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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 sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
Cannot is 0 - must is 1 - all others are in between.
V = lwh
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

2. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
0 is a multiple of every integer.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
If a is negative and b is positive - then a < 0 < b.

3. What is the Pythagorean theorem?
At least one of the factors is 0.
For any right triangle - a^2 + b^2 = c^2.
Is a right triangle with a ratio of sides x:xv3:2x.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

4. What is the formula for the area of a parallelogram?
A = bh
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Set x = 0 - and solve.
In the expression x^b - x is the base and b is the exponent.

5. What is an exponent?
For any right triangle - a^2 + b^2 = c^2.
Cannot is 0 - must is 1 - all others are in between.
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.

6. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
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.
Divide - then multiply by 100.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

7. What is an exterior angle of a triangle?
Set y = 0 - and solve.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Divide - then multiply by 100.

8. How you convert a fraction or a decimal to a percent?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Divide - then multiply by 100.
Shifted up 2 units.
(b^m)^n = b^mn

9. What is an exterior angle of a polygon?
The two pairs of opposite angles formed are equal to each other.
A = [(s^2*v3)/4]
An angle formed by extending the side of the polygon.
A^m/b^m = (a/b)^m

10. Properties of one 4
P(e) = (# of favorable outcomes)/(# of possible outcomes)
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

11. What is p?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
An integer greater than one that is not prime.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(Circumference/diameter) of a circle - or approximately 3.14.

12. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

13. What is a composite number?
At least one of the factors is 0.
(Circumference/diameter) of a circle - or approximately 3.14.
No matter how many angles there are - the sum around the point is 360°.
An integer greater than one that is not prime.

14. What is a negative exponent?
All positive and negative whole numbers - and zero.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any number n: x^-n means 1/x^n.
Set x = 0 - and solve.

15. What is the square root of a number?
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
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
At least one of the factors is 0.

16. In a circle of radius r - what is the formula for the circumference?
V = l^3
C = p2r
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Arc = (x°/360)(2pr) where x is the central angle.

17. What formula is used for an average?
For any number n: x^-n means 1/x^n.
Avg = sum of n numbers/n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted left 2 units.

18. For what values of a function is the function undefined?
360°
Shifted down 2 units.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The set of all ordered pairs (x -y) such that y = f(x).

19. What is an integer?
B^m*b^n = b^m+n
Equal slopes.
Is a right triangle with a ratio of sides x:xv3:2x.
All positive and negative whole numbers - and zero.

20. Important binomial 3
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = lwh
Set y = 0 - and solve.

21. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
An integer greater than one that is not prime.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Avg = sum of n numbers/n

22. What is the formula for the area of a triangle?
A = (1/2)bh.
Their sum is 90°.
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.

23. How do you find the probability that an event will occur?
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.
For any integer n: 1^n = 1.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

24. What is the midpoint formula?
A = [(s^2*v3)/4]
[(x1 + x2)/2] -[(y1 + y2)/2]
A = bh
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

25. What is the relationship between a radius of a circle and a line that is tangent to the circle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A fraction whose denominator is 100 i.e. 17% = 17/100
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Write the percent as a decimal - and multiply.

26. In a circle of radius r - what is the formula for the area?
1 is a divisor (or factor) of every integer.
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted right 2 units.
A = pr^2

27. What is true about the measures of the two acute angles in a right triangle?
Write the percent over 100 and reduce.
Their sum is 90°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Cannot is 0 - must is 1 - all others are in between.

28. Important binomial 1
The set of all ordered pairs (x -y) such that y = f(x).
(x + y)(x - y) = x^2 - y^2
Arc = (x°/360)(2pr) where x is the central angle.
Then the quotient y/x is a constant.

29. Properties of zero 5
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.
For any number n: x^-n means 1/x^n.
For any number b: b = -b if and only if b = 0.
The two pairs of opposite angles formed are equal to each other.

30. Properties of zero 3
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Their sum is 90°.
For any number a: a * 1 = a and a / 1 = a.
0 is a multiple of every integer.

31. How do you find the y-intercept of a graph?
A = (1/2)bh.
Then the product xy is a constant.
Set x = 0 - and solve.
V = pr^2h

32. What is the distance formula?
In the expression x^b - x is the base and b is the exponent.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
0 is a multiple of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

33. What is the sum of the measures of the four angles in a quadrilateral?
For any right triangle - a^2 + b^2 = c^2.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(n - 2)(180°)
360°

34. Properties of one 3
[(x1 + x2)/2] -[(y1 + y2)/2]
In the expression x^b - x is the base and b is the exponent.
1 is a divisor (or factor) of every integer.
Cannot is 0 - must is 1 - all others are in between.

35. How do you convert a percent to a fraction or a decimal?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Write the percent over 100 and reduce.
At least one of the factors is 0.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

36. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
The product of their slopes is -1 (negative reciprocal).
An equation that states that two ratios are equivalent. 4/6 = 10/15

37. What is a divisor and a factor of an integer?
A = (1/2)bh.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
At least one of the factors is 0.
They are both the same. A divisor or factor of an integer leaves no remainder.

38. What does it mean if y is inversely proportional to x?
B^m/b^n = b^m-n
Then the product xy is a constant.
Is a right triangle with a ratio of sides x:xv3:2x.
(Circumference/diameter) of a circle - or approximately 3.14.

39. Important binomial 2
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.
A^m*b^m = (ab)^m
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

40. How do you find a percent of a number?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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 up 2 units.
Write the percent as a decimal - and multiply.

41. What is the sum of the measures of all angles around a point?
Arc = (x°/360)(2pr) where x is the central angle.
No matter how many angles there are - the sum around the point is 360°.
Then the product xy is a constant.
For any integer n: 1^n = 1.

42. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
Divide - then multiply by 100.
Set x = 0 - and solve.
For any right triangle - a^2 + b^2 = c^2.

43. Properties of zero 4
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
D = 2r
Corresponding sides of similar triangles are in proportion.

44. What is the ratio of similitude?
They are both the same. A divisor or factor of an integer leaves no remainder.
The ratio of corresponding sides of similar triangles.
180°. If two or more angles form a straight angle - their sum is 180°.
V = lwh

45. What is the triangle inequality?
[(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.
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.

46. What is the formula for the surface area of a cube?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
1 is a divisor (or factor) of every integer.
A = 6(l^2)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

47. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
V = lwh
Equal slopes.
All positive and negative whole numbers - and zero.

48. If the product of two or more numbers is 0 - what do you know about the numbers?
360°
Write the percent over 100 and reduce.
The ratio of corresponding sides of similar triangles.
At least one of the factors is 0.

49. What are the sum - difference - products - and quotient of two numbers?
Arc = (x°/360)(2pr) where x is the central angle.
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

50. What are the properties of a square?
Even numbers are divisible by 2 and odd numbers are not.
Shifted up 2 units.
Then the product xy is a constant.
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.