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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 relationship between the graph of f(x) the graph of y = f(x + 2)?
B^m*b^n = b^m+n
Arc = (x°/360)(2pr) where x is the central angle.
Shifted left 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15

2. What is a negative exponent?
Shifted up 2 units.
For any number n: x^-n means 1/x^n.
For any integer n: 1^n = 1.
B^m/b^n = b^m-n

3. What is true about the slopes of perpendicular lines?
A = [(s^2*v3)/4]
(x + y)(x - y) = x^2 - y^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
The product of their slopes is -1 (negative reciprocal).

4. What is a fractional exponent?
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Set y = 0 - and solve.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

5. What is true about the areas of similar triangles?
Area = (x°/360)(pr^2) where x is the central angle.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Their sum is 90°.

6. Properties of zero 2
Equal slopes.
If a is negative and b is positive - then a < 0 < b.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
All positive and negative whole numbers - and zero.

7. In a circle of radius r - what is the formula for the area?
Then the product xy is a constant.
A = pr^2
Their sum is 180°.
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.

8. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
0 is the only number that is neither positive nor negative.
(n - 2)(180°)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

9. Important binomial 2
(Circumference/diameter) of a circle - or approximately 3.14.
An integer greater than one that is not prime.
In the expression x^b - x is the base and b is the exponent.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

10. What is an exponent?
Divide - then multiply by 100.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
In the expression x^b - x is the base and b is the exponent.
Corresponding sides of similar triangles are in proportion.

11. 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.
Set y = 0 - and solve.
Set x = 0 - and solve.
An angle formed by extending the side of the polygon.

12. Important binomial 1
Set x = 0 - and solve.
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(x + y)(x - y) = x^2 - y^2

13. What does it mean if y is directly proportional to x?
Shifted down 2 units.
Then the quotient y/x is a constant.
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

14. What is true about the measures of the four angles formed by two intersecting lines?
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The two pairs of opposite angles formed are equal to each other.

15. What is the sum of the measures of all angles around a point?
C = p2r
No matter how many angles there are - the sum around the point is 360°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Their sum is 180°.

16. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
360°
V = l^3
Shifted down 2 units.
For any number n: x^-n means 1/x^n.

17. What are similar triangles?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

18. In a circle of radius r - what is the formula for the diameter?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Equal slopes.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
D = 2r

19. What is the probability of an event that cannot occur? That must occur?
Set y = 0 - and solve.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(Circumference/diameter) of a circle - or approximately 3.14.
Cannot is 0 - must is 1 - all others are in between.

20. 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°.
A = lw
Then the quotient y/x is a constant.
Shifted down 2 units.

21. Properties of one 3
Area = (x°/360)(pr^2) where x is the central angle.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
1 is a divisor (or factor) of every integer.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

22. How do you find the slope of a line?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
M = (y2 - y1)/(x2 - x1)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

23. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted up 2 units.
Is a right triangle with a ratio of sides x:xv3:2x.
An integer greater than one that is not prime.

24. What is the sum of the measures of the n angles of a polygon with n sides?
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°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(n - 2)(180°)
Is a right triangle with a ratio of sides x:xv3:2x.

25. What is a prime number?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

26. What is the formula for the volume of a rectangular solid?
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.
Shifted right 2 units.
V = lwh
A = s^2 or A =d^2/2 where d is the diagonal

27. What is the distributive law?
A = pr^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.
For any integer n: 1^n = 1.

28. Properties of zero 3
Is a right triangle with a ratio of sides x:xv3:2x.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.
0 is a multiple of every integer.

29. How do we write the equation of a line?
Write the percent over 100 and reduce.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = 6(l^2)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

30. If the product of two or more numbers is 0 - what do you know about the numbers?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Set y = 0 - and solve.
D = 2r
At least one of the factors is 0.

31. What is the volume of a cube?
Even numbers are divisible by 2 and odd numbers are not.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
180°. If two or more angles form a straight angle - their sum is 180°.
V = l^3

32. How do you convert a percent to a fraction or a decimal?
D = 2r
Write the percent over 100 and reduce.
(Circumference/diameter) of a circle - or approximately 3.14.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

33. If you were given the graph of y = f(x) - what does f(a) represent?
Then the quotient y/x is a constant.
1 is a divisor (or factor) of every integer.
At least one of the factors is 0.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

34. Properties of square roots
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
An integer greater than one that is not prime.

35. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
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.
360°
Write the percent over 100 and reduce.
Set x = 0 - and solve.

36. What is true about the slopes of parallel lines?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is the only number that is neither positive nor negative.
1 is the smallest positive odd integer.
Equal slopes.

37. What is the formula for the surface area of a cube?
Shifted up 2 units.
A = 6(l^2)
All positive and negative whole numbers - and zero.
A = [(s^2*v3)/4]

38. Properties of zero 1
0 is the only number that is neither positive nor negative.
For any right triangle - a^2 + b^2 = c^2.
They are both the same. A divisor or factor of an integer leaves no remainder.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

39. What does it mean if y is inversely proportional to x?
A = (1/2)bh.
A = pr^2
(b^m)^n = b^mn
Then the product xy is a constant.

40. How you convert a fraction or a decimal to a percent?
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.
Divide - then multiply by 100.
Shifted left 2 units.

41. What is the triangle inequality?
1 is the smallest positive odd integer.
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.
Divide - then multiply by 100.
The set of all ordered pairs (x -y) such that y = f(x).

42. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Set y = 0 - and solve.
Then the product xy is a constant.

43. How do you calculate a weighted average?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.

44. What is the formula for the area of a triangle?
360°
A = pr^2
A = (1/2)bh.
Even numbers are divisible by 2 and odd numbers are not.

45. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
In the expression x^b - x is the base and b is the exponent.
A = pr^2
[(x1 + x2)/2] -[(y1 + y2)/2]

46. What are the sum - difference - products - and quotient of two numbers?
360°
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Set y = 0 - and solve.
Then the quotient y/x is a constant.

47. What is true about the measures of the three angles in a triangle?
V = lwh
Their sum is 180°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

48. What is a composite number?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
An integer greater than one that is not prime.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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°.

49. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = pr^2
In the expression x^b - x is the base and b is the exponent.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

50. What is the distance formula?
V = lwh
An angle formed by extending the side of the polygon.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = 2(lw + lh + hw)