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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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 true about the measures of the three angles in a triangle?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
All positive and negative whole numbers - and zero.
Their sum is 180°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

2. Properties of zero 5
Is a right triangle with a ratio of sides x:xv3:2x.
A = lw
For any number b: b = -b if and only if b = 0.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

3. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
Set x = 0 - and solve.

4. Law of exponents 2
B^m/b^n = b^m-n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Even numbers are divisible by 2 and odd numbers are not.

5. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any number a: a * 1 = a and a / 1 = a.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

6. What is a composite number?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number n: x^-n means 1/x^n.
(Circumference/diameter) of a circle - or approximately 3.14.
An integer greater than one that is not prime.

7. How do you calculate a weighted average?
A = bh
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An integer greater than one that is not prime.
All positive and negative whole numbers - and zero.

8. What is the formula for the volume of a cylinder?
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = pr^2h
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

9. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = pr^2
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

10. What is the formula for the surface area of a cube?
A = [(s^2*v3)/4]
A = 6(l^2)
M = (y2 - y1)/(x2 - x1)
A = pr^2

11. Law of exponents 5
A = bh
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.
Even numbers are divisible by 2 and odd numbers are not.
A^m/b^m = (a/b)^m

12. How do you find the x-intercept of a graph?
Divide - then multiply by 100.
Set y = 0 - and solve.
A = bh
No matter how many angles there are - the sum around the point is 360°.

13. What is a percent?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A fraction whose denominator is 100 i.e. 17% = 17/100
A^m*b^m = (ab)^m
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.

14. Law of exponents 4
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Set y = 0 - and solve.
Arc = (x°/360)(2pr) where x is the central angle.
A^m*b^m = (ab)^m

15. What is a prime number?
360°
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Avg = sum of n numbers/n
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.

16. What is the formula for the surface area of a rectangular solid?
Write the percent over 100 and reduce.
A = 2(lw + lh + hw)
V = l^3
Corresponding sides of similar triangles are in proportion.

17. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

18. If you were given the graph of y = f(x) - what does f(a) represent?
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
M = (y2 - y1)/(x2 - x1)

19. What is an even and an odd number?
In the expression x^b - x is the base and b is the exponent.
Even numbers are divisible by 2 and odd numbers are not.
Then the product xy is a constant.
M = (y2 - y1)/(x2 - x1)

20. Properties of zero 4
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.
(x + y)(x - y) = x^2 - y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

21. What is a divisor and a factor of an integer?
For any integer n: 1^n = 1.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
They are both the same. A divisor or factor of an integer leaves no remainder.
For any right triangle - a^2 + b^2 = c^2.

22. What is a negative exponent?
[(x1 + x2)/2] -[(y1 + y2)/2]
Even numbers are divisible by 2 and odd numbers are not.
Shifted up 2 units.
For any number n: x^-n means 1/x^n.

23. What are the properties of a parallelogram?
A^m/b^m = (a/b)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
All positive and negative whole numbers - and zero.

24. What is true about the slopes of parallel lines?
At least one of the factors is 0.
(b^m)^n = b^mn
Area = (x°/360)(pr^2) where x is the central angle.
Equal slopes.

25. Important binomial 1
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
A = s^2 or A =d^2/2 where d is the diagonal
A^m/b^m = (a/b)^m

26. 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 = (1/2)bh.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

27. 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.
Arc = (x°/360)(2pr) where x is the central angle.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

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°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
360°

29. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
Set x = 0 - and solve.
Avg = sum of n numbers/n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

30. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.

31. What are the quotient and the remainder?

32. What is true about the slopes of perpendicular lines?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(Circumference/diameter) of a circle - or approximately 3.14.
The product of their slopes is -1 (negative reciprocal).
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

33. Properties of one 3
1 is a divisor (or factor) of every integer.
Divide - then multiply by 100.
Arc = (x°/360)(2pr) where x is the central angle.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

34. How do you find the y-intercept of a graph?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Set x = 0 - and solve.
For any number a: a * 1 = a and a / 1 = a.

35. Properties of one 2
A = lw
For any right triangle - a^2 + b^2 = c^2.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any integer n: 1^n = 1.

36. In a circle of radius r - what is the formula for the circumference?
A = pr^2
C = p2r
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Their sum is 90°.

37. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Equal slopes.
Set y = 0 - and solve.
D = 2r

38. What do we mean by the slope of the line?
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted left 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

39. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
1 is a divisor (or factor) of every integer.
The two pairs of opposite angles formed are equal to each other.

40. What are the properties of a square?
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.
C = p2r
Shifted right 2 units.

41. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
Then the product xy is a constant.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = lw

42. How do you find a percent of a number?
Set y = 0 - and solve.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.

43. How do you calculate percent increases and decreases?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
If a is negative and b is positive - then a < 0 < b.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Write the percent over 100 and reduce.

44. What are the properties of a rectangle?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

45. For what values of a function is the function 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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The ratio of corresponding sides of similar triangles.
The two pairs of opposite angles formed are equal to each other.

46. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
V = lwh
For any number a: a * 1 = a and a / 1 = a.
Shifted up 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

47. What is the distributive law?
A = 6(l^2)
Set y = 0 - and solve.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = bh

48. If the product of two or more numbers is 0 - what do you know about the numbers?
A = 2(lw + lh + hw)
No matter how many angles there are - the sum around the point is 360°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
At least one of the factors is 0.

49. What is the sum of the measures of the n angles of a polygon with n sides?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
V = lwh
If a is negative and b is positive - then a < 0 < b.
(n - 2)(180°)

50. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
A = (1/2)bh.
The ratio of corresponding sides of similar triangles.
At least one of the factors is 0.