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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. How do you convert a percent to a fraction or a decimal?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A fraction whose denominator is 100 i.e. 17% = 17/100
Write the percent over 100 and reduce.

2. What is a multiple of an integer?
Shifted down 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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.
Cannot is 0 - must is 1 - all others are in between.

3. Properties of zero 4
180°. If two or more angles form a straight angle - their sum is 180°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
B^m/b^n = b^m-n

4. Law of exponents 1
(n - 2)(180°)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
B^m*b^n = b^m+n
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

5. What do we mean by the slope of the line?
If a is negative and b is positive - then a < 0 < b.
M = (y2 - y1)/(x2 - x1)
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.

6. What is an even and an odd number?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(b^m)^n = b^mn
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Even numbers are divisible by 2 and odd numbers are not.

7. How do you calculate a weighted average?
Is a right triangle with a ratio of sides x:xv3:2x.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.

8. What is a ratio?

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9. What is the sum of the measures of the n angles of a polygon with n sides?
Avg = sum of n numbers/n
1 is a divisor (or factor) of every integer.
[(x1 + x2)/2] -[(y1 + y2)/2]
(n - 2)(180°)

10. What is the formula for the volume of a cylinder?
V = pr^2h
Shifted down 2 units.
Shifted up 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

11. How do you find the slope of a line?
In the expression x^b - x is the base and b is the exponent.
M = (y2 - y1)/(x2 - x1)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
They are both the same. A divisor or factor of an integer leaves no remainder.

12. How you convert a fraction or a decimal to a percent?
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.
Divide - then multiply by 100.
Write the percent over 100 and reduce.
A = 6(l^2)

13. What does it mean if y is directly proportional to x?
V = lwh
Area = (x°/360)(pr^2) where x is the central angle.
Then the quotient y/x is a constant.
Shifted down 2 units.

14. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
If a is negative and b is positive - then a < 0 < b.
Shifted left 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A fraction whose denominator is 100 i.e. 17% = 17/100

15. What is the formula for the area of a rectangle?
A = lw
360°
The ratio of corresponding sides of similar triangles.
An angle formed by extending the side of the polygon.

16. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted up 2 units.

17. Properties of zero 3
Set y = 0 - and solve.
0 is a multiple of every integer.
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.

18. In a circle of radius r - what is the formula for the diameter?
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.
D = 2r
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

19. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
A = bh
How steep the line is. Horizontal line = 0 - vertical has no slope.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

20. How do you find the x-intercept of a graph?
A = lw
Set y = 0 - and solve.
0 is the only number that is neither positive nor negative.
Then the product xy is a constant.

21. What are the important properties of a 45-45 - 90 triangle?
A = (1/2)bh.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
1 is the smallest positive odd integer.
Write the percent over 100 and reduce.

22. What is an exponent?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any number n: x^-n means 1/x^n.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
In the expression x^b - x is the base and b is the exponent.

23. How do you calculate percent increases and decreases?
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.
For any number a: a * 1 = a and a / 1 = a.
An equation that states that two ratios are equivalent. 4/6 = 10/15

24. What formula is used for an average?
Avg = sum of n numbers/n
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = s^2 or A =d^2/2 where d is the diagonal

25. Properties of one 2
Even numbers are divisible by 2 and odd numbers are not.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any integer n: 1^n = 1.
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.

26. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
V = lwh
Set y = 0 - and solve.
Equal slopes.
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.

27. What is a percent?
The set of all ordered pairs (x -y) such that y = f(x).
A fraction whose denominator is 100 i.e. 17% = 17/100
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Their sum is 90°.

28. What is true about the measures of the three angles in a triangle?
D = 2r
Their sum is 180°.
V = lwh
They are both the same. A divisor or factor of an integer leaves no remainder.

29. What is a prime number?
All positive and negative whole numbers - and zero.
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.
An angle formed by extending the side of the polygon.
For any right triangle - a^2 + b^2 = c^2.

30. What are the sum - difference - products - and quotient of two numbers?
All positive and negative whole numbers - and zero.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(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.

31. What is the graph of a function?
Divide - then multiply by 100.
The set of all ordered pairs (x -y) such that y = f(x).
Shifted left 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

32. What is true about the slopes of parallel lines?
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°.
Equal slopes.
A = (1/2)bh.
For any right triangle - a^2 + b^2 = c^2.

33. What are the properties of a parallelogram?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
No matter how many angles there are - the sum around the point is 360°.
A = s^2 or A =d^2/2 where d is the diagonal

34. What is the volume of a cube?
V = l^3
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(n - 2)(180°)
Is a right triangle with a ratio of sides x:xv3:2x.

35. For what values of a function is the function undefined?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
1 is the smallest positive odd integer.
Equal slopes.

36. Properties of zero 2
The two pairs of opposite angles formed are equal to each other.
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15

37. What is a divisor and a factor of an integer?
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted left 2 units.
A = bh
They are both the same. A divisor or factor of an integer leaves no remainder.

38. What is a composite number?
At least one of the factors is 0.
An integer greater than one that is not prime.
A = (1/2)bh.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

39. What is the formula for the volume of a rectangular solid?
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.
Their sum is 180°.
V = lwh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

40. What is true about the slopes of perpendicular lines?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.
Write the percent over 100 and reduce.
The product of their slopes is -1 (negative reciprocal).

41. In a circle of radius r - what is the formula for the area?
Even numbers are divisible by 2 and odd numbers are not.
A = pr^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
All positive and negative whole numbers - and zero.

42. What is a Venn diagram?
A fraction whose denominator is 100 i.e. 17% = 17/100
They are both the same. A divisor or factor of an integer leaves no remainder.
At least one of the factors is 0.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

43. In a circle of radius r - what is the formula for the circumference?
360°
C = p2r
For any right triangle - a^2 + b^2 = c^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

44. What are similar triangles?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = (1/2)bh.
A = lw
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?
Shifted right 2 units.
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.
360°

46. What is the triangle inequality?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = bh
The set of all ordered pairs (x -y) such that y = f(x).
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.

47. Law of exponents 3
(b^m)^n = b^mn
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Write the percent over 100 and reduce.

48. What are the properties of a square?
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Arc = (x°/360)(2pr) where x is the central angle.

49. What is the sum of the measures of all angles around a point?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Avg = sum of n numbers/n
No matter how many angles there are - the sum around the point is 360°.
(x + y)(x - y) = x^2 - y^2

50. What are the properties of a rectangle?
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number n: x^-n means 1/x^n.