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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.
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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 distributive law?
M = (y2 - y1)/(x2 - x1)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Equal slopes.

2. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Then the quotient y/x is a constant.
Their sum is 180°.
They are both the same. A divisor or factor of an integer leaves no remainder.

3. How do we write the equation of a line?
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Divide - then multiply by 100.
Shifted right 2 units.

4. What is the formula for the area of a triangle?
A = bh
A = (1/2)bh.
360°
If a is negative and b is positive - then a < 0 < b.

5. Law of exponents 5
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The ratio of corresponding sides of similar triangles.
A^m/b^m = (a/b)^m
V = l^3

6. Important binomial 3
Avg = sum of n numbers/n
A = 2(lw + lh + hw)
180°. If two or more angles form a straight angle - their sum is 180°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

7. What is a divisor and a factor of an integer?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Their sum is 180°.
They are both the same. A divisor or factor of an integer leaves no remainder.
How steep the line is. Horizontal line = 0 - vertical has no slope.

8. What is true about the measures of the four angles formed by two intersecting lines?
Avg = sum of n numbers/n
Then the quotient y/x is a constant.
For any right triangle - a^2 + b^2 = c^2.
The two pairs of opposite angles formed are equal to each other.

9. What is p?
Area = (x°/360)(pr^2) where x is the central angle.
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.
The product of their slopes is -1 (negative reciprocal).
(Circumference/diameter) of a circle - or approximately 3.14.

10. What is the ratio of similitude?
(x + y)(x - y) = x^2 - y^2
The two pairs of opposite angles formed are equal to each other.
The ratio of corresponding sides of similar triangles.
Divide - then multiply by 100.

11. What do we mean by the slope of the line?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Divide - then multiply by 100.
A^m*b^m = (ab)^m

12. What is the sum of the measures of the four angles in a quadrilateral?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
360°
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
B^m*b^n = b^m+n

13. What is true about the slopes of perpendicular lines?
M = (y2 - y1)/(x2 - x1)
The product of their slopes is -1 (negative reciprocal).
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
D = 2r

14. What formula is used for an average?
Avg = sum of n numbers/n
Then the quotient y/x is a constant.
1 is a divisor (or factor) of every integer.
V = pr^2h

15. Law of exponents 4
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°.
A^m*b^m = (ab)^m
An equation that states that two ratios are equivalent. 4/6 = 10/15

16. What are the important properties of a 45-45 - 90 triangle?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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)

17. What is the square root of a number?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A^m/b^m = (a/b)^m
In the expression x^b - x is the base and b is the exponent.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

18. What are similar triangles?
An equation that states that two ratios are equivalent. 4/6 = 10/15
(Circumference/diameter) of a circle - or approximately 3.14.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.

19. Law of exponents 3
(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.
1 is the smallest positive odd integer.
The product of their slopes is -1 (negative reciprocal).

20. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
Shifted right 2 units.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An equation that states that two ratios are equivalent. 4/6 = 10/15

21. What is the formula for the area of a rectangle?
Avg = sum of n numbers/n
C = p2r
All positive and negative whole numbers - and zero.
A = lw

22. What is a Venn diagram?
A = pr^2
[(x1 + x2)/2] -[(y1 + y2)/2]
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = l^3

23. What is the formula for the volume of a rectangular solid?
V = lwh
V = pr^2h
Divide - then multiply by 100.
M = (y2 - y1)/(x2 - x1)

24. What is a composite number?
A = 6(l^2)
An integer greater than one that is not prime.
180°. If two or more angles form a straight angle - their sum is 180°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

25. What is the formula for the volume of a cylinder?
Shifted up 2 units.
All positive and negative whole numbers - and zero.
D = 2r
V = pr^2h

26. What is an exponent?
Even numbers are divisible by 2 and odd numbers are not.
180°. If two or more angles form a straight angle - their sum is 180°.
All positive and negative whole numbers - and zero.
In the expression x^b - x is the base and b is the exponent.

27. How do you find a percent of a number?
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.
Write the percent as a decimal - and multiply.
Cannot is 0 - must is 1 - all others are in between.

28. What is the graph of a function?
Even numbers are divisible by 2 and odd numbers are not.
The set of all ordered pairs (x -y) such that y = f(x).
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
All positive and negative whole numbers - and zero.

29. What are the properties of a square?
Arc = (x°/360)(2pr) where x is the central angle.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
180°. If two or more angles form a straight angle - their sum is 180°.
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.

30. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Their sum is 180°.

31. For what values of a function is the function undefined?
Their sum is 90°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
1 is a divisor (or factor) of every integer.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

32. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
Set y = 0 - and solve.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
B^m/b^n = b^m-n

33. Law of exponents 2
An integer greater than one that is not prime.
M = (y2 - y1)/(x2 - x1)
B^m/b^n = b^m-n
Avg = sum of n numbers/n

34. What are the quotient and the remainder?

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35. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
180°. If two or more angles form a straight angle - their sum is 180°.
Avg = sum of n numbers/n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

36. How do you find the length of an arc of a circle?
V = pr^2h
Write the percent over 100 and reduce.
Arc = (x°/360)(2pr) where x is the central angle.
Shifted right 2 units.

37. What is true about the areas of similar triangles?
Then the product xy is a constant.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Shifted right 2 units.

38. What is an even and an odd number?
A = pr^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°.
360°
Even numbers are divisible by 2 and odd numbers are not.

39. Properties of zero 3
0 is a multiple of every integer.
Their sum is 90°.
Shifted right 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15

40. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
Arc = (x°/360)(2pr) where x is the central angle.
1 is a divisor (or factor) of every integer.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

41. What is a function?
Their sum is 90°.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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°.

42. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
Area = (x°/360)(pr^2) where x is the central angle.
For any number n: x^-n means 1/x^n.
For any number a: a * 1 = a and a / 1 = a.

43. How do you find the x-intercept of a graph?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Set y = 0 - and solve.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = s^2 or A =d^2/2 where d is the diagonal

44. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
(n - 2)(180°)
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any right triangle - a^2 + b^2 = c^2.

45. What is a percent?
Avg = sum of n numbers/n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A fraction whose denominator is 100 i.e. 17% = 17/100
The set of all ordered pairs (x -y) such that y = f(x).

46. What is the measure of a straight angle?
An angle formed by extending the side of the polygon.
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.
180°. If two or more angles form a straight angle - their sum is 180°.
The two pairs of opposite angles formed are equal to each other.

47. What is the volume of a cube?
V = l^3
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Area = (x°/360)(pr^2) where x is the central angle.
0 is a multiple of every integer.

48. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
An integer greater than one that is not prime.
D = 2r
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

49. In a circle of radius r - what is the formula for the area?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = pr^2
For any right triangle - a^2 + b^2 = c^2.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

50. What is true about the slopes of parallel lines?
The two pairs of opposite angles formed are equal to each other.
Equal slopes.
Even numbers are divisible by 2 and odd numbers are not.
The ratio of corresponding sides of similar triangles.

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