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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. What is the ratio of similitude?
M = (y2 - y1)/(x2 - x1)
(Circumference/diameter) of a circle - or approximately 3.14.
The ratio of corresponding sides of similar triangles.
Shifted left 2 units.

2. What is the formula for the volume of a cylinder?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
V = pr^2h
Shifted right 2 units.
Shifted left 2 units.

3. What is the sum of the measures of all angles around a point?
Write the percent as a decimal - and multiply.
No matter how many angles there are - the sum around the point is 360°.
For any right triangle - a^2 + b^2 = c^2.
For any number n: x^-n means 1/x^n.

4. What is the volume of a cube?
For any number a: a * 1 = a and a / 1 = a.
A = 2(lw + lh + hw)
V = l^3
Write the percent over 100 and reduce.

5. 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.
180°. If two or more angles form a straight angle - their sum is 180°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

6. Properties of zero 4
The product of their slopes is -1 (negative reciprocal).
Set x = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

7. What is a negative exponent?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An angle formed by extending the side of the polygon.
For any number n: x^-n means 1/x^n.

8. What is the formula for the area of a rectangle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Avg = sum of n numbers/n
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = lw

9. What are similar triangles?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.
An angle formed by extending the side of the polygon.

10. What are the properties of a square?
V = pr^2h
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.
(b^m)^n = b^mn
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

11. Important binomial 2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
In the expression x^b - x is the base and b is the exponent.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

12. 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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
At least one of the factors is 0.
1 is the smallest positive odd integer.

13. What is the sum of the measures of the four angles in a quadrilateral?
M = (y2 - y1)/(x2 - x1)
In the expression x^b - x is the base and b is the exponent.
A = (1/2)bh.
360°

14. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
The two pairs of opposite angles formed are equal to each other.
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.
Shifted down 2 units.
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.

15. What is a fractional exponent?
(Circumference/diameter) of a circle - or approximately 3.14.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Their sum is 180°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

16. What is an even and an odd number?
Set x = 0 - and solve.
1 is the smallest positive odd integer.
[(x1 + x2)/2] -[(y1 + y2)/2]
Even numbers are divisible by 2 and odd numbers are not.

17. Law of exponents 1
B^m*b^n = b^m+n
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.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

18. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
V = pr^2h
A = (1/2)bh.
The set of all ordered pairs (x -y) such that y = f(x).

19. What is true about the measures of the four angles formed by two intersecting lines?
Their sum is 90°.
180°. If two or more angles form a straight angle - their sum is 180°.
Set y = 0 - and solve.
The two pairs of opposite angles formed are equal to each other.

20. How do you find the x-intercept of a graph?
A = 2(lw + lh + hw)
Set y = 0 - and solve.
Is a right triangle with a ratio of sides x:xv3:2x.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

21. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
0 is the only number that is neither positive nor negative.
Their sum is 180°.
Their sum is 90°.

22. How you convert a fraction or a decimal to a percent?
0 is a multiple of every integer.
Divide - then multiply by 100.
A fraction whose denominator is 100 i.e. 17% = 17/100
For any number n: x^-n means 1/x^n.

23. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
No matter how many angles there are - the sum around the point is 360°.
Set x = 0 - and solve.
D = 2r

24. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An equation that states that two ratios are equivalent. 4/6 = 10/15

25. What is the formula for the volume of a rectangular solid?
The set of all ordered pairs (x -y) such that y = f(x).
1 is a divisor (or factor) of every integer.
V = lwh
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

26. How do you convert a percent to a fraction or a decimal?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Write the percent over 100 and reduce.
M = (y2 - y1)/(x2 - x1)
Then the product xy is a constant.

27. What is the formula for the area of a parallelogram?
V = l^3
A = bh
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

28. What is the formula for the surface area of a cube?
Set x = 0 - and solve.
A = 6(l^2)
D = 2r
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.

29. What is the sum of the measures of the n angles of a polygon with n sides?
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.
(b^m)^n = b^mn
The set of all ordered pairs (x -y) such that y = f(x).
(n - 2)(180°)

30. How do you find a percent of a number?
360°
Write the percent as a decimal - and multiply.
360°
Shifted left 2 units.

31. What is true about the slopes of parallel lines?
All positive and negative whole numbers - and zero.
Equal slopes.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^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.

32. Properties of one 3
Divide - then multiply by 100.
(x + y)(x - y) = x^2 - y^2
A = (1/2)bh.
1 is a divisor (or factor) of every integer.

33. What is a function?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
[(x1 + x2)/2] -[(y1 + y2)/2]
1 is a divisor (or factor) of every integer.

34. 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.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = (1/2)bh.
Write the percent as a decimal - and multiply.

35. What is the measure of a straight angle?
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 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.
180°. If two or more angles form a straight angle - their sum is 180°.

36. Important binomial 1
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.
(x + y)(x - y) = x^2 - y^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Cannot is 0 - must is 1 - all others are in between.

37. In a circle of radius r - what is the formula for the area?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = pr^2
Their sum is 180°.
0 is a multiple of every integer.

38. What are the important properties of a 45-45 - 90 triangle?
Write the percent as a decimal - and multiply.
V = l^3
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Divide - then multiply by 100.

39. What is a Venn diagram?
1 is the smallest positive odd integer.
A^m*b^m = (ab)^m
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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°.

40. What is a divisor and a factor of an integer?
The two pairs of opposite angles formed are equal to each other.
1 is the smallest positive odd integer.
They are both the same. A divisor or factor of an integer leaves no remainder.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

41. What does it mean if y is inversely proportional to x?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An equation that states that two ratios are equivalent. 4/6 = 10/15
The set of all ordered pairs (x -y) such that y = f(x).
Then the product xy is a constant.

42. What is a composite number?
The two pairs of opposite angles formed are equal to each other.
An integer greater than one that is not prime.
A fraction whose denominator is 100 i.e. 17% = 17/100
Cannot is 0 - must is 1 - all others are in between.

43. How do you calculate a weighted average?
Area = (x°/360)(pr^2) where x is the central angle.
0 is the only number that is neither positive nor negative.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = 6(l^2)

44. Properties of zero 5
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 b: b = -b if and only if b = 0.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted down 2 units.

45. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The two pairs of opposite angles formed are equal to each other.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = (1/2)bh.

46. What is true about the areas of similar triangles?
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 90°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

47. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
A = 6(l^2)
Even numbers are divisible by 2 and odd numbers are not.
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

48. If you were given the graph of y = f(x) - what does f(a) represent?
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 positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

49. If the product of two or more numbers is 0 - what do you know about the numbers?
180°. If two or more angles form a straight angle - their sum is 180°.
At least one of the factors is 0.
An integer greater than one that is not prime.
A = [(s^2*v3)/4]

50. What is the formula for the surface area 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.
A = 2(lw + lh + hw)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
An equation that states that two ratios are equivalent. 4/6 = 10/15