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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 an exterior angle of a polygon?
[(x1 + x2)/2] -[(y1 + y2)/2]
An angle formed by extending the side of the polygon.
Then the product xy is a constant.
Is a right triangle with a ratio of sides x:xv3:2x.

2. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
The two pairs of opposite angles formed are equal to each other.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

3. What are the properties of a rectangle?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = lw

4. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
How steep the line is. Horizontal line = 0 - vertical has no slope.
A^m/b^m = (a/b)^m
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

5. Law of exponents 4
A = (1/2)bh.
Write the percent over 100 and reduce.
Even numbers are divisible by 2 and odd numbers are not.
A^m*b^m = (ab)^m

6. What is the distributive law?
A = (1/2)bh.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

7. How do you convert a percent to a fraction or a decimal?
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.
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.
(b^m)^n = b^mn
Write the percent over 100 and reduce.

8. What is a negative exponent?
For any number n: x^-n means 1/x^n.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

9. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
An equation that states that two ratios are equivalent. 4/6 = 10/15

10. What is a function?
A = pr^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
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

11. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

12. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Area = (x°/360)(pr^2) where x is the central angle.
Write the percent over 100 and reduce.
Their sum is 180°.

13. Properties of one 1
An equation that states that two ratios are equivalent. 4/6 = 10/15
0 is a multiple of every integer.
For any right triangle - a^2 + b^2 = c^2.
For any number a: a * 1 = a and a / 1 = a.

14. Properties of zero 3
0 is a multiple of every integer.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
V = l^3

15. 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.
B^m*b^n = b^m+n
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.

16. Important binomial 3
B^m*b^n = b^m+n
For any right triangle - a^2 + b^2 = c^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Avg = sum of n numbers/n

17. What is the Pythagorean theorem?
A^m/b^m = (a/b)^m
A^m*b^m = (ab)^m
For any right triangle - a^2 + b^2 = c^2.
For any number a: a * 1 = a and a / 1 = a.

18. 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.
No matter how many angles there are - the sum around the point is 360°.
For any number a: a * 1 = a and a / 1 = a.
Cannot is 0 - must is 1 - all others are in between.

19. 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°.
Even numbers are divisible by 2 and odd numbers are not.
Shifted left 2 units.

20. What does it mean if y is directly proportional to x?
0 is the only number that is neither positive nor negative.
Then the quotient y/x is a constant.
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.
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.

21. What are the properties of a parallelogram?
They are both the same. A divisor or factor of an integer leaves no remainder.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

22. What is a prime number?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number n: x^-n means 1/x^n.
A = [(s^2*v3)/4]
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.

23. What is true about the areas of similar triangles?
(b^m)^n = b^mn
Cannot is 0 - must is 1 - all others are in between.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
B^m/b^n = b^m-n

24. What is a proportion?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An equation that states that two ratios are equivalent. 4/6 = 10/15
[(x1 + x2)/2] -[(y1 + y2)/2]

25. What is a multiple of an integer?
1 is the smallest positive odd integer.
The ratio of corresponding sides of similar triangles.
Cannot is 0 - must is 1 - all others are in between.
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 is true about the measures of the four angles formed by two intersecting lines?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Shifted left 2 units.
B^m*b^n = b^m+n
The two pairs of opposite angles formed are equal to each other.

27. What is the midpoint formula?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Is a right triangle with a ratio of sides x:xv3:2x.
V = l^3
[(x1 + x2)/2] -[(y1 + y2)/2]

28. What does it mean if y is inversely proportional to x?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.
Write the percent over 100 and reduce.
Then the product xy is a constant.

29. How do you find the slope of a line?
Divide - then multiply by 100.
Corresponding sides of similar triangles are in proportion.
M = (y2 - y1)/(x2 - x1)
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 the distance formula?
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

31. What is the formula for the surface area of a cube?
A = 6(l^2)
An angle formed by extending the side of the polygon.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
1 is the smallest positive odd integer.

32. Law of exponents 1
B^m*b^n = b^m+n
For any number n: x^-n means 1/x^n.
C = p2r
A = lw

33. What is the formula for the area of a rectangle?
Shifted left 2 units.
At least one of the factors is 0.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = lw

34. Properties of one 3
1 is a divisor (or factor) of every integer.
D = 2r
A = [(s^2*v3)/4]
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

35. What is p?
Divide - then multiply by 100.
(Circumference/diameter) of a circle - or approximately 3.14.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any number b: b = -b if and only if b = 0.

36. What is the square root of a number?
Their sum is 180°.
1 is the smallest positive odd integer.
(x + y)(x - y) = x^2 - y^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

37. What are the important properties of 30-60-90 triangle?
360°
Is a right triangle with a ratio of sides x:xv3:2x.
B^m*b^n = b^m+n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

38. In a circle of radius r - what is the formula for the circumference?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = s^2 or A =d^2/2 where d is the diagonal
C = p2r

39. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
If a is negative and b is positive - then a < 0 < b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x + y)(x - y) = x^2 - y^2
Shifted up 2 units.

40. What are the important properties of a 45-45 - 90 triangle?
V = l^3
An integer greater than one that is not prime.
1 is a divisor (or factor) of every integer.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

41. Properties of zero 2
A^m/b^m = (a/b)^m
V = l^3
If a is negative and b is positive - then a < 0 < b.
A = pr^2

42. How you convert a fraction or a decimal to a percent?
Area = (x°/360)(pr^2) where x is the central angle.
Divide - then multiply by 100.
For any number b: b = -b if and only if b = 0.
For any integer n: 1^n = 1.

43. What is a divisor and a factor of an 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.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = bh
D = 2r

44. In a circle of radius r - what is the formula for the area?
A = pr^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An angle formed by extending the side of the polygon.
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.

45. What is the formula for the volume of a rectangular solid?
Their sum is 90°.
An angle formed by extending the side of the polygon.
V = lwh
How steep the line is. Horizontal line = 0 - vertical has no slope.

46. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Set x = 0 - and solve.
A = 2(lw + lh + hw)
Their sum is 180°.
Shifted right 2 units.

47. What is true about the slopes of perpendicular 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.
C = p2r
The product of their slopes is -1 (negative reciprocal).
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

48. What is the measure of a straight angle?
(b^m)^n = b^mn
180°. If two or more angles form a straight angle - their sum is 180°.
Corresponding sides of similar triangles are in proportion.
For any number n: x^-n means 1/x^n.

49. What is true about the slopes of parallel lines?
Set x = 0 - and solve.
A = pr^2
Equal slopes.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

50. What is true about the measures of the three angles in a triangle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Their sum is 180°.
Is a right triangle with a ratio of sides x:xv3:2x.
M = (y2 - y1)/(x2 - x1)