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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.
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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 a Venn diagram?
At least one of the factors is 0.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

2. What is the measure of a straight angle?
For any number n: x^-n means 1/x^n.
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 = [(s^2*v3)/4]
180°. If two or more angles form a straight angle - their sum is 180°.

3. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If a is negative and b is positive - then a < 0 < b.
A = (1/2)bh.
For any number b: b = -b if and only if b = 0.

4. In a circle of radius r - what is the formula for the circumference?
A = bh
A^m/b^m = (a/b)^m
C = p2r
M = (y2 - y1)/(x2 - x1)

5. How do you find the probability that an event will occur?
Then the product xy is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(b^m)^n = b^mn
1 is the smallest positive odd integer.

6. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
360°
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
All positive and negative whole numbers - and zero.

7. What is the formula for the surface area of a rectangular solid?
Shifted right 2 units.
(b^m)^n = b^mn
For any number n: x^-n means 1/x^n.
A = 2(lw + lh + hw)

8. What is a prime number?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
0 is a multiple of every integer.
An angle formed by extending the side of the polygon.
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.

9. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
Shifted left 2 units.
C = p2r
(b^m)^n = b^mn

10. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A = s^2 or A =d^2/2 where d is the diagonal
360°
Shifted down 2 units.
All positive and negative whole numbers - and zero.

11. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
D = 2r
For any number a: a * 1 = a and a / 1 = a.
(Circumference/diameter) of a circle - or approximately 3.14.

12. What is a fractional exponent?
M = (y2 - y1)/(x2 - x1)
The set of all ordered pairs (x -y) such that y = f(x).
How steep the line is. Horizontal line = 0 - vertical has no slope.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

13. What is a divisor and a factor of an integer?
At least one of the factors is 0.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = s^2 or A =d^2/2 where d is the diagonal
Even numbers are divisible by 2 and odd numbers are not.

14. How do you find the length of an arc of a circle?
A fraction whose denominator is 100 i.e. 17% = 17/100
Avg = sum of n numbers/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°.
Arc = (x°/360)(2pr) where x is the central angle.

15. What is an even and an odd number?
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
360°

16. Law of exponents 1
B^m*b^n = b^m+n
The ratio of corresponding sides of similar triangles.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The two pairs of opposite angles formed are equal to each other.

17. Properties of one 4
1 is the smallest positive odd integer.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
In the expression x^b - x is the base and b is the exponent.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

18. What is true about the measures of the two acute angles in a right triangle?
360°
Their sum is 90°.
(Circumference/diameter) of a circle - or approximately 3.14.
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.

19. What is a ratio?

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20. What is a function?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
360°
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

21. What are the important properties of a 45-45 - 90 triangle?
1 is a divisor (or factor) of every integer.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Divide - then multiply by 100.

22. Law of exponents 4
A = lw
For any integer n: 1^n = 1.
A^m*b^m = (ab)^m
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

23. Law of exponents 3
For any number a: a * 1 = a and a / 1 = a.
(b^m)^n = b^mn
Divide - then multiply by 100.
A = s^2 or A =d^2/2 where d is the diagonal

24. In a circle of radius r - what is the formula for the area?
A = 6(l^2)
A = pr^2
They are both the same. A divisor or factor of an integer leaves no remainder.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

25. What is a negative exponent?
Set x = 0 - and solve.
Shifted up 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
For any number n: x^-n means 1/x^n.

26. What is the triangle inequality?
In the expression x^b - x is the base and b is the exponent.
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.
[(x1 + x2)/2] -[(y1 + y2)/2]

27. Properties of zero 2
Cannot is 0 - must is 1 - all others are in between.
If a is negative and b is positive - then a < 0 < b.
The product of their slopes is -1 (negative reciprocal).
B^m/b^n = b^m-n

28. What is the area of a square?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = s^2 or A =d^2/2 where d is the diagonal
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

29. In a circle of radius r - what is the formula for the diameter?
D = 2r
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = s^2 or A =d^2/2 where d is the diagonal
Arc = (x°/360)(2pr) where x is the central angle.

30. Law of exponents 2
B^m/b^n = b^m-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.
At least one of the factors is 0.
All positive and negative whole numbers - and zero.

31. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
V = pr^2h
Their sum is 180°.
(Circumference/diameter) of a circle - or approximately 3.14.

32. Properties of square roots
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

33. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted up 2 units.
The two pairs of opposite angles formed are equal to each other.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

34. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any number b: b = -b if and only if b = 0.

35. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
1 is the smallest positive odd integer.
Shifted up 2 units.
Shifted left 2 units.
D = 2r

36. Law of exponents 5
360°
A^m/b^m = (a/b)^m
180°. If two or more angles form a straight angle - their sum is 180°.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

37. What is the distributive law?
0 is a multiple of every integer.
The product of their slopes is -1 (negative reciprocal).
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Write the percent as a decimal - and multiply.

38. What is a proportion?
1 is a divisor (or factor) of every integer.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Then the quotient y/x is a constant.

39. What are similar triangles?
Shifted up 2 units.
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

40. Important binomial 1
1 is a divisor (or factor) of every integer.
(x + y)(x - y) = x^2 - y^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
B^m*b^n = b^m+n

41. What is true about the measures of the three angles in a triangle?
Area = (x°/360)(pr^2) where x is the central angle.
D = 2r
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Their sum is 180°.

42. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
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 any right triangle - a^2 + b^2 = c^2.
(n - 2)(180°)

43. What does it mean if y is directly proportional to x?
Avg = sum of n numbers/n
Then the quotient y/x is a constant.
B^m*b^n = b^m+n
A^m/b^m = (a/b)^m

44. What is an exterior angle of a polygon?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Their sum is 90°.
An angle formed by extending the side of the polygon.
At least one of the factors is 0.

45. What is the Pythagorean theorem?
If a is negative and b is positive - then a < 0 < b.
For any number b: b = -b if and only if b = 0.
Then the product xy is a constant.
For any right triangle - a^2 + b^2 = c^2.

46. What is the sum of the measures of the n angles of a polygon with n sides?
An integer greater than one that is not prime.
The ratio of corresponding sides of similar triangles.
180°. If two or more angles form a straight angle - their sum is 180°.
(n - 2)(180°)

47. What are the properties of a rectangle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(n - 2)(180°)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

48. What is an integer?
A = pr^2
For any number b: b = -b if and only if b = 0.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
All positive and negative whole numbers - and zero.

49. If the product of two or more numbers is 0 - what do you know about the numbers?
(Circumference/diameter) of a circle - or approximately 3.14.
A = (1/2)bh.
1 is a divisor (or factor) of every integer.
At least one of the factors is 0.

50. 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.
An angle formed by extending the side of the polygon.
All positive and negative whole numbers - and zero.
B^m/b^n = b^m-n

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