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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 are similar triangles?
Set x = 0 - and solve.
M = (y2 - y1)/(x2 - x1)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

2. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
360°
0 is the only number that is neither positive nor negative.
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

3. What is the distributive law?
A = bh
A = s^2 or A =d^2/2 where d is the diagonal
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.

4. What is p?
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.
(Circumference/diameter) of a circle - or approximately 3.14.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.

5. How do you find the y-intercept of a graph?
A = pr^2
Set x = 0 - and solve.
C = p2r
At least one of the factors is 0.

6. Law of exponents 3
(b^m)^n = b^mn
Arc = (x°/360)(2pr) where x is the central angle.
Write the percent over 100 and reduce.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

7. What is the formula for the surface area of a rectangular solid?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = 2(lw + lh + hw)
For any right triangle - a^2 + b^2 = c^2.
Shifted down 2 units.

8. What is a percent?
[(x1 + x2)/2] -[(y1 + y2)/2]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A fraction whose denominator is 100 i.e. 17% = 17/100

9. What is an integer?
All positive and negative whole numbers - and zero.
(Circumference/diameter) of a circle - or approximately 3.14.
For any number n: x^-n means 1/x^n.
Their sum is 90°.

10. What is the formula for the area of a rectangle?
Is a right triangle with a ratio of sides x:xv3:2x.
[(x1 + x2)/2] -[(y1 + y2)/2]
A = bh
A = lw

11. What does it mean if y is directly proportional to x?
Even numbers are divisible by 2 and odd numbers are not.
Then the quotient y/x is a constant.
A = 6(l^2)
A^m*b^m = (ab)^m

12. Law of exponents 2
B^m/b^n = b^m-n
For any number a: a * 1 = a and a / 1 = a.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The set of all ordered pairs (x -y) such that y = f(x).

13. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
V = l^3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted up 2 units.

14. What is true about the measures of the four angles formed by two intersecting lines?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Their sum is 180°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The two pairs of opposite angles formed are equal to each other.

15. For what values of a function is the function undefined?
The set of all ordered pairs (x -y) such that y = f(x).
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Write the percent as a decimal - and multiply.
B^m/b^n = b^m-n

16. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
The two pairs of opposite angles formed are equal to each other.
Set x = 0 - and solve.
For any number b: b = -b if and only if b = 0.

17. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
The two pairs of opposite angles formed are equal to each other.
B^m*b^n = b^m+n
Arc = (x°/360)(2pr) where x is the central angle.

18. What is the formula for the area of a parallelogram?
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.
A = 6(l^2)
A = bh
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

19. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(x + y)(x - y) = x^2 - y^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.

20. 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*b^n = b^m+n
A^m/b^m = (a/b)^m
Divide - then multiply by 100.

21. What are the sum - difference - products - and quotient of two numbers?
A = (1/2)bh.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Divide - then multiply by 100.

22. Properties of square roots
A = bh
Is a right triangle with a ratio of sides x:xv3:2x.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
1 is a divisor (or factor) of every integer.

23. What is a function?
For any number n: x^-n means 1/x^n.
An integer greater than one that is not prime.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

24. What is a fractional exponent?
Even numbers are divisible by 2 and odd numbers are not.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
360°
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

25. If you were given the graph of y = f(x) - what does f(a) represent?
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 = (1/2)bh.
A = pr^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

26. Law of exponents 5
(Circumference/diameter) of a circle - or approximately 3.14.
A^m/b^m = (a/b)^m
Write the percent as a decimal - and multiply.
A = [(s^2*v3)/4]

27. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = bh
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

28. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

29. What are the properties of a square?
They are both the same. A divisor or factor of an integer leaves no remainder.
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 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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

30. What are the important properties of 30-60-90 triangle?
Arc = (x°/360)(2pr) where x is the central angle.
C = p2r
A = lw
Is a right triangle with a ratio of sides x:xv3:2x.

31. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
The product of their slopes is -1 (negative reciprocal).
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Set x = 0 - and solve.

32. What is a proportion?
[(x1 + x2)/2] -[(y1 + y2)/2]
An equation that states that two ratios are equivalent. 4/6 = 10/15
360°
Area = (x°/360)(pr^2) where x is the central angle.

33. In a circle of radius r - what is the formula for the circumference?
C = p2r
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Equal slopes.
The set of all ordered pairs (x -y) such that y = f(x).

34. What do we mean by the slope of the line?
Write the percent as a decimal - and multiply.
How steep the line is. Horizontal line = 0 - vertical has no slope.
D = 2r
Write the percent over 100 and reduce.

35. What is the Pythagorean theorem?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Their sum is 180°.
For any right triangle - a^2 + b^2 = c^2.
0 is a multiple of every integer.

36. What is the formula for the surface area of a cube?
An integer greater than one that is not prime.
A = 6(l^2)
V = pr^2h
[(x1 + x2)/2] -[(y1 + y2)/2]

37. What is true about the measures of the two acute angles in a right triangle?
Shifted down 2 units.
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 90°.
Divide - then multiply by 100.

38. What is the graph of a function?
Then the product xy is a constant.
The set of all ordered pairs (x -y) such that y = f(x).
A = (1/2)bh.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

39. How do you calculate a weighted average?
Shifted up 2 units.
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.

40. What is a divisor and a factor of an integer?
[(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.
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.

41. Important binomial 1
For any right triangle - a^2 + b^2 = c^2.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = lw
(x + y)(x - y) = x^2 - y^2

42. Properties of one 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
1 is a divisor (or factor) of every integer.
Write the percent over 100 and reduce.
For any number a: a * 1 = a and a / 1 = a.

43. What is special formula for the area of an equilateral triangle?
Set y = 0 - and solve.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = [(s^2*v3)/4]
The set of all ordered pairs (x -y) such that y = f(x).

44. Properties of one 2
For any integer n: 1^n = 1.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted up 2 units.
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.

45. What are the properties of a rectangle?
Their sum is 90°.
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.
360°

46. In a circle of radius r - what is the formula for the area?
They are both the same. A divisor or factor of an integer leaves no remainder.
A = pr^2
Avg = sum of n numbers/n
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

47. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
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°.
0 is a multiple of every integer.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

48. What is an even and an odd number?
B^m*b^n = b^m+n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.

49. What is an exterior angle of a polygon?
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.
An angle formed by extending the side of the polygon.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

50. In a circle of radius r - what is the formula for the diameter?
0 is the only number that is neither positive nor negative.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
D = 2r
Shifted left 2 units.