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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. If the product of two or more numbers is 0 - what do you know about the numbers?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Corresponding sides of similar triangles are in proportion.
Avg = sum of n numbers/n
At least one of the factors is 0.

2. What are the quotient and the remainder?

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3. In a circle of radius r - what is the formula for the circumference?
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.
Write the percent over 100 and reduce.
V = lwh
C = p2r

4. What is the sum of the measures of the n angles of a polygon with n sides?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Avg = sum of n numbers/n
(n - 2)(180°)
Arc = (x°/360)(2pr) where x is the central angle.

5. How do you find the probability that an event will occur?
Equal slopes.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 180°.
They are both the same. A divisor or factor of an integer leaves no remainder.

6. Properties of one 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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted up 2 units.
1 is the smallest positive odd integer.

7. How do you calculate a weighted average?
A^m*b^m = (ab)^m
The two pairs of opposite angles formed are equal to each other.
V = l^3
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

8. How do you convert a percent to a fraction or a decimal?
No matter how many angles there are - the sum around the point is 360°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Write the percent over 100 and reduce.
How steep the line is. Horizontal line = 0 - vertical has no slope.

9. What is the formula for the volume of a rectangular solid?
V = lwh
All positive and negative whole numbers - and zero.
A = pr^2
The set of all ordered pairs (x -y) such that y = f(x).

10. How do we write the equation of a line?
Cannot is 0 - must is 1 - all others are in between.
M = (y2 - y1)/(x2 - x1)
A fraction whose denominator is 100 i.e. 17% = 17/100
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

11. What is the formula for the surface area of a rectangular solid?
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.
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°.

12. What is true about the measures of the four angles formed by two intersecting lines?
Their sum is 90°.
A = pr^2
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The two pairs of opposite angles formed are equal to each other.

13. What is the distributive law?
A = 6(l^2)
A^m*b^m = (ab)^m
0 is a multiple of every integer.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

14. What is a ratio?

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15. What is the measure of a straight angle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
180°. If two or more angles form a straight angle - their sum is 180°.
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°.

16. Law of exponents 5
Shifted right 2 units.
Area = (x°/360)(pr^2) where x is the central angle.
A^m/b^m = (a/b)^m
A^m*b^m = (ab)^m

17. Law of exponents 3
B^m/b^n = b^m-n
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°.
The set of all ordered pairs (x -y) such that y = f(x).
(b^m)^n = b^mn

18. What is the sum of the measures of the four angles in a quadrilateral?
All positive and negative whole numbers - and zero.
360°
An integer greater than one that is not prime.
[(x1 + x2)/2] -[(y1 + y2)/2]

19. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(Circumference/diameter) of a circle - or approximately 3.14.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

20. Properties of zero 2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
If a is negative and b is positive - then a < 0 < b.
Their sum is 180°.
Write the percent over 100 and reduce.

21. What is the square root of a number?
For any integer n: 1^n = 1.
360°
Shifted down 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

22. What is a fractional exponent?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = [(s^2*v3)/4]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

23. How do you find the length of an arc of a circle?
Then the product xy is a constant.
Arc = (x°/360)(2pr) where x is the central angle.
For any right triangle - a^2 + b^2 = c^2.
A = 2(lw + lh + hw)

24. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
If a is negative and b is positive - then a < 0 < b.
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

25. What are the sum - difference - products - and quotient of two numbers?
For any right triangle - a^2 + b^2 = c^2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
360°

26. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted right 2 units.

27. What is true about the areas of similar triangles?
0 is the only number that is neither positive nor negative.
Set x = 0 - and solve.
A = s^2 or A =d^2/2 where d is the diagonal
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

28. What is the triangle inequality?
[(x1 + x2)/2] -[(y1 + y2)/2]
Divide - then multiply by 100.
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°.

29. What is the volume of a cube?
V = l^3
Even numbers are divisible by 2 and odd numbers are not.
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.
An angle formed by extending the side of the polygon.

30. 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.
For any number b: b = -b if and only if b = 0.
Shifted right 2 units.
In the expression x^b - x is the base and b is the exponent.

31. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
A = lw
B^m*b^n = b^m+n
(b^m)^n = b^mn
Shifted up 2 units.

32. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
1 is the smallest positive odd integer.
Avg = sum of n numbers/n
V = pr^2h

33. Properties of square roots
Their sum is 90°.
Write the percent over 100 and reduce.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
How steep the line is. Horizontal line = 0 - vertical has no slope.

34. Properties of zero 4
The two pairs of opposite angles formed are equal to each other.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any number n: x^-n means 1/x^n.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

35. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
A = 2(lw + lh + hw)
V = l^3
If a is negative and b is positive - then a < 0 < b.

36. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
For any integer n: 1^n = 1.
Set y = 0 - and solve.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

37. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
A = (1/2)bh.
All positive and negative whole numbers - and zero.
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.

38. How you convert a fraction or a decimal to a percent?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Divide - then multiply by 100.
For any number n: x^-n means 1/x^n.
M = (y2 - y1)/(x2 - x1)

39. Properties of zero 3
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A^m*b^m = (ab)^m
0 is a multiple of every integer.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

40. How do you find the slope of a line?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
M = (y2 - y1)/(x2 - x1)
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

41. Properties of one 2
A fraction whose denominator is 100 i.e. 17% = 17/100
For any integer n: 1^n = 1.
A = bh
Set y = 0 - and solve.

42. What are the median and the mode of a set of data?
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
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
M = (y2 - y1)/(x2 - x1)

43. What is a multiple 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.
A^m/b^m = (a/b)^m
An integer greater than one that is not prime.
Arc = (x°/360)(2pr) where x is the central angle.

44. In a circle of radius r - what is the formula for the diameter?
A = 6(l^2)
D = 2r
Their sum is 180°.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

45. What is a function?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(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.

46. What is a Venn diagram?
Cannot is 0 - must is 1 - all others are in between.
D = 2r
A = s^2 or A =d^2/2 where d is the diagonal
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

47. What is true about the slopes of perpendicular lines?
Set x = 0 - and solve.
The product of their slopes is -1 (negative reciprocal).
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
An angle formed by extending the side of the polygon.

48. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The set of all ordered pairs (x -y) such that y = f(x).
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°.
Set x = 0 - and solve.

49. Properties of zero 5
Write the percent as a decimal - and multiply.
0 is the only number that is neither positive nor negative.
For any number b: b = -b if and only if b = 0.
(x + y)(x - y) = x^2 - y^2

50. How do you find the area of a sector of a circle?
Divide - then multiply by 100.
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.
Area = (x°/360)(pr^2) where x is the central angle.
Arc = (x°/360)(2pr) where x is the central angle.