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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. Properties of one 3
For any number n: x^-n means 1/x^n.
A = 2(lw + lh + hw)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
1 is a divisor (or factor) of every integer.

2. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Avg = sum of n numbers/n
A^m*b^m = (ab)^m
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

3. What is the formula for the volume of a cylinder?
An angle formed by extending the side of the polygon.
B^m/b^n = b^m-n
V = pr^2h
A = bh

4. What is an exterior angle of a polygon?
Then the product xy is a constant.
An angle formed by extending the side of the polygon.
Avg = sum of n numbers/n
Then the quotient y/x is a constant.

5. What does it mean if y is directly proportional to x?
For any number n: x^-n means 1/x^n.
M = (y2 - y1)/(x2 - x1)
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 quotient y/x is a constant.

6. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For any number b: b = -b if and only if b = 0.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted up 2 units.
Then the quotient y/x is a constant.

7. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
V = pr^2h
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°.
1 is the smallest positive odd integer.
The ratio of corresponding sides of similar triangles.

8. What is the midpoint formula?
A = s^2 or A =d^2/2 where d is the diagonal
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number n: x^-n means 1/x^n.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

9. What is the ratio of similitude?
Area = (x°/360)(pr^2) where x is the central angle.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Equal slopes.
The ratio of corresponding sides of similar triangles.

10. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
The ratio of corresponding sides of similar triangles.
An integer greater than one that is not prime.
C = p2r

11. What is the formula for the surface area of a cube?
Shifted left 2 units.
A = 6(l^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.
Shifted down 2 units.

12. What is the triangle inequality?
(x + y)(x - y) = x^2 - y^2
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.
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted down 2 units.

13. What is true about the measures of the three angles in a triangle?
A^m*b^m = (ab)^m
Their sum is 180°.
V = pr^2h
At least one of the factors is 0.

14. 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).
Their sum is 180°.
V = l^3

15. What are the quotient and the remainder?

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16. What is the volume of a cube?
1 is the smallest positive odd integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = pr^2h
V = l^3

17. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
360°
B^m*b^n = b^m+n
An angle formed by extending the side of the polygon.

18. How do you calculate percent increases and decreases?
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
Cannot is 0 - must is 1 - all others are in between.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

19. What is a Venn diagram?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
In the expression x^b - x is the base and b is the exponent.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

20. Properties of one 4
1 is the smallest positive odd integer.
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°.
Shifted right 2 units.

21. How do we write the equation of a line?
They are both the same. A divisor or factor of an integer leaves no remainder.
Set x = 0 - and solve.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

22. What is a composite number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
1 is the smallest positive odd integer.
C = p2r
An integer greater than one that is not prime.

23. What is the sum of the measures of the n angles of a polygon with n sides?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(n - 2)(180°)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

24. What does it mean if y is inversely proportional to x?
The two pairs of opposite angles formed are equal to each other.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
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.
Then the product xy is a constant.

25. In a circle of radius r - what is the formula for the area?
A = pr^2
B^m*b^n = b^m+n
In the expression x^b - x is the base and b is the exponent.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

26. What is the formula for the area of a triangle?
Even numbers are divisible by 2 and odd numbers are not.
Arc = (x°/360)(2pr) where x is the central angle.
A = (1/2)bh.
A = lw

27. What are the properties of a rectangle?
An angle formed by extending the side of the polygon.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Corresponding sides of similar triangles are in proportion.

28. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Cannot is 0 - must is 1 - all others are in between.
Write the percent as a decimal - and multiply.
Shifted left 2 units.
(n - 2)(180°)

29. Law of exponents 5
A^m/b^m = (a/b)^m
M = (y2 - y1)/(x2 - x1)
1 is a divisor (or factor) of every integer.
Shifted down 2 units.

30. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Write the percent over 100 and reduce.
For any number a: a * 1 = a and a / 1 = a.
A = bh

31. 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.
Shifted up 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
An angle formed by extending the side of the polygon.

32. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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°.
An integer greater than one that is not prime.
B^m/b^n = b^m-n

33. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
A = 6(l^2)
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

34. What are the properties of a parallelogram?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(b^m)^n = b^mn
Divide - then multiply by 100.

35. Properties of zero 2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
If a is negative and b is positive - then a < 0 < b.
The set of all ordered pairs (x -y) such that y = f(x).
Write the percent over 100 and reduce.

36. What is an exterior angle of a triangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Then the product xy is a constant.
Divide - then multiply by 100.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

37. What is the sum of the measures of the four angles in a quadrilateral?
A fraction whose denominator is 100 i.e. 17% = 17/100
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
360°

38. How do you find the area of a sector of a circle?
0 is the only number that is neither positive nor negative.
A = bh
Area = (x°/360)(pr^2) where x is the central angle.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

39. What is a function?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

40. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A = lw
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.
0 is the only number that is neither positive nor negative.
Shifted down 2 units.

41. Important binomial 2
Arc = (x°/360)(2pr) where x is the central angle.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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.

42. If the product of two or more numbers is 0 - what do you know about the numbers?
A = (1/2)bh.
At least one of the factors is 0.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.

43. What are the properties of a square?
A = 6(l^2)
An angle formed by extending the side of the polygon.
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.
A^m*b^m = (ab)^m

44. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
An integer greater than one that is not prime.
They are both the same. A divisor or factor of an integer leaves no remainder.
Arc = (x°/360)(2pr) where x is the central angle.

45. How do you calculate a weighted average?
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.
V = pr^2h
For any number a: a * 1 = a and a / 1 = a.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

46. 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.
Write the percent as a decimal - and multiply.
Is a right triangle with a ratio of sides x:xv3:2x.
The ratio of corresponding sides of similar triangles.

47. What is a proportion?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
1 is the smallest positive odd integer.

48. How do you find the length of an arc of a circle?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number b: b = -b if and only if b = 0.
(b^m)^n = b^mn
Arc = (x°/360)(2pr) where x is the central angle.

49. What is the formula for the volume of a rectangular solid?
V = lwh
A = 2(lw + lh + hw)
Area = (x°/360)(pr^2) where x is the central angle.
(b^m)^n = b^mn

50. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Then the product xy is a constant.
Write the percent as a decimal - and multiply.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.