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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 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.
(n - 2)(180°)
Avg = sum of n numbers/n
C = p2r

2. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
C = p2r
For any number a: a * 1 = a and a / 1 = a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

3. In a circle of radius r - what is the formula for the area?
A^m*b^m = (ab)^m
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = pr^2
An equation that states that two ratios are equivalent. 4/6 = 10/15

4. How do you find the length of an arc of a circle?
A^m/b^m = (a/b)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Arc = (x°/360)(2pr) where x is the central angle.
A = s^2 or A =d^2/2 where d is the diagonal

5. What is the midpoint formula?
For any number a: a * 1 = a and a / 1 = a.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
[(x1 + x2)/2] -[(y1 + y2)/2]
(n - 2)(180°)

6. In a circle of radius r - what is the formula for the circumference?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Avg = sum of n numbers/n
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
C = p2r

7. 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°.
0 is the only number that is neither positive nor negative.
A = bh
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.

8. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
Even numbers are divisible by 2 and odd numbers are not.
360°
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

9. Important binomial 3
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = l^3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The product of their slopes is -1 (negative reciprocal).

10. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
In the expression x^b - x is the base and b is the exponent.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

11. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.
The product of their slopes is -1 (negative reciprocal).
Shifted up 2 units.

12. What is the distance formula?
They are both the same. A divisor or factor of an integer leaves no remainder.
M = (y2 - y1)/(x2 - x1)
[(x1 + x2)/2] -[(y1 + y2)/2]
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

13. What is the formula for the area of a triangle?
B^m/b^n = b^m-n
Cannot is 0 - must is 1 - all others are in between.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = (1/2)bh.

14. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
(b^m)^n = b^mn
V = pr^2h
For any number a: a * 1 = a and a / 1 = a.

15. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
1 is the smallest positive odd integer.
An integer greater than one that is not prime.
Shifted up 2 units.
Set y = 0 - and solve.

16. What is the formula for the area of a rectangle?
Set y = 0 - and solve.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = lw

17. What is a ratio?

18. What formula is used for an average?
For any right triangle - a^2 + b^2 = c^2.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
No matter how many angles there are - the sum around the point is 360°.
Avg = sum of n numbers/n

19. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Even numbers are divisible by 2 and odd numbers are not.
A = pr^2
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 = bh

20. Law of exponents 5
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Cannot is 0 - must is 1 - all others are in between.
A^m/b^m = (a/b)^m

21. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted right 2 units.
B^m/b^n = b^m-n

22. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(b^m)^n = b^mn
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The two pairs of opposite angles formed are equal to each other.

23. What is special formula for the area of an equilateral triangle?
Their sum is 180°.
Divide - then multiply by 100.
A = [(s^2*v3)/4]
V = lwh

24. Important binomial 1
1 is the smallest positive odd integer.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Even numbers are divisible by 2 and odd numbers are not.
(x + y)(x - y) = x^2 - y^2

25. Properties of zero 3
D = 2r
The two pairs of opposite angles formed are equal to each other.
0 is a multiple of every integer.
Shifted left 2 units.

26. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
Arc = (x°/360)(2pr) where x is the central angle.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

27. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
180°. If two or more angles form a straight angle - their sum is 180°.
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.

28. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
C = p2r
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted right 2 units.

29. What is a negative exponent?
Their sum is 180°.
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.
A = 6(l^2)

30. What is the formula for the volume of a cylinder?
Shifted right 2 units.
V = pr^2h
A = 2(lw + lh + hw)
180°. If two or more angles form a straight angle - their sum is 180°.

31. What is the formula for the surface area of a cube?
A = 6(l^2)
Arc = (x°/360)(2pr) where x is the central angle.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
No matter how many angles there are - the sum around the point is 360°.

32. How do you calculate a weighted average?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
D = 2r
Shifted left 2 units.

33. What is the square root of a number?
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Avg = sum of n numbers/n
V = l^3

34. What is a composite number?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
An integer greater than one that is not prime.
For any number a: a * 1 = a and a / 1 = a.
Write the percent over 100 and reduce.

35. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted down 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

36. What is an integer?
Divide - then multiply by 100.
A = pr^2
The product of their slopes is -1 (negative reciprocal).
All positive and negative whole numbers - and zero.

37. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
360°
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted up 2 units.

38. What does it mean if y is directly proportional to x?
0 is the only number that is neither positive nor negative.
M = (y2 - y1)/(x2 - x1)
Then the quotient y/x is a constant.
0 is a multiple of every integer.

39. Law of exponents 1
Area = (x°/360)(pr^2) where x is the central angle.
Is a right triangle with a ratio of sides x:xv3:2x.
B^m*b^n = b^m+n
Write the percent as a decimal - and multiply.

40. Properties of zero 5
0 is a multiple of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
D = 2r
For any number b: b = -b if and only if b = 0.

41. What is the relationship between the graph of f(x) the graph of y = f(x + 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°.
Shifted left 2 units.
An integer greater than one that is not prime.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

42. 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.
A fraction whose denominator is 100 i.e. 17% = 17/100
Write the percent as a decimal - and multiply.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

43. What is an even and an odd number?
The product of their slopes is -1 (negative reciprocal).
Corresponding sides of similar triangles are in proportion.
Even numbers are divisible by 2 and odd numbers are not.
How steep the line is. Horizontal line = 0 - vertical has no slope.

44. What is the probability of an event that cannot occur? That must occur?
A = 6(l^2)
Cannot is 0 - must is 1 - all others are in between.
A^m/b^m = (a/b)^m
Avg = sum of n numbers/n

45. What do we mean by the slope of the line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
How steep the line is. Horizontal line = 0 - vertical has no slope.
360°
A^m/b^m = (a/b)^m

46. Properties of one 3
1 is a divisor (or factor) of every integer.
[(x1 + x2)/2] -[(y1 + y2)/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.
V = l^3

47. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
A = 2(lw + lh + hw)
Arc = (x°/360)(2pr) where x is the central angle.
All positive and negative whole numbers - and zero.

48. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
V = pr^2h
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = s^2 or A =d^2/2 where d is the diagonal

49. What are similar triangles?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The product of their slopes is -1 (negative reciprocal).
A = 6(l^2)

50. What is a multiple of an integer?
How steep the line is. Horizontal line = 0 - vertical has no slope.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.