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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. How do you find the length of an arc of a circle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Arc = (x°/360)(2pr) where x is the central angle.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted down 2 units.

2. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
Their sum is 180°.
The ratio of corresponding sides of similar triangles.
0 is a multiple of every integer.

3. Law of exponents 2
B^m/b^n = b^m-n
The product of their slopes is -1 (negative reciprocal).
Divide - then multiply by 100.
V = lwh

4. What important property do similar triangles have?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
Corresponding sides of similar triangles are in proportion.

5. Important binomial 1
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Divide - then multiply by 100.
(x + y)(x - y) = x^2 - y^2
A^m*b^m = (ab)^m

6. Law of exponents 5
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.
A^m/b^m = (a/b)^m
For any number a: a * 1 = a and a / 1 = a.
(b^m)^n = b^mn

7. What do we mean by the slope of the line?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any number b: b = -b if and only if b = 0.
Then the quotient y/x is a constant.
How steep the line is. Horizontal line = 0 - vertical has no slope.

8. What is the Pythagorean theorem?
A fraction whose denominator is 100 i.e. 17% = 17/100
For any right triangle - a^2 + b^2 = c^2.
(Circumference/diameter) of a circle - or approximately 3.14.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

9. In a circle of radius r - what is the formula for the circumference?
C = p2r
Cannot is 0 - must is 1 - all others are in between.
The two pairs of opposite angles formed are equal to each other.
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.

10. What is an exterior angle of a polygon?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(x + y)(x - y) = x^2 - y^2
An angle formed by extending the side of the polygon.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

11. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
1 is a divisor (or factor) of every integer.
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.
M = (y2 - y1)/(x2 - x1)

12. Important binomial 3
For any right triangle - a^2 + b^2 = c^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Even numbers are divisible by 2 and odd numbers are not.
Shifted left 2 units.

13. What is the volume of a cube?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = l^3
A = 2(lw + lh + hw)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

14. What is the sum of the measures of all angles around a point?
B^m*b^n = b^m+n
A = s^2 or A =d^2/2 where d is the diagonal
Is a right triangle with a ratio of sides x:xv3:2x.
No matter how many angles there are - the sum around the point is 360°.

15. What is true about the measures of the three angles in a triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Their sum is 180°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

16. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
An integer greater than one that is not prime.
Shifted left 2 units.
M = (y2 - y1)/(x2 - x1)

17. What is true about the slopes of parallel lines?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Equal slopes.
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 number n: x^-n means 1/x^n.

18. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
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 the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Their sum is 90°.

19. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
0 is a multiple of every integer.
D = 2r
Shifted left 2 units.

20. What is the triangle inequality?
(Circumference/diameter) of a circle - or approximately 3.14.
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 x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.

21. What is the ratio of similitude?
A = lw
The ratio of corresponding sides of similar triangles.
An equation that states that two ratios are equivalent. 4/6 = 10/15
[(x1 + x2)/2] -[(y1 + y2)/2]

22. In a circle of radius r - what is the formula for the diameter?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
C = p2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
D = 2r

23. What is the distance formula?
Their sum is 180°.
Shifted up 2 units.
Corresponding sides of similar triangles are in proportion.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

24. What are the properties of a square?
At least one of the factors is 0.
A = [(s^2*v3)/4]
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.
(b^m)^n = b^mn

25. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Divide - then multiply by 100.
V = pr^2h
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

26. What is the formula for the volume of a rectangular solid?
1 is the smallest positive odd integer.
V = lwh
Divide - then multiply by 100.
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.

27. How do you find the x-intercept of a graph?
1 is the smallest positive odd integer.
Shifted down 2 units.
Set y = 0 - and solve.
A fraction whose denominator is 100 i.e. 17% = 17/100

28. Properties of zero 5
1 is a divisor (or factor) of every integer.
At least one of the factors is 0.
For any number b: b = -b if and only if b = 0.
A^m/b^m = (a/b)^m

29. Important binomial 2
At least one of the factors is 0.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Write the percent as a decimal - and multiply.
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.

30. What is a multiple of an integer?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Arc = (x°/360)(2pr) where x is the central angle.
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.

31. What formula is used for an average?
A = [(s^2*v3)/4]
A = (1/2)bh.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Avg = sum of n numbers/n

32. What is the formula for the area of a rectangle?
An angle formed by extending the side of the polygon.
A = lw
Set x = 0 - and solve.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

33. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
V = l^3
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any number a: a * 1 = a and a / 1 = a.

34. What is the formula for the area of a triangle?
An angle formed by extending the side of the polygon.
V = lwh
A = (1/2)bh.
They are both the same. A divisor or factor of an integer leaves no remainder.

35. Properties of one 3
A^m*b^m = (ab)^m
1 is a divisor (or factor) of every integer.
Set y = 0 - and solve.
0 is a multiple of every integer.

36. What is the midpoint formula?
Area = (x°/360)(pr^2) where x is the central angle.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
[(x1 + x2)/2] -[(y1 + y2)/2]
An equation that states that two ratios are equivalent. 4/6 = 10/15

37. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Corresponding sides of similar triangles are in proportion.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(n - 2)(180°)
M = (y2 - y1)/(x2 - x1)

38. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted up 2 units.
For any number n: x^-n means 1/x^n.

39. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted left 2 units.
At least one of the factors is 0.
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.
Shifted up 2 units.

40. Properties of zero 2
1 is the smallest positive odd integer.
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If a is negative and b is positive - then a < 0 < b.

41. Properties of square roots
Divide - then multiply by 100.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = lwh

42. What is an exterior angle of a triangle?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = lw
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

43. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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°.
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.

44. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Cannot is 0 - must is 1 - all others are in between.
Area = (x°/360)(pr^2) where x is the central angle.

45. What are the properties of a parallelogram?
A^m/b^m = (a/b)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
In the expression x^b - x is the base and b is the exponent.
Shifted down 2 units.

46. Law of exponents 4
A^m*b^m = (ab)^m
Cannot is 0 - must is 1 - all others are in between.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
0 is a multiple of every integer.

47. Properties of one 1
(n - 2)(180°)
Then the product xy is a constant.
For any number a: a * 1 = a and a / 1 = a.
A fraction whose denominator is 100 i.e. 17% = 17/100

48. Properties of zero 1
No matter how many angles there are - the sum around the point is 360°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
0 is the only number that is neither positive nor negative.

49. How do you find the area of a sector of a circle?
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.
Area = (x°/360)(pr^2) where x is the central angle.
Cannot is 0 - must is 1 - all others are in between.

50. What is true about the measures of the two acute angles in a right triangle?
A = 2(lw + lh + hw)
Their sum is 90°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Equal slopes.