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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 quotient and the remainder?

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2. If you were given the graph of y = f(x) - what does f(a) represent?
For any number b: b = -b if and only if b = 0.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
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.

3. What is a negative exponent?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number a: a * 1 = a and a / 1 = a.
For any number n: x^-n means 1/x^n.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

4. In a circle of radius r - what is the formula for the area?
A = pr^2
A = bh
1 is a divisor (or factor) of every integer.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

5. Important binomial 3
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
At least one of the factors is 0.
1 is a divisor (or factor) of every integer.

6. In a circle of radius r - what is the formula for the circumference?
C = p2r
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.
Then the product xy is a constant.
An angle formed by extending the side of the polygon.

7. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Then the quotient y/x is a constant.
At least one of the factors is 0.
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.
Shifted left 2 units.

8. What is true about the measures of the two acute angles in a right triangle?
For any number b: b = -b if and only if b = 0.
Their sum is 90°.
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

9. Properties of zero 2
A = s^2 or A =d^2/2 where d is the diagonal
If a is negative and b is positive - then a < 0 < b.
The ratio of corresponding sides of similar triangles.
Area = (x°/360)(pr^2) where x is the central angle.

10. How do you calculate a weighted average?
For any integer n: 1^n = 1.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Is a right triangle with a ratio of sides x:xv3:2x.

11. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
They are both the same. A divisor or factor of an integer leaves no remainder.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

12. In a circle of radius r - what is the formula for the diameter?
D = 2r
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Area = (x°/360)(pr^2) where x is the central angle.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

13. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

14. Properties of square roots
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
They are both the same. A divisor or factor of an integer leaves no remainder.
Even numbers are divisible by 2 and odd numbers are not.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

15. What is a ratio?

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16. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
Shifted right 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Even numbers are divisible by 2 and odd numbers are not.

17. What is the distance formula?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Arc = (x°/360)(2pr) where x is the central angle.

18. What is the measure of a straight angle?
Divide - then multiply by 100.
Cannot is 0 - must is 1 - all others are in between.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
180°. If two or more angles form a straight angle - their sum is 180°.

19. Properties of zero 4
They are both the same. A divisor or factor of an integer leaves no remainder.
V = pr^2h
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

20. Properties of zero 1
0 is the only number that is neither positive nor negative.
Shifted down 2 units.
A = 2(lw + lh + hw)
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.

21. What are the properties of a square?
Arc = (x°/360)(2pr) where x is the central angle.
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted right 2 units.
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.

22. Law of exponents 5
A^m/b^m = (a/b)^m
Avg = sum of n numbers/n
Write the percent over 100 and reduce.
Their sum is 90°.

23. What is true about the measures of the three angles in a triangle?
Shifted left 2 units.
Their sum is 180°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
[(x1 + x2)/2] -[(y1 + y2)/2]

24. What does it mean if y is directly proportional to x?
A^m*b^m = (ab)^m
Then the quotient y/x is a constant.
Divide - then multiply by 100.
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.

25. Properties of zero 5
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any number b: b = -b if and only if b = 0.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
V = pr^2h

26. What is the formula for the area of a triangle?
A = (1/2)bh.
V = l^3
Then the product xy is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

27. How do you calculate percent increases and decreases?
Corresponding sides of similar triangles are in proportion.
0 is the only number that is neither positive nor negative.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

28. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(n - 2)(180°)
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.

29. What formula is used for an average?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The two pairs of opposite angles formed are equal to each other.
Avg = sum of n numbers/n
Then the product xy is a constant.

30. What is special formula for the area of an equilateral triangle?
Corresponding sides of similar triangles are in proportion.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = [(s^2*v3)/4]
Write the percent as a decimal - and multiply.

31. What is true about the slopes of perpendicular lines?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The product of their slopes is -1 (negative reciprocal).
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.

32. What is the sum of the measures of the n angles of a polygon with n sides?
In the expression x^b - x is the base and b is the exponent.
(n - 2)(180°)
Their sum is 180°.
360°

33. What is the triangle inequality?
A = s^2 or A =d^2/2 where d is the diagonal
B^m/b^n = b^m-n
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.

34. Important binomial 1
Cannot is 0 - must is 1 - all others are in between.
(x + y)(x - y) = x^2 - y^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

35. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
V = l^3
Set x = 0 - and solve.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

36. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
C = p2r
For any number n: x^-n means 1/x^n.

37. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Arc = (x°/360)(2pr) where x is the central angle.
0 is a multiple of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted right 2 units.

38. Properties of one 2
B^m*b^n = b^m+n
Equal slopes.
For any integer n: 1^n = 1.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

39. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
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 fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Shifted down 2 units.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

40. What is a divisor and a factor of an integer?
Their sum is 180°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted down 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.

41. How do you convert a percent to a fraction or a decimal?
B^m/b^n = b^m-n
Write the percent over 100 and reduce.
Even numbers are divisible by 2 and odd numbers are not.
Cannot is 0 - must is 1 - all others are in between.

42. Law of exponents 3
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(b^m)^n = b^mn
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted down 2 units.

43. What does it mean if y is inversely proportional to x?
Arc = (x°/360)(2pr) where x is the central angle.
Then the product xy is a constant.
Shifted down 2 units.
Write the percent as a decimal - and multiply.

44. What is the formula for the volume of a rectangular solid?
V = lwh
The two pairs of opposite angles formed are equal to each other.
If a is negative and b is positive - then a < 0 < b.
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°.

45. Important binomial 2
Then the quotient y/x is a constant.
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 down 2 units.

46. What is an exponent?
[(x1 + x2)/2] -[(y1 + y2)/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.
In the expression x^b - x is the base and b is the exponent.
0 is the only number that is neither positive nor negative.

47. What is an even and an odd number?
Arc = (x°/360)(2pr) where x is the central angle.
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 180°.
V = pr^2h

48. How do you find the area of a sector of a circle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Area = (x°/360)(pr^2) where x is the central angle.
0 is the only number that is neither positive nor negative.

49. What are the important properties of 30-60-90 triangle?
In the expression x^b - x is the base and b is the exponent.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Is a right triangle with a ratio of sides x:xv3:2x.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

50. What is the probability of an event that cannot occur? That must occur?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
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 ratio of corresponding sides of similar triangles.
Cannot is 0 - must is 1 - all others are in between.