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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. Properties of zero 1
Shifted right 2 units.
0 is the only number that is neither positive nor negative.
Their sum is 180°.
V = pr^2h

2. If you were given the graph of y = f(x) - what does f(a) represent?
V = pr^2h
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.

3. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Write the percent over 100 and reduce.

4. How do you calculate a weighted average?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For any number a: a * 1 = a and a / 1 = a.
(b^m)^n = b^mn
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

5. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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 = (1/2)bh.

6. What is the sum of the measures of all angles around a point?
1 is the smallest positive odd integer.
No matter how many angles there are - the sum around the point is 360°.
V = lwh
(x + y)(x - y) = x^2 - y^2

7. What are the sum - difference - products - and quotient of two numbers?
V = lwh
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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°.
How steep the line is. Horizontal line = 0 - vertical has no slope.

8. Law of exponents 1
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = [(s^2*v3)/4]
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
B^m*b^n = b^m+n

9. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If a is negative and b is positive - then a < 0 < b.
Their sum is 180°.

10. What is a prime number?
For any right triangle - a^2 + b^2 = c^2.
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.

11. What is a percent?
Write the percent over 100 and reduce.
For any number a: a * 1 = a and a / 1 = a.
A fraction whose denominator is 100 i.e. 17% = 17/100
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

12. Properties of zero 5
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
[(x1 + x2)/2] -[(y1 + y2)/2]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any number b: b = -b if and only if b = 0.

13. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
Is a right triangle with a ratio of sides x:xv3:2x.
(Circumference/diameter) of a circle - or approximately 3.14.
An equation that states that two ratios are equivalent. 4/6 = 10/15

14. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
An angle formed by extending the side of the polygon.
Even numbers are divisible by 2 and odd numbers are not.
1 is the smallest positive odd integer.

15. What is special formula for the area of an equilateral triangle?
M = (y2 - y1)/(x2 - x1)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = [(s^2*v3)/4]
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

16. Important binomial 1
(x + y)(x - y) = x^2 - y^2
The two pairs of opposite angles formed are equal to each other.
How steep the line is. Horizontal line = 0 - vertical has no slope.
They are both the same. A divisor or factor of an integer leaves no remainder.

17. Properties of square roots
Shifted right 2 units.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(n - 2)(180°)
P(e) = (# of favorable outcomes)/(# of possible outcomes)

18. What is p?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(Circumference/diameter) of a circle - or approximately 3.14.
1 is the smallest positive odd integer.
Their sum is 180°.

19. 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 = 6(l^2)
A = (1/2)bh.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

20. How do you convert a percent to a fraction or a decimal?
A = 2(lw + lh + hw)
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.
Write the percent over 100 and reduce.
For any number b: b = -b if and only if b = 0.

21. What is a proportion?
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.
An angle formed by extending the side of the polygon.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any right triangle - a^2 + b^2 = c^2.

22. What is the formula for the area of a triangle?
At least one of the factors is 0.
A = (1/2)bh.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
M = (y2 - y1)/(x2 - x1)

23. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = 2(lw + lh + hw)
Equal slopes.

24. In a circle of radius r - what is the formula for the diameter?
(Circumference/diameter) of a circle - or approximately 3.14.
D = 2r
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Arc = (x°/360)(2pr) where x is the central angle.

25. What formula is used for an average?
The product of their slopes is -1 (negative reciprocal).
Avg = sum of n numbers/n
(x + y)(x - y) = x^2 - y^2
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

26. What is the graph of a function?
Write the percent over 100 and reduce.
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.
The set of all ordered pairs (x -y) such that y = f(x).
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

27. 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.
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°.
The product of their slopes is -1 (negative reciprocal).
At least one of the factors is 0.

28. What is the triangle inequality?
If a is negative and b is positive - then a < 0 < b.
A^m/b^m = (a/b)^m
0 is the only number that is neither positive nor negative.
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. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = bh
Is a right triangle with a ratio of sides x:xv3:2x.
C = p2r

30. What is the volume of a cube?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted up 2 units.
V = l^3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

31. What are the properties of a square?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.
180°. If two or more angles form a straight angle - their sum is 180°.
A = lw

32. What is a fractional exponent?
In the expression x^b - x is the base and b is the exponent.
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.
Even numbers are divisible by 2 and odd numbers are not.

33. How do we write the equation of a line?
For any number b: b = -b if and only if b = 0.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
At least one of the factors is 0.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

34. What is an exterior angle of a triangle?
No matter how many angles there are - the sum around the point is 360°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

35. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
V = lwh
D = 2r
Shifted right 2 units.

36. What is a multiple of an integer?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number n: x^-n means 1/x^n.
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.

37. What is true about the slopes of perpendicular lines?
A = s^2 or A =d^2/2 where d is the diagonal
The product of their slopes is -1 (negative reciprocal).
For any right triangle - a^2 + b^2 = c^2.
B^m/b^n = b^m-n

38. How do you find the y-intercept of a graph?
For any number a: a * 1 = a and a / 1 = a.
Set x = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.
The set of all ordered pairs (x -y) such that y = f(x).

39. What is a composite number?
Shifted up 2 units.
An integer greater than one that is not prime.
A = s^2 or A =d^2/2 where d is the diagonal
Area = (x°/360)(pr^2) where x is the central angle.

40. What is the Pythagorean theorem?
360°
D = 2r
Shifted down 2 units.
For any right triangle - a^2 + b^2 = c^2.

41. What does it mean if y is directly proportional to x?
The two pairs of opposite angles formed are equal to each other.
Then the quotient y/x is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
180°. If two or more angles form a straight angle - their sum is 180°.

42. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
1 is the smallest positive odd integer.
0 is a multiple of every integer.
360°
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

43. What is a Venn diagram?
Divide - then multiply by 100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If a is negative and b is positive - then a < 0 < b.
(b^m)^n = b^mn

44. How do you find the x-intercept of a graph?
No matter how many angles there are - the sum around the point is 360°.
Set y = 0 - and solve.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.

45. What is the formula for the surface area of a cube?
For any number n: x^-n means 1/x^n.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Write the percent over 100 and reduce.
A = 6(l^2)

46. How do you calculate percent increases and decreases?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
[(x1 + x2)/2] -[(y1 + y2)/2]
Area = (x°/360)(pr^2) where x is the central angle.

47. How do you find the length of an arc of a circle?
Then the product xy is a constant.
Arc = (x°/360)(2pr) where x is the central angle.
Is a right triangle with a ratio of sides x:xv3:2x.
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.

48. Properties of zero 3
0 is a multiple of every integer.
M = (y2 - y1)/(x2 - x1)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

49. What is the distributive law?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Is a right triangle with a ratio of sides x:xv3:2x.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

50. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Divide - then multiply by 100.
Shifted up 2 units.
Shifted right 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.