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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 a proportion?
For any number b: b = -b if and only if b = 0.
An equation that states that two ratios are equivalent. 4/6 = 10/15
V = lwh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

2. Properties of zero 3
In the expression x^b - x is the base and b is the exponent.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
0 is a multiple of every integer.

3. What is true about the measures of the four angles formed by two intersecting lines?
A^m/b^m = (a/b)^m
The two pairs of opposite angles formed are equal to each other.
360°
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

4. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
1 is a divisor (or factor) of every integer.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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°.

5. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A = 6(l^2)
Divide - then multiply by 100.
Shifted down 2 units.
Their sum is 180°.

6. What is the sum of the measures of all angles around a point?
360°
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
The set of all ordered pairs (x -y) such that y = f(x).
No matter how many angles there are - the sum around the point is 360°.

7. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
1 is the smallest positive odd integer.
M = (y2 - y1)/(x2 - x1)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

8. What is a composite number?
(Circumference/diameter) of a circle - or approximately 3.14.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
An integer greater than one that is not prime.
V = l^3

9. How do you find the slope of a line?
Then the quotient y/x is a constant.
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.
M = (y2 - y1)/(x2 - x1)

10. How do you convert a percent to a fraction or a decimal?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^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.
Write the percent over 100 and reduce.

11. What is true about the measures of the three angles in a triangle?
Set y = 0 - and solve.
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 180°.
1 is a divisor (or factor) of every integer.

12. For what values of a function is the function undefined?
Area = (x°/360)(pr^2) where x is the central angle.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = 2(lw + lh + hw)

13. What are the median and the mode of a set of data?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
V = pr^2h
Their sum is 180°.
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.

14. What are the properties of a square?
(x + y)(x - y) = x^2 - y^2
For any number n: x^-n means 1/x^n.
(b^m)^n = b^mn
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.

15. What is the formula for the surface area of a rectangular solid?
They are both the same. A divisor or factor of an integer leaves no remainder.
A = 2(lw + lh + hw)
M = (y2 - y1)/(x2 - x1)
Area = (x°/360)(pr^2) where x is the central angle.

16. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
D = 2r
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The product of their slopes is -1 (negative reciprocal).

17. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
C = p2r
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

18. How do you find the y-intercept of a graph?
V = l^3
(x + y)(x - y) = x^2 - y^2
Set x = 0 - and solve.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

19. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
1 is a divisor (or factor) of every integer.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

20. What is a percent?
The product of their slopes is -1 (negative reciprocal).
How steep the line is. Horizontal line = 0 - vertical has no slope.
A fraction whose denominator is 100 i.e. 17% = 17/100
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

21. What is the probability of an event that cannot occur? That must occur?
1 is a divisor (or factor) of every integer.
Cannot is 0 - must is 1 - all others are in between.
V = l^3
A = pr^2

22. Law of exponents 5
Shifted left 2 units.
B^m*b^n = b^m+n
For any number b: b = -b if and only if b = 0.
A^m/b^m = (a/b)^m

23. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
If a is negative and b is positive - then a < 0 < b.
An integer greater than one that is not prime.

24. What is a fractional exponent?
A = [(s^2*v3)/4]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(Circumference/diameter) of a circle - or approximately 3.14.

25. What is the formula for the volume of a rectangular solid?
V = lwh
A^m*b^m = (ab)^m
(b^m)^n = b^mn
Their sum is 180°.

26. What is the distributive law?
B^m/b^n = b^m-n
For any integer n: 1^n = 1.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = 6(l^2)

27. What is the formula for the surface area of a cube?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = 6(l^2)
Even numbers are divisible by 2 and odd numbers are not.
For any integer n: 1^n = 1.

28. What is the ratio of similitude?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Then the quotient y/x is a constant.
The ratio of corresponding sides of similar triangles.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

29. 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.
B^m/b^n = b^m-n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

30. How do we write the equation of a line?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Is a right triangle with a ratio of sides x:xv3:2x.
Arc = (x°/360)(2pr) where x is the central angle.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

31. Law of exponents 2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
B^m/b^n = b^m-n

32. What is the formula for the area of a triangle?
V = lwh
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = (1/2)bh.
B^m*b^n = b^m+n

33. Law of exponents 1
0 is a multiple of every integer.
B^m*b^n = b^m+n
Shifted left 2 units.
D = 2r

34. In a circle of radius r - what is the formula for the diameter?
D = 2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = [(s^2*v3)/4]

35. What is an exterior angle of a triangle?
A = pr^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.
No matter how many angles there are - the sum around the point is 360°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

36. What is an exterior angle of a polygon?
A = [(s^2*v3)/4]
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
An angle formed by extending the side of the polygon.
M = (y2 - y1)/(x2 - x1)

37. What is the formula for the area of a parallelogram?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = bh
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

38. What is a divisor and a factor of an integer?
[(x1 + x2)/2] -[(y1 + y2)/2]
They are both the same. A divisor or factor of an integer leaves no remainder.
If a is negative and b is positive - then a < 0 < b.
For any number a: a * 1 = a and a / 1 = a.

39. If the product of two or more numbers is 0 - what do you know about the numbers?
A = 2(lw + lh + hw)
Shifted up 2 units.
At least one of the factors is 0.
They are both the same. A divisor or factor of an integer leaves no remainder.

40. What is a Venn diagram?
Set y = 0 - and solve.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Even numbers are divisible by 2 and odd numbers are not.
180°. If two or more angles form a straight angle - their sum is 180°.

41. What is the sum of the measures of the n angles of a polygon with n sides?
All positive and negative whole numbers - and zero.
Set x = 0 - and solve.
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.
(n - 2)(180°)

42. What is the relationship between a radius of a circle and a line that is tangent to the circle?
A = bh
For any number a: a * 1 = a and a / 1 = a.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

43. What are the important properties of a 45-45 - 90 triangle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Set y = 0 - and solve.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = s^2 or A =d^2/2 where d is the diagonal

44. Properties of one 2
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any integer n: 1^n = 1.
(n - 2)(180°)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

45. How do you calculate percent increases and decreases?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Shifted left 2 units.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Corresponding sides of similar triangles are in proportion.

46. What is a prime number?
A = bh
A = lw
360°
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.

47. What is an exponent?
[(x1 + x2)/2] -[(y1 + y2)/2]
C = p2r
In the expression x^b - x is the base and b is the exponent.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

48. In a circle of radius r - what is the formula for the area?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = pr^2
Then the product xy is a constant.
D = 2r

49. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
1 is a divisor (or factor) of every integer.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

50. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted up 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.