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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 even and an odd number?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(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.
Even numbers are divisible by 2 and odd numbers are not.

2. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
B^m/b^n = b^m-n
For any number a: a * 1 = a and a / 1 = a.

3. What is the formula for the area of a parallelogram?
D = 2r
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = bh

4. What is true about the slopes of parallel lines?
Equal slopes.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.
1 is the smallest positive odd integer.

5. How do you find the length of an arc of a circle?
The ratio of corresponding sides of similar triangles.
Shifted down 2 units.
1 is a divisor (or factor) of every integer.
Arc = (x°/360)(2pr) where x is the central angle.

6. What is an exterior angle of a triangle?
If a is negative and b is positive - then a < 0 < b.
Divide - then multiply by 100.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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°.

7. What is true about the slopes of perpendicular lines?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = 6(l^2)
An angle formed by extending the side of the polygon.
The product of their slopes is -1 (negative reciprocal).

8. Law of exponents 1
B^m*b^n = b^m+n
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.
Area = (x°/360)(pr^2) where x is the central angle.
Shifted left 2 units.

9. What is true about the measures of the two acute angles in a right triangle?
The two pairs of opposite angles formed are equal to each other.
The set of all ordered pairs (x -y) such that y = f(x).
Area = (x°/360)(pr^2) where x is the central angle.
Their sum is 90°.

10. How do you find the area of a sector of a circle?
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.
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.

11. What is the distributive law?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any right triangle - a^2 + b^2 = c^2.

12. What is the triangle inequality?
At least one of the factors is 0.
The product of their slopes is -1 (negative reciprocal).
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

13. Important binomial 3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 90°.
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

14. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
An angle formed by extending the side of the polygon.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

15. What is the sum of the measures of all angles around a point?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = lw
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°.
No matter how many angles there are - the sum around the point is 360°.

16. How do you calculate a weighted average?
Shifted up 2 units.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
D = 2r

17. In a circle of radius r - what is the formula for the diameter?
C = p2r
B^m/b^n = b^m-n
An angle formed by extending the side of the polygon.
D = 2r

18. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted up 2 units.
Corresponding sides of similar triangles are in proportion.
Write the percent over 100 and reduce.

19. Important binomial 1
(x + y)(x - y) = x^2 - y^2
(n - 2)(180°)
V = l^3
Is a right triangle with a ratio of sides x:xv3:2x.

20. What are the properties of a square?
In the expression x^b - x is the base and b is the exponent.
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.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Equal slopes.

21. Law of exponents 4
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(x + y)(x - y) = x^2 - y^2
A^m*b^m = (ab)^m
(b^m)^n = b^mn

22. What is special formula for the area of an equilateral triangle?
A = (1/2)bh.
B^m/b^n = b^m-n
A = [(s^2*v3)/4]
They are both the same. A divisor or factor of an integer leaves no remainder.

23. How do we write the equation of a line?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A^m/b^m = (a/b)^m

24. What do we mean by the slope of the line?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

25. What is the area of a square?
A^m/b^m = (a/b)^m
A = s^2 or A =d^2/2 where d is the diagonal
(n - 2)(180°)
In the expression x^b - x is the base and b is the exponent.

26. Properties of zero 4
A^m*b^m = (ab)^m
0 is the only number that is neither positive nor negative.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Avg = sum of n numbers/n

27. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
B^m/b^n = b^m-n
Shifted down 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

28. What is the volume of a cube?
B^m/b^n = b^m-n
V = l^3
Write the percent as a decimal - and multiply.
(x + y)(x - y) = x^2 - y^2

29. What is the distance formula?
Divide - then multiply by 100.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted right 2 units.
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.

30. How do you calculate percent increases and decreases?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = pr^2h
An equation that states that two ratios are equivalent. 4/6 = 10/15

31. What is the sum of the measures of the four angles in a quadrilateral?
A = (1/2)bh.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
[(x1 + x2)/2] -[(y1 + y2)/2]
360°

32. If the product of two or more numbers is 0 - what do you know about the numbers?
Area = (x°/360)(pr^2) where x is the central angle.
Equal slopes.
At least one of the factors is 0.
For any right triangle - a^2 + b^2 = c^2.

33. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
If a is negative and b is positive - then a < 0 < b.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(x + y)(x - y) = x^2 - y^2

34. Properties of zero 2
An angle formed by extending the side of the polygon.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If a is negative and b is positive - then a < 0 < b.
Shifted right 2 units.

35. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted down 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

36. How do you find a percent of a number?
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.
Then the quotient y/x is a constant.
Write the percent as a decimal - and multiply.
360°

37. What is the formula for the volume of a cylinder?
V = pr^2h
360°
B^m*b^n = b^m+n
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

38. What are the properties of a rectangle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Is a right triangle with a ratio of sides x:xv3:2x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

39. Properties of zero 5
For any number b: b = -b if and only if b = 0.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = lw
360°

40. What is a percent?
Write the percent over 100 and reduce.
Even numbers are divisible by 2 and odd numbers are not.
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 fraction whose denominator is 100 i.e. 17% = 17/100

41. How do you find the slope of a line?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
360°
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
M = (y2 - y1)/(x2 - x1)

42. What is a ratio?

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43. What is the relationship between a radius of a circle and a line that is tangent to the circle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any integer n: 1^n = 1.
Shifted up 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

44. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
C = p2r
Their sum is 90°.

45. Important binomial 2
The two pairs of opposite angles formed are equal to each other.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted right 2 units.

46. What is the midpoint formula?
Shifted up 2 units.
Set x = 0 - and solve.
[(x1 + x2)/2] -[(y1 + y2)/2]
V = lwh

47. In a circle of radius r - what is the formula for the area?
For any number a: a * 1 = a and a / 1 = a.
V = l^3
A = pr^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

48. What is a negative exponent?
For any number n: x^-n means 1/x^n.
Write the percent as a decimal - and multiply.
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.
Even numbers are divisible by 2 and odd numbers are not.

49. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Their sum is 90°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
C = p2r

50. Law of exponents 3
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.
Cannot is 0 - must is 1 - all others are in between.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(b^m)^n = b^mn