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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 are the properties of a square?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any number n: x^-n means 1/x^n.
Arc = (x°/360)(2pr) where x is the central angle.
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.

2. What are the important properties of 30-60-90 triangle?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Is a right triangle with a ratio of sides x:xv3:2x.
Avg = sum of n numbers/n
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

3. What is an integer?
Shifted up 2 units.
Shifted left 2 units.
All positive and negative whole numbers - and zero.
1 is the smallest positive odd integer.

4. How do you convert a percent to a fraction or a decimal?
V = lwh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Write the percent over 100 and reduce.
180°. If two or more angles form a straight angle - their sum is 180°.

5. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Write the percent over 100 and reduce.
Their sum is 180°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.

6. What is a Venn diagram?
A = (1/2)bh.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted right 2 units.
For any number a: a * 1 = a and a / 1 = a.

7. What is the formula for the area of a parallelogram?
A = 6(l^2)
Is a right triangle with a ratio of sides x:xv3:2x.
A = bh
Cannot is 0 - must is 1 - all others are in between.

8. What is a negative exponent?
0 is the only number that is neither positive nor negative.
(x + y)(x - y) = x^2 - y^2
Then the quotient y/x is a constant.
For any number n: x^-n means 1/x^n.

9. What are the important properties of a 45-45 - 90 triangle?
180°. If two or more angles form a straight angle - their sum is 180°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
They are both the same. A divisor or factor of an integer leaves no remainder.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

10. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
The set of all ordered pairs (x -y) such that y = f(x).
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted right 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

11. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
The product of their slopes is -1 (negative reciprocal).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Equal slopes.

12. What is the midpoint formula?
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.
360°
[(x1 + x2)/2] -[(y1 + y2)/2]
The product of their slopes is -1 (negative reciprocal).

13. 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.
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.
(Circumference/diameter) of a circle - or approximately 3.14.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

14. What is the Pythagorean theorem?
Shifted down 2 units.
A = 2(lw + lh + hw)
Equal slopes.
For any right triangle - a^2 + b^2 = c^2.

15. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
Cannot is 0 - must is 1 - all others are in between.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Avg = sum of n numbers/n

16. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
Set x = 0 - and solve.
A = 2(lw + lh + hw)
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

17. What is the formula for the surface area of a cube?
Their sum is 90°.
At least one of the factors is 0.
Shifted right 2 units.
A = 6(l^2)

18. 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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.
Write the percent over 100 and reduce.

19. What is a percent?
360°
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A fraction whose denominator is 100 i.e. 17% = 17/100
(x + y)(x - y) = x^2 - y^2

20. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
V = lwh
V = l^3
A = 2(lw + lh + hw)

21. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
Shifted up 2 units.
Avg = sum of n numbers/n
Their sum is 180°.

22. What is an exponent?
Cannot is 0 - must is 1 - all others are in between.
A = 2(lw + lh + hw)
Write the percent as a decimal - and multiply.
In the expression x^b - x is the base and b is the exponent.

23. What are the properties of a rectangle?
B^m/b^n = b^m-n
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

24. What is the ratio of similitude?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Arc = (x°/360)(2pr) where x is the central angle.
The ratio of corresponding sides of similar triangles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

25. Properties of square roots
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
[(x1 + x2)/2] -[(y1 + y2)/2]
A = bh

26. What are the sum - difference - products - and quotient of two numbers?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(b^m)^n = b^mn
Write the percent over 100 and reduce.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

27. In a circle of radius r - what is the formula for the area?
M = (y2 - y1)/(x2 - x1)
A = pr^2
For any number a: a * 1 = a and a / 1 = a.
A^m*b^m = (ab)^m

28. Important binomial 3
M = (y2 - y1)/(x2 - x1)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(Circumference/diameter) of a circle - or approximately 3.14.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

29. Properties of zero 3
360°
0 is a multiple of every integer.
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

30. What is an exterior angle of a polygon?
In the expression x^b - x is the base and b is the exponent.
Arc = (x°/360)(2pr) where x is the central angle.
A = pr^2
An angle formed by extending the side of the polygon.

31. What is true about the measures of the two acute angles in a right triangle?
Then the product xy is a constant.
Their sum is 90°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = 2(lw + lh + hw)

32. Properties of zero 4
For any number n: x^-n means 1/x^n.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
An equation that states that two ratios are equivalent. 4/6 = 10/15
No matter how many angles there are - the sum around the point is 360°.

33. What is the formula for the volume of a rectangular solid?
A = pr^2
At least one of the factors is 0.
V = lwh
Write the percent over 100 and reduce.

34. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
For any number n: x^-n means 1/x^n.
A = 6(l^2)
M = (y2 - y1)/(x2 - x1)

35. What is the formula for the area of a rectangle?
(Circumference/diameter) of a circle - or approximately 3.14.
A^m/b^m = (a/b)^m
A = lw
(n - 2)(180°)

36. Law of exponents 3
(b^m)^n = b^mn
No matter how many angles there are - the sum around the point is 360°.
Write the percent as a decimal - and multiply.
A fraction whose denominator is 100 i.e. 17% = 17/100

37. What formula is used for an average?
B^m*b^n = b^m+n
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Avg = sum of n numbers/n
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

38. What is the volume of a cube?
The two pairs of opposite angles formed are equal to each other.
V = l^3
Set y = 0 - and solve.
All positive and negative whole numbers - and zero.

39. Important binomial 1
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
If a is negative and b is positive - then a < 0 < b.
(x + y)(x - y) = x^2 - y^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

40. What does it mean if y is inversely proportional to x?
Write the percent as a decimal - and multiply.
Shifted down 2 units.
Then the product xy is a constant.
A = 6(l^2)

41. How do you calculate percent increases and decreases?
Cannot is 0 - must is 1 - all others are in between.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A^m*b^m = (ab)^m

42. If you were given the graph of y = f(x) - what does f(a) represent?
V = l^3
Then the quotient y/x is a constant.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A^m/b^m = (a/b)^m

43. How do we write the equation of a line?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the quotient y/x is a constant.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = pr^2

44. What is true about the slopes of perpendicular lines?
Corresponding sides of similar triangles are in proportion.
The product of their slopes is -1 (negative reciprocal).
All positive and negative whole numbers - and zero.
M = (y2 - y1)/(x2 - x1)

45. What is a proportion?
V = lwh
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted up 2 units.

46. What is a composite number?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An integer greater than one that is not prime.
(Circumference/diameter) of a circle - or approximately 3.14.
M = (y2 - y1)/(x2 - x1)

47. Properties of one 2
[(x1 + x2)/2] -[(y1 + y2)/2]
For any integer n: 1^n = 1.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

48. What is the distributive law?
Shifted right 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.

49. What is the formula for the volume of a cylinder?
An angle formed by extending the side of the polygon.
(b^m)^n = b^mn
V = pr^2h
How steep the line is. Horizontal line = 0 - vertical has no slope.

50. How you convert a fraction or a decimal to a percent?
B^m*b^n = b^m+n
Divide - then multiply by 100.
Cannot is 0 - must is 1 - all others are in between.
V = l^3