the polygon.

38. Law of exponents 2
B^m/b^n = b^m-n
Set y = 0 - and solve.
The set of all ordered pairs (x -y) such that y = f(x).
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

39. What are the sum - difference - products - and quotient of two numbers?
B^m/b^n = b^m-n
A^m*b^m = (ab)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

40. What is a function?
360°
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Write the percent as a decimal - and multiply.
M = (y2 - y1)/(x2 - x1)

41. Law of exponents 1
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
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An angle formed by extending the side of the polygon.

42. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
A^m*b^m = (ab)^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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

43. How do you find a percent of a number?
Then the product xy is a constant.
Write the percent as a decimal - and multiply.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A^m*b^m = (ab)^m

44. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
180°. If two or more angles form a straight angle - their sum is 180°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.

45. What is the volume of a cube?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
They are both the same. A divisor or factor of an integer leaves no remainder.
V = l^3
Shifted left 2 units.

46. What is true about the slopes of perpendicular lines?
360°
The product of their slopes is -1 (negative reciprocal).
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
V = lwh

47. How do you convert a percent to a fraction or a decimal?
(x + y)(x - y) = x^2 - y^2
A = 2(lw + lh + hw)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Write the percent over 100 and reduce.

48. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
360°
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.

49. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
1 is a divisor (or factor) of every integer.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
0 is the only number that is neither positive nor negative.

50. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
The two pairs of opposite angles formed are equal to each other.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted up 2 units.