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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 is the formula for the volume of a rectangular solid?
C = p2r
V = lwh
A = [(s^2*v3)/4]
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

2. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
All positive and negative whole numbers - and zero.
For any integer n: 1^n = 1.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

3. What are the quotient and the remainder?

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4. In a circle of radius r - what is the formula for the area?
A = pr^2
A^m/b^m = (a/b)^m
Cannot is 0 - must is 1 - all others are in between.
B^m/b^n = b^m-n

5. What is the formula for the volume of a cylinder?
(b^m)^n = b^mn
B^m/b^n = b^m-n
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.
V = pr^2h

6. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

7. What is a ratio?

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8. Properties of one 4
(b^m)^n = b^mn
1 is the smallest positive odd integer.
A = lw
Then the product xy is a constant.

9. What is the formula for the area of a triangle?
A = (1/2)bh.
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.
(Circumference/diameter) of a circle - or approximately 3.14.

10. What is special formula for the area of an equilateral triangle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = [(s^2*v3)/4]
The two pairs of opposite angles formed are equal to each other.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

11. If the product of two or more numbers is 0 - what do you know about the numbers?
[(x1 + x2)/2] -[(y1 + y2)/2]
How steep the line is. Horizontal line = 0 - vertical has no slope.
1 is a divisor (or factor) of every integer.
At least one of the factors is 0.

12. In a circle of radius r - what is the formula for the diameter?
D = 2r
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Write the percent over 100 and reduce.

13. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = [(s^2*v3)/4]
A = bh
A = 2(lw + lh + hw)

14. What are similar triangles?
1 is the smallest positive odd integer.
Avg = sum of n numbers/n
No matter how many angles there are - the sum around the point is 360°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

15. How do you calculate percent increases and decreases?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A^m*b^m = (ab)^m
For any right triangle - a^2 + b^2 = c^2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

16. What is the probability of an event that cannot occur? That must occur?
They are both the same. A divisor or factor of an integer leaves no remainder.
Cannot is 0 - must is 1 - all others are in between.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
At least one of the factors is 0.

17. What is true about the measures of the two acute angles in a right triangle?
B^m*b^n = b^m+n
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 90°.
Shifted down 2 units.

18. Properties of one 1
(b^m)^n = b^mn
180°. If two or more angles form a straight angle - their sum is 180°.
For any number a: a * 1 = a and a / 1 = a.
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.

19. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
A = (1/2)bh.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Avg = sum of n numbers/n

20. Properties of zero 4
Then the quotient y/x is a constant.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

21. How do you find a percent of a number?
1 is the smallest positive odd integer.
Write the percent as a decimal - and multiply.
V = l^3
No matter how many angles there are - the sum around the point is 360°.

22. What is the sum of the measures of the four angles in a quadrilateral?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
360°

23. How do you find the y-intercept of a graph?
A = s^2 or A =d^2/2 where d is the diagonal
Shifted down 2 units.
Set x = 0 - and solve.
Set y = 0 - and solve.

24. What does it mean if y is directly proportional to x?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted down 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.
Then the quotient y/x is a constant.

25. 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.
A^m*b^m = (ab)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = 6(l^2)

26. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

27. What is an exterior angle of a triangle?
Their sum is 90°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any right triangle - a^2 + b^2 = c^2.
1 is the smallest positive odd integer.

28. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
A = [(s^2*v3)/4]
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
360°
Arc = (x°/360)(2pr) where x is the central angle.

29. What is a function?
For any number n: x^-n means 1/x^n.
Shifted left 2 units.
V = l^3
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

30. 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.
Cannot is 0 - must is 1 - all others are in between.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Corresponding sides of similar triangles are in proportion.

31. What are the sum - difference - products - and quotient of two numbers?
Their sum is 90°.
B^m*b^n = b^m+n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any integer n: 1^n = 1.

32. What are the properties of a rectangle?
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.
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

33. How do we write the equation of a line?
Cannot is 0 - must is 1 - all others are in between.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
0 is a multiple of every integer.
V = pr^2h

34. What is a prime number?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
1 is a divisor (or factor) of every integer.
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 any number a: a * 1 = a and a / 1 = a.

35. What is the graph of a function?
B^m/b^n = b^m-n
(b^m)^n = b^mn
The set of all ordered pairs (x -y) such that y = f(x).
V = l^3

36. What are the important properties of 30-60-90 triangle?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Is a right triangle with a ratio of sides x:xv3:2x.
A^m*b^m = (ab)^m
A = pr^2

37. What is a Venn diagram?
For any integer n: 1^n = 1.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any number a: a * 1 = a and a / 1 = a.
A^m/b^m = (a/b)^m

38. What is the Pythagorean theorem?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.
Then the product xy is a constant.

39. What is a fractional exponent?
For any right triangle - a^2 + b^2 = c^2.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any number a: a * 1 = a and a / 1 = a.
The two pairs of opposite angles formed are equal to each other.

40. What is the formula for the area of a parallelogram?
A = bh
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 the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
M = (y2 - y1)/(x2 - x1)

41. Properties of zero 3
0 is a multiple of every integer.
Area = (x°/360)(pr^2) where x is the central angle.
In the expression x^b - x is the base and b is the exponent.
(b^m)^n = b^mn

42. What is the volume of a cube?
No matter how many angles there are - the sum around the point is 360°.
V = l^3
0 is the only number that is neither positive nor negative.
Set x = 0 - and solve.

43. What does it mean if y is inversely proportional to x?
All positive and negative whole numbers - and zero.
Is a right triangle with a ratio of sides x:xv3:2x.
For any number b: b = -b if and only if b = 0.
Then the product xy is a constant.

44. What is the triangle inequality?
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = pr^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

45. What important property do similar triangles have?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
They are both the same. A divisor or factor of an integer leaves no remainder.
Corresponding sides of similar triangles are in proportion.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

46. What formula is used for an average?
Set x = 0 - and solve.
V = pr^2h
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Avg = sum of n numbers/n

47. How do you find the x-intercept of a graph?
0 is a multiple of every integer.
Then the quotient y/x is a constant.
Set y = 0 - and solve.
Their sum is 180°.

48. Law of exponents 5
0 is the only number that is neither positive nor negative.
A^m/b^m = (a/b)^m
1 is a divisor (or factor) of every integer.
(Circumference/diameter) of a circle - or approximately 3.14.

49. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted right 2 units.
360°
How steep the line is. Horizontal line = 0 - vertical has no slope.

50. What is the distance formula?
Avg = sum of n numbers/n
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]