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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 fractional exponent?
A = (1/2)bh.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.
A^m/b^m = (a/b)^m

2. What is an exponent?
An integer greater than one that is not prime.
Set y = 0 - and solve.
In the expression x^b - x is the base and b is the exponent.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

3. What formula is used for an average?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Their sum is 90°.
Avg = sum of n numbers/n
How steep the line is. Horizontal line = 0 - vertical has no slope.

4. What is the volume of a cube?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Cannot is 0 - must is 1 - all others are in between.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = l^3

5. Properties of one 2
For any integer n: 1^n = 1.
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.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

6. What are the sum - difference - products - and quotient of two numbers?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Then the product xy is a constant.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted left 2 units.

7. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(x + y)(x - y) = x^2 - y^2
They are both the same. A divisor or factor of an integer leaves no remainder.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

8. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
0 is a multiple of every integer.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted right 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

9. What is true about the measures of the three angles in a triangle?
(x + y)(x - y) = x^2 - y^2
Their sum is 180°.
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted left 2 units.

10. What is the Pythagorean theorem?
Area = (x°/360)(pr^2) where x is the central angle.
A = s^2 or A =d^2/2 where d is the diagonal
For any right triangle - a^2 + b^2 = c^2.
At least one of the factors is 0.

11. What is the formula for the area of a parallelogram?
The product of their slopes is -1 (negative reciprocal).
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.
A = bh
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°.

12. What is a negative exponent?
Set y = 0 - and solve.
For any number n: x^-n means 1/x^n.
Shifted right 2 units.
An angle formed by extending the side of the polygon.

13. Properties of zero 2
A = [(s^2*v3)/4]
The product of their slopes is -1 (negative reciprocal).
Their sum is 90°.
If a is negative and b is positive - then a < 0 < b.

14. What is the distributive law?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any number n: x^-n means 1/x^n.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

15. What do we mean by the slope of the line?
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.
Avg = sum of n numbers/n
0 is the only number that is neither positive nor negative.
How steep the line is. Horizontal line = 0 - vertical has no slope.

16. What is the formula for the surface area of a rectangular solid?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = 2(lw + lh + hw)
180°. If two or more angles form a straight angle - their sum is 180°.
A = [(s^2*v3)/4]

17. Law of exponents 4
A^m*b^m = (ab)^m
Is a right triangle with a ratio of sides x:xv3:2x.
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

18. What is the sum of the measures of the four angles in a quadrilateral?
All positive and negative whole numbers - and zero.
360°
For any number b: b = -b if and only if b = 0.
180°. If two or more angles form a straight angle - their sum is 180°.

19. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
A = 2(lw + lh + hw)
360°
For any right triangle - a^2 + b^2 = c^2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

20. How do you calculate percent increases and decreases?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.

21. What is an even and an odd number?
Their sum is 180°.
Even numbers are divisible by 2 and odd numbers are not.
B^m/b^n = b^m-n
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

22. What does it mean if y is directly proportional to x?
Avg = sum of n numbers/n
Then the quotient y/x is a constant.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Arc = (x°/360)(2pr) where x is the central angle.

23. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = pr^2h
Then the quotient y/x is a constant.

24. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
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.
Shifted up 2 units.

25. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Divide - then multiply by 100.
V = lwh
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Their sum is 90°.

26. What is the formula for the area of a rectangle?
An integer greater than one that is not prime.
The two pairs of opposite angles formed are equal to each other.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = lw

27. What are the median and the mode of a set of data?
Shifted right 2 units.
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.

28. What is the sum of the measures of the n angles of a polygon with n sides?
(b^m)^n = b^mn
Area = (x°/360)(pr^2) where x is the central angle.
Avg = sum of n numbers/n
(n - 2)(180°)

29. Law of exponents 3
Write the percent over 100 and reduce.
Corresponding sides of similar triangles are in proportion.
(b^m)^n = b^mn
Area = (x°/360)(pr^2) where x is the central angle.

30. Properties of zero 1
All positive and negative whole numbers - and zero.
0 is the only number that is neither positive nor negative.
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.

31. What is a divisor and a factor of an integer?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted left 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
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.

32. How do we write the equation of a line?
A = (1/2)bh.
Is a right triangle with a ratio of sides x:xv3:2x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If a is negative and b is positive - then a < 0 < b.

33. What is true about the slopes of parallel lines?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Then the quotient y/x is a constant.
A fraction whose denominator is 100 i.e. 17% = 17/100
Equal slopes.

34. What is the sum of the measures of all angles around a point?
A fraction whose denominator is 100 i.e. 17% = 17/100
A^m*b^m = (ab)^m
A = 2(lw + lh + hw)
No matter how many angles there are - the sum around the point is 360°.

35. In a circle of radius r - what is the formula for the circumference?
A = 6(l^2)
C = p2r
A = s^2 or A =d^2/2 where d is the diagonal
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

36. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
V = pr^2h
Shifted up 2 units.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

37. What is a proportion?
Shifted up 2 units.
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
360°

38. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
0 is a multiple of every integer.
Then the product xy is a constant.

39. What are the important properties of a 45-45 - 90 triangle?
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.
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.
C = p2r

40. What is a composite number?
V = lwh
(x + y)(x - y) = x^2 - y^2
An integer greater than one that is not prime.
B^m/b^n = b^m-n

41. How do you convert a percent to a fraction or a decimal?
V = pr^2h
The product of their slopes is -1 (negative reciprocal).
Write the percent over 100 and reduce.
360°

42. How do you find the length of an arc of a circle?
Set y = 0 - and solve.
(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
Arc = (x°/360)(2pr) where x is the central angle.

43. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Then the quotient y/x is a constant.
A = bh
For any number n: x^-n means 1/x^n.
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°.

44. What is the formula for the volume of a cylinder?
V = pr^2h
V = lwh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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. What are the properties of a rectangle?
V = pr^2h
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = (1/2)bh.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

46. What is a prime number?
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.
1 is a divisor (or factor) of every integer.
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.
At least one of the factors is 0.

47. How do you calculate a weighted average?
[(x1 + x2)/2] -[(y1 + y2)/2]
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The two pairs of opposite angles formed are equal to each other.

48. What are the properties of a square?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.
0 is the only number that is neither positive nor negative.
Avg = sum of n numbers/n

49. What are similar triangles?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Divide - then multiply by 100.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = bh

50. How do you find the x-intercept of a graph?
In the expression x^b - x is the base and b is the exponent.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Set y = 0 - and solve.
Equal slopes.