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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?
Their sum is 180°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Equal slopes.
A = (1/2)bh.

2. What are the properties of a rectangle?
Write the percent as a decimal - and multiply.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
0 is the only number that is neither positive nor negative.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

3. 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.
For any number b: b = -b if and only if b = 0.
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.
The set of all ordered pairs (x -y) such that y = f(x).

4. What is the distributive law?
All positive and negative whole numbers - and zero.
Arc = (x°/360)(2pr) where x is the central angle.
Their sum is 180°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

5. How you convert a fraction or a decimal to a percent?
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number a: a * 1 = a and a / 1 = a.
Divide - then multiply by 100.
Their sum is 180°.

6. What is the sum of the measures of the four angles in a quadrilateral?
Is a right triangle with a ratio of sides x:xv3:2x.
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.
360°
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

7. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any right triangle - a^2 + b^2 = c^2.
Shifted left 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.

8. What is the area of a square?
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.
A = s^2 or A =d^2/2 where d is the diagonal
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.

9. What is a fractional exponent?
Even numbers are divisible by 2 and odd numbers are not.
1 is a divisor (or factor) of every integer.
Then the product xy is a constant.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

10. How do you find the length of an arc of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
Arc = (x°/360)(2pr) where x is the central angle.
For any number n: x^-n means 1/x^n.
Shifted left 2 units.

11. In a circle of radius r - what is the formula for the area?
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = pr^2
For any right triangle - a^2 + b^2 = c^2.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

12. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
360°
(b^m)^n = b^mn

13. How do you find the area of a sector of a circle?
A^m/b^m = (a/b)^m
Area = (x°/360)(pr^2) where x is the central angle.
A = 2(lw + lh + hw)
A = lw

14. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
They are both the same. A divisor or factor of an integer leaves no remainder.
At least one of the factors is 0.
Shifted down 2 units.
1 is the smallest positive odd integer.

15. 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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
An angle formed by extending the side of the polygon.
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.

16. What is true about the areas of similar triangles?
Divide - then multiply by 100.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x + y)(x - y) = x^2 - y^2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

17. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Equal slopes.
Corresponding sides of similar triangles are in proportion.
Avg = sum of n numbers/n
360°

18. What does it mean if y is inversely proportional to x?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Corresponding sides of similar triangles are in proportion.
Then the product xy is a constant.
0 is the only number that is neither positive nor negative.

19. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
Is a right triangle with a ratio of sides x:xv3:2x.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

20. What is a Venn diagram?
The product of their slopes is -1 (negative reciprocal).
At least one of the factors is 0.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any right triangle - a^2 + b^2 = c^2.

21. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = 6(l^2)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

22. What is a composite number?
Shifted down 2 units.
Set x = 0 - and solve.
An integer greater than one that is not prime.
A^m*b^m = (ab)^m

23. What is a function?
C = p2r
0 is a multiple of every integer.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The product of their slopes is -1 (negative reciprocal).

24. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Cannot is 0 - must is 1 - all others are in between.
The product of their slopes is -1 (negative reciprocal).
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Write the percent as a decimal - and multiply.

25. What is the formula for the surface area of a cube?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any integer n: 1^n = 1.
Write the percent over 100 and reduce.
A = 6(l^2)

26. How do you find the y-intercept of a graph?
180°. If two or more angles form a straight angle - their sum is 180°.
C = p2r
Set x = 0 - and solve.
An equation that states that two ratios are equivalent. 4/6 = 10/15

27. If the product of two or more numbers is 0 - what do you know about the numbers?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
The two pairs of opposite angles formed are equal to each other.
At least one of the factors is 0.

28. What is the formula for the volume of a rectangular solid?
A = [(s^2*v3)/4]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = lwh
V = l^3

29. What is the triangle inequality?
Write the percent as a decimal - and multiply.
Equal slopes.
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

30. 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°.
Then the product xy is a constant.
They are both the same. A divisor or factor of an integer leaves no remainder.
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.

31. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.

32. What is the square root of a number?
(n - 2)(180°)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

33. What is a percent?
V = lwh
1 is a divisor (or factor) of every integer.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = 2(lw + lh + hw)

34. Properties of one 4
1 is the smallest positive odd integer.
Shifted down 2 units.
A^m/b^m = (a/b)^m
A = bh

35. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = s^2 or A =d^2/2 where d is the diagonal

36. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
Set x = 0 - and solve.
For any right triangle - a^2 + b^2 = c^2.
Shifted down 2 units.

37. Properties of zero 3
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Set y = 0 - and solve.
0 is a multiple of every integer.
Shifted right 2 units.

38. Important binomial 1
An angle formed by extending the side of the polygon.
(b^m)^n = b^mn
(x + y)(x - y) = x^2 - y^2
Is a right triangle with a ratio of sides x:xv3:2x.

39. Law of exponents 2
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.
For any number n: x^-n means 1/x^n.
(n - 2)(180°)
B^m/b^n = b^m-n

40. What does it mean if y is directly proportional to x?
Equal slopes.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Then the quotient y/x is a constant.
Shifted up 2 units.

41. 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 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.
C = p2r
Set x = 0 - and solve.

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

43. What is an integer?
V = pr^2h
All positive and negative whole numbers - and zero.
No matter how many angles there are - the sum around the point is 360°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

44. Properties of one 2
For any integer n: 1^n = 1.
B^m/b^n = b^m-n
At least one of the factors is 0.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

45. How do you calculate a weighted average?
They are both the same. A divisor or factor of an integer leaves no remainder.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Write the percent over 100 and reduce.

46. Important binomial 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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

47. What is an exterior angle of a triangle?
C = p2r
In the expression x^b - x is the base and b is the exponent.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
They are both the same. A divisor or factor of an integer leaves no remainder.

48. If you were given the graph of y = f(x) - what does f(a) represent?
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.
(b^m)^n = b^mn
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

49. How do you find the slope of a line?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
M = (y2 - y1)/(x2 - x1)
Write the percent as a decimal - and multiply.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

50. How do you find a percent of a number?
The set of all ordered pairs (x -y) such that y = f(x).
1 is a divisor (or factor) of every integer.
No matter how many angles there are - the sum around the point is 360°.
Write the percent as a decimal - and multiply.