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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 are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = 2(lw + lh + hw)
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.
For any number n: x^-n means 1/x^n.

2. 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.
Set y = 0 - and solve.
A fraction whose denominator is 100 i.e. 17% = 17/100
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

3. Law of exponents 2
For any number a: a * 1 = a and a / 1 = a.
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°.
B^m/b^n = b^m-n
V = l^3

4. Properties of square roots
For any number n: x^-n means 1/x^n.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(b^m)^n = b^mn

5. What is the formula for the area of a triangle?
A = (1/2)bh.
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.
The product of their slopes is -1 (negative reciprocal).
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

6. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
The product of their slopes is -1 (negative reciprocal).
Arc = (x°/360)(2pr) where x is the central angle.
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°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

7. What is the formula for the volume of a cylinder?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Then the product xy is a constant.
V = pr^2h
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

8. How do you find the y-intercept of a graph?
(n - 2)(180°)
Set x = 0 - and solve.
A = (1/2)bh.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

9. If the product of two or more numbers is 0 - what do you know about the numbers?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Then the product xy is a constant.
360°
At least one of the factors is 0.

10. In a circle of radius r - what is the formula for the area?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
1 is a divisor (or factor) of every integer.
For any number b: b = -b if and only if b = 0.
A = pr^2

11. What formula is used for an average?
At least one of the factors is 0.
A = pr^2
Their sum is 90°.
Avg = sum of n numbers/n

12. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Then the product xy is a constant.
Is a right triangle with a ratio of sides x:xv3:2x.
A = s^2 or A =d^2/2 where d is the diagonal

13. What is the formula for the volume of a rectangular solid?
[(x1 + x2)/2] -[(y1 + y2)/2]
V = lwh
A = (1/2)bh.
180°. If two or more angles form a straight angle - their sum is 180°.

14. What is a multiple of an integer?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Then the quotient y/x is a constant.
(b^m)^n = b^mn
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.

15. What is a divisor and a factor of an integer?
Area = (x°/360)(pr^2) where x is the central angle.
They are both the same. A divisor or factor of an integer leaves no remainder.
0 is the only number that is neither positive nor negative.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

16. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
V = l^3
The set of all ordered pairs (x -y) such that y = f(x).
A fraction whose denominator is 100 i.e. 17% = 17/100

17. What is true about the measures of the three angles in a triangle?
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.
Their sum is 180°.
The product of their slopes is -1 (negative reciprocal).

18. 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.
V = l^3
The set of all ordered pairs (x -y) such that y = f(x).
P(e) = (# of favorable outcomes)/(# of possible outcomes)

19. How do you find a percent of a number?
Then the quotient y/x is a constant.
For any right triangle - a^2 + b^2 = c^2.
V = lwh
Write the percent as a decimal - and multiply.

20. What is the volume of a cube?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = l^3
The ratio of corresponding sides of similar triangles.
For any integer n: 1^n = 1.

21. What is true about the slopes of perpendicular lines?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The product of their slopes is -1 (negative reciprocal).
Set y = 0 - and solve.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

22. What are the properties of a parallelogram?
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.
0 is the only number that is neither positive nor negative.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

23. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted down 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]

24. Properties of zero 1
0 is the only number that is neither positive nor negative.
No matter how many angles there are - the sum around the point is 360°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.

25. If you were given the graph of y = f(x) - what does f(a) represent?
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The ratio of corresponding sides of similar triangles.
Even numbers are divisible by 2 and odd numbers are not.

26. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
Their sum is 90°.
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.

27. What is the triangle inequality?
Divide - then multiply by 100.
Shifted up 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.
V = lwh

28. What is the distributive law?
180°. If two or more angles form a straight angle - their sum is 180°.
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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

29. 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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any integer n: 1^n = 1.
(Circumference/diameter) of a circle - or approximately 3.14.

30. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The set of all ordered pairs (x -y) such that y = f(x).
Even numbers are divisible by 2 and odd numbers are not.

31. What are the important properties of a 45-45 - 90 triangle?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(x + y)(x - y) = x^2 - y^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Set y = 0 - and solve.

32. Properties of zero 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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.
If a is negative and b is positive - then a < 0 < b.

33. What does it mean if y is inversely proportional to x?
For any number n: x^-n means 1/x^n.
At least one of the factors is 0.
Then the product xy is a constant.
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.

34. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
How steep the line is. Horizontal line = 0 - vertical has no slope.

35. In a circle of radius r - what is the formula for the circumference?
0 is a multiple of every integer.
C = p2r
An equation that states that two ratios are equivalent. 4/6 = 10/15
[(x1 + x2)/2] -[(y1 + y2)/2]

36. What is the measure of a straight angle?
M = (y2 - y1)/(x2 - x1)
B^m/b^n = b^m-n
180°. If two or more angles form a straight angle - their sum is 180°.
Write the percent over 100 and reduce.

37. What is the Pythagorean theorem?
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°.
Their sum is 180°.
Set y = 0 - and solve.
For any right triangle - a^2 + b^2 = c^2.

38. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted left 2 units.

39. What is true about the measures of the four angles formed by two intersecting lines?
Shifted right 2 units.
The two pairs of opposite angles formed are equal to each other.
Arc = (x°/360)(2pr) where x is the central angle.
1 is a divisor (or factor) of every integer.

40. How do you find the length of an arc of a circle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Arc = (x°/360)(2pr) where x is the central angle.
Write the percent over 100 and reduce.
[(x1 + x2)/2] -[(y1 + y2)/2]

41. What is a prime number?
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
V = lwh
The two pairs of opposite angles formed are equal to each other.

42. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
A = lw
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

43. What are the quotient and the remainder?

44. How do you calculate percent increases and decreases?
For any integer n: 1^n = 1.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
In the expression x^b - x is the base and b is the exponent.
(Circumference/diameter) of a circle - or approximately 3.14.

45. What is a proportion?
V = l^3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An equation that states that two ratios are equivalent. 4/6 = 10/15

46. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
An equation that states that two ratios are equivalent. 4/6 = 10/15

47. Important binomial 1
A = s^2 or A =d^2/2 where d is the diagonal
At least one of the factors is 0.
Cannot is 0 - must is 1 - all others are in between.
(x + y)(x - y) = x^2 - y^2

48. What are the important properties of 30-60-90 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.
For any number n: x^-n means 1/x^n.
Is a right triangle with a ratio of sides x:xv3:2x.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

49. 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
For any integer n: 1^n = 1.
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.

50. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
If a is negative and b is positive - then a < 0 < b.
Shifted right 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.