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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 are the important properties of a 45-45 - 90 triangle?
Cannot is 0 - must is 1 - all others are in between.
Then the product xy is a constant.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Is a right triangle with a ratio of sides x:xv3:2x.

2. Properties of zero 2
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.
If a is negative and b is positive - then a < 0 < b.
D = 2r
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

3. Properties of zero 5
B^m/b^n = b^m-n
For any number b: b = -b if and only if b = 0.
Divide - then multiply by 100.
Shifted left 2 units.

4. What is the triangle inequality?
An integer greater than one that is not prime.
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.
Their sum is 90°.
Write the percent as a decimal - and multiply.

5. What does it mean if y is directly proportional to x?
180°. If two or more angles form a straight angle - their sum is 180°.
V = l^3
Then the quotient y/x is a constant.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

6. How do you find the probability that an event will occur?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted right 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Is a right triangle with a ratio of sides x:xv3:2x.

7. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
V = lwh
For any number b: b = -b if and only if b = 0.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^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°.

8. What is the formula for the area of a parallelogram?
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 integer n: 1^n = 1.
A = bh
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

9. Important binomial 3
(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.
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°.

10. Important binomial 1
[(x1 + x2)/2] -[(y1 + y2)/2]
Cannot is 0 - must is 1 - all others are in between.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x + y)(x - y) = x^2 - y^2

11. 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.
Corresponding sides of similar triangles are in proportion.
Equal slopes.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

12. What is the formula for the area of a rectangle?
A = lw
For any integer n: 1^n = 1.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Is a right triangle with a ratio of sides x:xv3:2x.

13. What is a divisor and a factor of an integer?
An equation that states that two ratios are equivalent. 4/6 = 10/15
In the expression x^b - x is the base and b is the exponent.
A = lw
They are both the same. A divisor or factor of an integer leaves no remainder.

14. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Area = (x°/360)(pr^2) where x is the central angle.
Shifted up 2 units.
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.

15. What is true about the slopes of perpendicular lines?
Then the quotient y/x is a constant.
The product of their slopes is -1 (negative reciprocal).
Shifted right 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

16. Properties of one 3
Shifted left 2 units.
Divide - then multiply by 100.
1 is a divisor (or factor) of every integer.
Equal slopes.

17. How do you find the area of a sector of a circle?
Even numbers are divisible by 2 and odd numbers are not.
Area = (x°/360)(pr^2) where x is the central angle.
Shifted right 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

18. What are the important properties of 30-60-90 triangle?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Is a right triangle with a ratio of sides x:xv3:2x.
Then the quotient y/x is a constant.
Equal slopes.

19. What are similar triangles?
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Shifted right 2 units.

20. Properties of zero 1
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any number a: a * 1 = a and a / 1 = a.
0 is the only number that is neither positive nor negative.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

21. What are the sum - difference - products - and quotient of two numbers?
V = pr^2h
(b^m)^n = b^mn
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

22. Properties of zero 3
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is a multiple of every integer.
D = 2r
A = s^2 or A =d^2/2 where d is the diagonal

23. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
An integer greater than one that is not prime.
0 is a multiple of every integer.

24. What is p?
How steep the line is. Horizontal line = 0 - vertical has no slope.
V = l^3
(Circumference/diameter) of a circle - or approximately 3.14.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

25. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
B^m/b^n = b^m-n
For any number a: a * 1 = a and a / 1 = a.
For any right triangle - a^2 + b^2 = c^2.

26. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).
They are both the same. A divisor or factor of an integer leaves no remainder.

27. What is the relationship between a radius of a circle and a line that is tangent to the circle?
A = bh
Divide - then multiply by 100.
A = lw
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

28. What formula is used for an average?
In the expression x^b - x is the base and b is the exponent.
Avg = sum of n numbers/n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
All positive and negative whole numbers - and zero.

29. 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.
Divide - then multiply by 100.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

30. What is an exterior angle of a triangle?
Shifted down 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any integer n: 1^n = 1.

31. What is a Venn diagram?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(n - 2)(180°)
Area = (x°/360)(pr^2) where x is the central angle.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

32. What are the median and the mode of a set of data?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.
(Circumference/diameter) of a circle - or approximately 3.14.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

33. What is the formula for the volume of a cylinder?
Shifted left 2 units.
V = pr^2h
No matter how many angles there are - the sum around the point is 360°.
Is a right triangle with a ratio of sides x:xv3:2x.

34. What is the area of a square?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Write the percent over 100 and reduce.
A = s^2 or A =d^2/2 where d is the diagonal
Area = (x°/360)(pr^2) where x is the central angle.

35. What is true about the measures of the three angles in a triangle?
180°. If two or more angles form a straight angle - their sum is 180°.
A = [(s^2*v3)/4]
0 is a multiple of every integer.
Their sum is 180°.

36. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
The ratio of corresponding sides of similar triangles.
180°. If two or more angles form a straight angle - their sum is 180°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

37. Properties of square roots
D = 2r
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

38. 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
(x + y)(x - y) = x^2 - y^2
V = l^3

39. What is the sum of the measures of the four angles in a quadrilateral?
In the expression x^b - x is the base and b is the exponent.
All positive and negative whole numbers - and zero.
360°
Their sum is 180°.

40. How do you convert a percent to a fraction or a decimal?
1 is the smallest positive odd integer.
V = l^3
Arc = (x°/360)(2pr) where x is the central angle.
Write the percent over 100 and reduce.

41. In a circle of radius r - what is the formula for the circumference?
They are both the same. A divisor or factor of an integer leaves no remainder.
C = p2r
A = (1/2)bh.
At least one of the factors is 0.

42. What are the quotient and the remainder?

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43. Properties of one 4
The ratio of corresponding sides of similar triangles.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.

44. What is a negative exponent?
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any number n: x^-n means 1/x^n.
Arc = (x°/360)(2pr) where x is the central angle.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

45. What is the distributive law?
If a is negative and b is positive - then a < 0 < b.
No matter how many angles there are - the sum around the point is 360°.
The product of their slopes is -1 (negative reciprocal).
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

46. What important property do similar triangles have?
Write the percent over 100 and reduce.
An angle formed by extending the side of the polygon.
Corresponding sides of similar triangles are in proportion.
0 is the only number that is neither positive nor negative.

47. In a circle of radius r - what is the formula for the diameter?
D = 2r
B^m*b^n = b^m+n
An equation that states that two ratios are equivalent. 4/6 = 10/15
No matter how many angles there are - the sum around the point is 360°.

48. What is an exponent?
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.
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

49. Law of exponents 5
If a is negative and b is positive - then a < 0 < b.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.

50. How do you calculate percent increases and decreases?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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]