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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 we write the equation of a line?
360°
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Cannot is 0 - must is 1 - all others are in between.
A^m*b^m = (ab)^m

2. How do you calculate a weighted average?
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.
A = lw
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

3. Law of exponents 5
1 is a divisor (or factor) of every integer.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A^m/b^m = (a/b)^m
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.

4. Properties of square roots
A = s^2 or A =d^2/2 where d is the diagonal
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x + y)(x - y) = x^2 - y^2
The set of all ordered pairs (x -y) such that y = f(x).

5. Law of exponents 2
(Circumference/diameter) of a circle - or approximately 3.14.
B^m/b^n = b^m-n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
0 is the only number that is neither positive nor negative.

6. What is true about the measures of the three angles in a triangle?
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.
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 180°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

7. How you convert a fraction or a decimal to a percent?
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 a: a * 1 = a and a / 1 = a.
Divide - then multiply by 100.
Write the percent as a decimal - and multiply.

8. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
D = 2r
Shifted up 2 units.
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 = 2(lw + lh + hw)

9. What is the distance formula?
A = 6(l^2)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
The ratio of corresponding sides of similar triangles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

10. 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.
Write the percent as a decimal - and multiply.
A = [(s^2*v3)/4]
1 is a divisor (or factor) of every integer.

11. What is the formula for the surface area of a cube?
Set y = 0 - and solve.
A = 6(l^2)
For any integer n: 1^n = 1.
1 is the smallest positive odd integer.

12. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted down 2 units.

13. What are the properties of a rectangle?
The product of their slopes is -1 (negative reciprocal).
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted down 2 units.

14. What is the formula for the area of a parallelogram?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = bh
Shifted up 2 units.

15. What is the formula for the area of a rectangle?
A = (1/2)bh.
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°.
0 is the only number that is neither positive nor negative.
A = lw

16. What does it mean if y is inversely proportional to x?
For any right triangle - a^2 + b^2 = c^2.
Then the product xy is a constant.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.

17. How do you convert a percent to a fraction or a decimal?
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

18. What is true about the measures of the four angles formed by two intersecting lines?
Shifted up 2 units.
V = pr^2h
For any integer n: 1^n = 1.
The two pairs of opposite angles formed are equal to each other.

19. What is a function?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The ratio of corresponding sides of similar triangles.
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.

20. What are the important properties of 30-60-90 triangle?
Corresponding sides of similar triangles are in proportion.
Is a right triangle with a ratio of sides x:xv3:2x.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
V = pr^2h

21. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
(b^m)^n = b^mn
[(x1 + x2)/2] -[(y1 + y2)/2]
C = p2r
360°

22. What is the probability of an event that cannot occur? That must occur?
360°
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.
Area = (x°/360)(pr^2) where x is the central angle.
Cannot is 0 - must is 1 - all others are in between.

23. What is the sum of the measures of all angles around a point?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
No matter how many angles there are - the sum around the point is 360°.
A^m/b^m = (a/b)^m
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

24. How do you calculate percent increases and decreases?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = 6(l^2)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any number b: b = -b if and only if b = 0.

25. In a circle of radius r - what is the formula for the diameter?
D = 2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
360°

26. What is p?
The ratio of corresponding sides of similar triangles.
Their sum is 180°.
(Circumference/diameter) of a circle - or approximately 3.14.
[(x1 + x2)/2] -[(y1 + y2)/2]

27. Law of exponents 1
Their sum is 90°.
B^m*b^n = b^m+n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = (1/2)bh.

28. Important binomial 3
Is a right triangle with a ratio of sides x:xv3:2x.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted right 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]

29. How do you find the probability that an event will occur?
A = 6(l^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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

30. Properties of zero 1
0 is the only number that is neither positive nor negative.
If a is negative and b is positive - then a < 0 < b.
B^m*b^n = b^m+n
An integer greater than one that is not prime.

31. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

32. What is true about the slopes of perpendicular lines?
M = (y2 - y1)/(x2 - x1)
V = pr^2h
For any integer n: 1^n = 1.
The product of their slopes is -1 (negative reciprocal).

33. Properties of zero 4
Write the percent over 100 and reduce.
Even numbers are divisible by 2 and odd numbers are not.
0 is the only number that is neither positive nor negative.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

34. Important binomial 1
Is a right triangle with a ratio of sides x:xv3:2x.
At least one of the factors is 0.
(x + y)(x - y) = x^2 - y^2
C = p2r

35. Properties of one 1
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For any number a: a * 1 = a and a / 1 = a.
Shifted down 2 units.
Corresponding sides of similar triangles are in proportion.

36. How do you find the length of an arc of a circle?
Write the percent as a decimal - and multiply.
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 two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Arc = (x°/360)(2pr) where x is the central angle.

37. What is the area of a square?
Then the product xy is a constant.
At least one of the factors is 0.
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.
A = s^2 or A =d^2/2 where d is the diagonal

38. 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.
Even numbers are divisible by 2 and odd numbers are not.
Shifted up 2 units.
Their sum is 180°.

39. What is a Venn diagram?
At least one of the factors is 0.
V = pr^2h
B^m/b^n = b^m-n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

40. Important binomial 2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
The product of their slopes is -1 (negative reciprocal).

41. What is the formula for the volume of a rectangular solid?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Even numbers are divisible by 2 and odd numbers are not.
V = lwh
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

42. In a circle of radius r - what is the formula for the circumference?
V = pr^2h
Write the percent as a decimal - and multiply.
A fraction whose denominator is 100 i.e. 17% = 17/100
C = p2r

43. Properties of zero 2
0 is the only number that is neither positive nor negative.
If a is negative and b is positive - then a < 0 < b.
B^m/b^n = b^m-n
A = [(s^2*v3)/4]

44. What is true about the slopes of parallel lines?
Equal slopes.
(Circumference/diameter) of a circle - or approximately 3.14.
For any number n: x^-n means 1/x^n.
Write the percent over 100 and reduce.

45. What is the sum of the measures of the n angles of a polygon with n sides?
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.
Then the product xy is a constant.
(n - 2)(180°)
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.

46. What is the sum of the measures of the four angles in a quadrilateral?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
360°
A = pr^2
A = [(s^2*v3)/4]

47. What formula is used for an average?
A = s^2 or A =d^2/2 where d is the diagonal
In the expression x^b - x is the base and b is the exponent.
Shifted left 2 units.
Avg = sum of n numbers/n

48. What are the properties of a square?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any right triangle - a^2 + b^2 = c^2.
Cannot is 0 - must is 1 - all others are in between.
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.

49. What is the triangle inequality?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Their sum is 180°.
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

50. What is a ratio?

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