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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 a radius of a circle and a line that is tangent to the circle?
Avg = sum of n numbers/n
Set x = 0 - and solve.
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

2. What is an exterior angle of a triangle?
C = p2r
Corresponding sides of similar triangles are in proportion.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

3. Properties of one 4
M = (y2 - y1)/(x2 - x1)
1 is the smallest positive odd integer.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x + y)(x - y) = x^2 - y^2

4. What is the square root of a number?
Corresponding sides of similar triangles are in proportion.
(Circumference/diameter) of a circle - or approximately 3.14.
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

5. How do you find the x-intercept of a graph?
Cannot is 0 - must is 1 - all others are in between.
A = [(s^2*v3)/4]
(b^m)^n = b^mn
Set y = 0 - and solve.

6. What is an exponent?
Shifted up 2 units.
Shifted down 2 units.
A = pr^2
In the expression x^b - x is the base and b is the exponent.

7. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
All positive and negative whole numbers - and zero.
V = lwh
For any number n: x^-n means 1/x^n.

8. In a circle of radius r - what is the formula for the circumference?
C = p2r
A fraction whose denominator is 100 i.e. 17% = 17/100
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(b^m)^n = b^mn

9. Law of exponents 1
B^m*b^n = b^m+n
0 is a multiple of every integer.
A = lw
Arc = (x°/360)(2pr) where x is the central angle.

10. What is the sum of the measures of all angles around a point?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Write the percent over 100 and reduce.
No matter how many angles there are - the sum around the point is 360°.
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.

11. What is the sum of the measures of the n angles of a polygon with n sides?
Avg = sum of n numbers/n
(n - 2)(180°)
A = [(s^2*v3)/4]
V = lwh

12. What are similar triangles?
A = bh
For any number n: x^-n means 1/x^n.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

13. Law of exponents 2
Arc = (x°/360)(2pr) 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.
B^m/b^n = b^m-n
360°

14. What is a function?
If a is negative and b is positive - then a < 0 < b.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

15. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Then the quotient y/x is a constant.
For any number b: b = -b if and only if b = 0.
The two pairs of opposite angles formed are equal to each other.

16. What is the formula for the surface area of a rectangular solid?
(b^m)^n = b^mn
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.
A = 2(lw + lh + hw)
B^m*b^n = b^m+n

17. What is special formula for the area of an equilateral triangle?
A = lw
A = [(s^2*v3)/4]
A^m*b^m = (ab)^m
D = 2r

18. Properties of zero 2
0 is a multiple of every integer.
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.
If a is negative and b is positive - then a < 0 < b.

19. Important binomial 3
V = lwh
At least one of the factors is 0.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any number n: x^-n means 1/x^n.

20. Important binomial 1
All positive and negative whole numbers - and zero.
For any number n: x^-n means 1/x^n.
(x + y)(x - y) = x^2 - y^2
[(x1 + x2)/2] -[(y1 + y2)/2]

21. What is a Venn diagram?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
1 is the smallest positive odd integer.
V = l^3

22. Properties of zero 3
0 is a multiple of every integer.
V = lwh
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = [(s^2*v3)/4]

23. How do you find the area of a sector of a circle?
0 is the only number that is neither positive nor negative.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Area = (x°/360)(pr^2) where x is the central angle.
A^m/b^m = (a/b)^m

24. What is the formula for the area of a triangle?
Arc = (x°/360)(2pr) where x is the central angle.
360°
0 is the only number that is neither positive nor negative.
A = (1/2)bh.

25. What is a multiple of an integer?
V = l^3
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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.

26. What are the median and the mode of a set of data?
Avg = sum of n numbers/n
V = pr^2h
1 is a divisor (or factor) 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.

27. Properties of one 2
For any integer n: 1^n = 1.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = s^2 or A =d^2/2 where d is the diagonal
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

28. What is the distance formula?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.

29. What do we mean by the slope of the line?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
(n - 2)(180°)

30. How do we write the equation of a line?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = s^2 or A =d^2/2 where d is the diagonal
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

31. How do you find the length of an arc of a circle?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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 every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Arc = (x°/360)(2pr) where x is the central angle.

32. What are the important properties of 30-60-90 triangle?
A = lw
Then the quotient y/x is a constant.
Area = (x°/360)(pr^2) where x is the central angle.
Is a right triangle with a ratio of sides x:xv3:2x.

33. For what values of a function is the function undefined?
B^m/b^n = b^m-n
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Shifted left 2 units.
B^m*b^n = b^m+n

34. Law of exponents 4
The set of all ordered pairs (x -y) such that y = f(x).
A^m*b^m = (ab)^m
A^m/b^m = (a/b)^m
[(x1 + x2)/2] -[(y1 + y2)/2]

35. What is the measure of a straight angle?
Write the percent as a decimal - and multiply.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
[(x1 + x2)/2] -[(y1 + y2)/2]
180°. If two or more angles form a straight angle - their sum is 180°.

36. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Set y = 0 - and solve.
Shifted right 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

37. Properties of zero 5
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = 2(lw + lh + hw)
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 b: b = -b if and only if b = 0.

38. Law of exponents 3
If a is negative and b is positive - then a < 0 < b.
Shifted left 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(b^m)^n = b^mn

39. How do you find a percent of a number?
An integer greater than one that is not prime.
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Write the percent as a decimal - and multiply.

40. What is a negative exponent?
Shifted left 2 units.
Set x = 0 - and solve.
At least one of the factors is 0.
For any number n: x^-n means 1/x^n.

41. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(b^m)^n = b^mn
M = (y2 - y1)/(x2 - x1)
They are both the same. A divisor or factor of an integer leaves no remainder.

42. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted left 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

43. What is true about the measures of the four angles formed by two intersecting lines?
A = lw
V = pr^2h
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The two pairs of opposite angles formed are equal to each other.

44. What is true about the measures of the three angles in a triangle?
A^m/b^m = (a/b)^m
At least one of the factors is 0.
Their sum is 180°.
Equal slopes.

45. What is the Pythagorean theorem?
Equal slopes.
For any right triangle - a^2 + b^2 = c^2.
No matter how many angles there are - the sum around the point is 360°.
Then the product xy is a constant.

46. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Even numbers are divisible by 2 and odd numbers are not.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Shifted left 2 units.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

47. Properties of one 1
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any number a: a * 1 = a and a / 1 = a.
For any right triangle - a^2 + b^2 = c^2.
Set x = 0 - and solve.

48. What is a fractional exponent?
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = lwh

49. Law of exponents 5
(Circumference/diameter) of a circle - or approximately 3.14.
360°
Their sum is 90°.
A^m/b^m = (a/b)^m

50. How do you convert a percent to a fraction or a decimal?
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.
1 is the smallest positive odd integer.
Write the percent over 100 and reduce.