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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. How do you convert a percent to a fraction or a decimal?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Write the percent over 100 and reduce.
Shifted down 2 units.

2. How do you calculate percent increases and decreases?
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted left 2 units.

3. What are the quotient and the remainder?

4. What does it mean if y is inversely proportional to x?
D = 2r
Then the product xy is a constant.
Set y = 0 - and solve.
An equation that states that two ratios are equivalent. 4/6 = 10/15

5. 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.
A = pr^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.

6. What is the sum of the measures of all angles around a point?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = pr^2
No matter how many angles there are - the sum around the point is 360°.

7. What is the formula for the area of a triangle?
A = (1/2)bh.
Is a right triangle with a ratio of sides x:xv3:2x.
360°
A^m*b^m = (ab)^m

8. 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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
In the expression x^b - x is the base and b is the exponent.
M = (y2 - y1)/(x2 - x1)

9. In a circle of radius r - what is the formula for the circumference?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
C = p2r
V = lwh
360°

10. How you convert a fraction or a decimal to a percent?
The ratio of corresponding sides of similar triangles.
A = pr^2
Divide - then multiply by 100.
(b^m)^n = b^mn

11. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
360°
All positive and negative whole numbers - and zero.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

12. How do you find the x-intercept of a graph?
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 left 2 units.
Set y = 0 - and solve.
Then the quotient y/x is a constant.

13. What is the sum of the measures of the n angles of a polygon with n sides?
Avg = sum of n numbers/n
A = 2(lw + lh + hw)
Shifted down 2 units.
(n - 2)(180°)

14. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted right 2 units.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

15. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
A = 2(lw + lh + hw)
A^m*b^m = (ab)^m
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.

16. How do you find the y-intercept of a graph?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(n - 2)(180°)
Set x = 0 - and solve.
For any number n: x^-n means 1/x^n.

17. Properties of zero 1
V = l^3
0 is the only number that is neither positive nor negative.
A fraction whose denominator is 100 i.e. 17% = 17/100
(b^m)^n = b^mn

18. Important binomial 3
An equation that states that two ratios are equivalent. 4/6 = 10/15
Set y = 0 - and solve.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Avg = sum of n numbers/n

19. What does it mean if y is directly proportional to x?
For any number n: x^-n means 1/x^n.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Then the quotient y/x is a constant.
A = pr^2

20. Properties of zero 5
Corresponding sides of similar triangles are in proportion.
A = 6(l^2)
For any number b: b = -b if and only if b = 0.
The two pairs of opposite angles formed are equal to each other.

21. What important property do similar triangles have?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Corresponding sides of similar triangles are in proportion.
If a is negative and b is positive - then a < 0 < b.

22. What is true about the measures of the three angles in a triangle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 180°.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Shifted right 2 units.

23. What is an integer?
All positive and negative whole numbers - and zero.
Their sum is 180°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Set y = 0 - and solve.

24. What is the ratio of similitude?
Is a right triangle with a ratio of sides x:xv3:2x.
For any number a: a * 1 = a and a / 1 = a.
The ratio of corresponding sides of similar triangles.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

25. What is a multiple of an integer?
0 is a multiple of every integer.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.
M = (y2 - y1)/(x2 - x1)

26. How do you find the length of an arc of a circle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Set x = 0 - and solve.
[(x1 + x2)/2] -[(y1 + y2)/2]
Arc = (x°/360)(2pr) where x is the central angle.

27. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
Then the quotient y/x is a constant.
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any number b: b = -b if and only if b = 0.

28. What are similar triangles?
A = [(s^2*v3)/4]
The two pairs of opposite angles formed are equal to each other.
Cannot is 0 - must is 1 - all others are in between.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

29. Properties of one 2
For any number b: b = -b if and only if b = 0.
For any integer n: 1^n = 1.
A = [(s^2*v3)/4]
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

30. What is the formula for the volume of a rectangular solid?
A = pr^2
0 is the only number that is neither positive nor negative.
V = lwh
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

31. What is true about the slopes of perpendicular lines?
A = lw
The product of their slopes is -1 (negative reciprocal).
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted left 2 units.

32. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
B^m*b^n = b^m+n
A = [(s^2*v3)/4]
(n - 2)(180°)

33. What is the midpoint formula?
At least one of the factors is 0.
An angle formed by extending the side of the polygon.
[(x1 + x2)/2] -[(y1 + y2)/2]
(n - 2)(180°)

34. If the product of two or more numbers is 0 - what do you know about the numbers?
Then the quotient y/x is a constant.
Area = (x°/360)(pr^2) where x is the central angle.
At least one of the factors is 0.
They are both the same. A divisor or factor of an integer leaves no remainder.

35. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The product of their slopes is -1 (negative reciprocal).
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = 6(l^2)

36. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted left 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

37. What is a ratio?

38. What is a negative exponent?
For any number n: x^-n means 1/x^n.
Their sum is 180°.
M = (y2 - y1)/(x2 - x1)
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

39. What is the formula for the volume of a cylinder?
Equal slopes.
V = pr^2h
Cannot is 0 - must is 1 - all others are in between.
0 is the only number that is neither positive nor negative.

40. Properties of zero 4
1 is the smallest positive odd integer.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The two pairs of opposite angles formed are equal to each other.

41. What are the properties of a square?
A = pr^2
Cannot is 0 - must is 1 - all others are in between.
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.
No matter how many angles there are - the sum around the point is 360°.

42. What is a prime number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An integer greater than one that is not prime.
In the expression x^b - x is the base and b is the exponent.
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.

43. What is true about the slopes of parallel lines?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.
Set y = 0 - and solve.
Equal slopes.

44. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Divide - then multiply by 100.
Arc = (x°/360)(2pr) where x is the central 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.

45. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
V = lwh
1 is a divisor (or factor) of every integer.
0 is a multiple of every integer.

46. What is the measure of a straight angle?
A = bh
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
180°. If two or more angles form a straight angle - their sum is 180°.
V = pr^2h

47. In a circle of radius r - what is the formula for the area?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = pr^2
360°

48. What is a divisor and a factor of an integer?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Even numbers are divisible by 2 and odd numbers are not.
They are both the same. A divisor or factor of an integer leaves no remainder.
M = (y2 - y1)/(x2 - x1)

49. What is the probability of an event that cannot occur? That must occur?
For any right triangle - a^2 + b^2 = c^2.
Cannot is 0 - must is 1 - all others are in between.
Avg = sum of n numbers/n
1 is the smallest positive odd integer.

50. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
(n - 2)(180°)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted up 2 units.