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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 the ratio of similitude?
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/b^n = b^m-n
The ratio of corresponding sides of similar triangles.
At least one of the factors is 0.

2. What is the formula for the area of a parallelogram?
Shifted left 2 units.
A = bh
Arc = (x°/360)(2pr) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.

3. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted right 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.

4. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Set x = 0 - and solve.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

5. What is special formula for the area of an equilateral triangle?
360°
Avg = sum of n numbers/n
For any number b: b = -b if and only if b = 0.
A = [(s^2*v3)/4]

6. Properties of zero 1
A = bh
All positive and negative whole numbers - and zero.
A fraction whose denominator is 100 i.e. 17% = 17/100
0 is the only number that is neither positive nor negative.

7. What is an integer?
All positive and negative whole numbers - and zero.
1 is a divisor (or factor) of every integer.
Set x = 0 - and solve.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

8. Properties of zero 2
The ratio of corresponding sides of similar triangles.
Write the percent as a decimal - and multiply.
If a is negative and b is positive - then a < 0 < b.
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.

9. What is a divisor and a factor of an integer?
An angle formed by extending the side of the polygon.
They are both the same. A divisor or factor of an integer leaves no remainder.
D = 2r
The product of their slopes is -1 (negative reciprocal).

10. What does it mean if y is directly proportional to x?
An angle formed by extending the side of the polygon.
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.
Then the quotient y/x is a constant.
A = 2(lw + lh + hw)

11. What is the Pythagorean theorem?
180°. If two or more angles form a straight angle - 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 right triangle - a^2 + b^2 = c^2.
Write the percent as a decimal - and multiply.

12. What is a fractional exponent?
0 is a multiple of every integer.
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.
Arc = (x°/360)(2pr) where x is the central angle.

13. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Write the percent over 100 and reduce.
For any number a: a * 1 = a and a / 1 = a.

14. What is a negative exponent?
1 is the smallest positive odd integer.
Is a right triangle with a ratio of sides x:xv3:2x.
For any number n: x^-n means 1/x^n.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

15. What is true about the slopes of parallel lines?
A = (1/2)bh.
For any integer n: 1^n = 1.
If a is negative and b is positive - then a < 0 < b.
Equal slopes.

16. How do you find the x-intercept of a graph?
V = lwh
Set y = 0 - and solve.
180°. If two or more angles form a straight angle - their sum is 180°.
(x + y)(x - y) = x^2 - y^2

17. Law of exponents 5
For any number a: a * 1 = a and a / 1 = a.
A^m/b^m = (a/b)^m
Even numbers are divisible by 2 and odd numbers are not.
The set of all ordered pairs (x -y) such that y = f(x).

18. Important binomial 2
A = pr^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

19. What is a Venn diagram?
All positive and negative whole numbers - and zero.
180°. If two or more angles form a straight angle - their sum is 180°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any integer n: 1^n = 1.

20. What are the important properties of 30-60-90 triangle?
The set of all ordered pairs (x -y) such that y = f(x).
0 is the only number that is neither positive nor negative.
Is a right triangle with a ratio of sides x:xv3:2x.
How steep the line is. Horizontal line = 0 - vertical has no slope.

21. What is the square root of a number?
A = 6(l^2)
180°. If two or more angles form a straight angle - their sum is 180°.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
0 is the only number that is neither positive nor negative.

22. What important property do similar triangles have?
Then the product xy is a constant.
Corresponding sides of similar triangles are in proportion.
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.

23. Properties of zero 3
0 is a multiple of every integer.
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°)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

24. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A^m/b^m = (a/b)^m

25. What are the sum - difference - products - and quotient of two numbers?
Corresponding sides of similar triangles are in proportion.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

26. Law of exponents 4
A^m*b^m = (ab)^m
Corresponding sides of similar triangles are in proportion.
D = 2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

27. How do you calculate percent increases and decreases?
For any number a: a * 1 = a and a / 1 = a.
(n - 2)(180°)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.

28. What is the relationship between the graph of f(x) the graph of y = f(x + 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.
M = (y2 - y1)/(x2 - x1)
Shifted left 2 units.
Divide - then multiply by 100.

29. Important binomial 1
Shifted up 2 units.
For any number a: a * 1 = a and a / 1 = a.
Write the percent over 100 and reduce.
(x + y)(x - y) = x^2 - y^2

30. What are the properties of a rectangle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The two pairs of opposite angles formed are equal to each other.
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.

31. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
360°
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.
At least one of the factors is 0.

32. What is the sum of the measures of the n angles of a polygon with n sides?
Divide - then multiply by 100.
(n - 2)(180°)
Corresponding sides of similar triangles are in proportion.
How steep the line is. Horizontal line = 0 - vertical has no slope.

33. What is the midpoint formula?
If a is negative and b is positive - then a < 0 < b.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
[(x1 + x2)/2] -[(y1 + y2)/2]
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

34. What is a prime 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.
Shifted left 2 units.
Equal slopes.
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.

35. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
A = bh
A fraction whose denominator is 100 i.e. 17% = 17/100
A = 2(lw + lh + hw)

36. 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.
Corresponding sides of similar triangles are in proportion.
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.

37. Properties of one 3
360°
Shifted right 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
1 is a divisor (or factor) of every integer.

38. What is the triangle inequality?
[(x1 + x2)/2] -[(y1 + y2)/2]
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.
For any number a: a * 1 = a and a / 1 = a.

39. What is true about the measures of the four angles formed by two intersecting lines?
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The two pairs of opposite angles formed are equal to each other.
A^m/b^m = (a/b)^m

40. What is a function?
Is a right triangle with a ratio of sides x:xv3:2x.
Their sum is 180°.
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

41. What is the graph of a function?
1 is a divisor (or factor) of every integer.
The set of all ordered pairs (x -y) such that y = f(x).
A = [(s^2*v3)/4]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

42. What is the formula for the surface area of a rectangular solid?
Shifted right 2 units.
A = 2(lw + lh + hw)
(x + y)(x - y) = x^2 - y^2
Cannot is 0 - must is 1 - all others are in between.

43. What is the distributive law?
Then the quotient y/x is a constant.
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted left 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

44. In a circle of radius r - what is the formula for the area?
V = pr^2h
An angle formed by extending the side of the polygon.
A = pr^2
No matter how many angles there are - the sum around the point is 360°.

45. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
All positive and negative whole numbers - and zero.
Then the product xy is a constant.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

46. What is the area of a square?
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.
0 is the only number that is neither positive nor negative.
1 is the smallest positive odd integer.
A = s^2 or A =d^2/2 where d is the diagonal

47. Law of exponents 2
Is a right triangle with a ratio of sides x:xv3:2x.
For any integer n: 1^n = 1.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
B^m/b^n = b^m-n

48. Law of exponents 1
No matter how many angles there are - the sum around the point is 360°.
B^m*b^n = b^m+n
[(x1 + x2)/2] -[(y1 + y2)/2]
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

49. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Is a right triangle with a ratio of sides x:xv3:2x.
180°. If two or more angles form a straight angle - their sum is 180°.

50. What are the important properties of a 45-45 - 90 triangle?
A = s^2 or A =d^2/2 where d is the diagonal
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
360°
Set y = 0 - and solve.