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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. Properties of one 3
Cannot is 0 - must is 1 - all others are in between.
A = bh
1 is a divisor (or factor) of every integer.
360°

2. If you were given the graph of y = f(x) - what does f(a) represent?
B^m/b^n = b^m-n
Set x = 0 - and solve.
A^m/b^m = (a/b)^m
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

3. 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.
1 is a divisor (or factor) of every integer.
A = [(s^2*v3)/4]
V = lwh

4. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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°.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Equal slopes.

5. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(b^m)^n = b^mn
B^m*b^n = b^m+n
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 the distributive law?
0 is the only number that is neither positive nor negative.
0 is a multiple of every integer.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

7. What is the probability of an event that cannot occur? That must occur?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Cannot is 0 - must is 1 - all others are in between.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Their sum is 90°.

8. Properties of one 2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any integer n: 1^n = 1.

9. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
1 is a divisor (or factor) of every integer.
A^m/b^m = (a/b)^m
Shifted left 2 units.

10. What is an even and an odd number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Even numbers are divisible by 2 and odd numbers are not.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

11. 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.
M = (y2 - y1)/(x2 - x1)
They are both the same. A divisor or factor of an integer leaves no remainder.
Set x = 0 - and solve.

12. Properties of zero 1
1 is a divisor (or factor) of every integer.
0 is the only number that is neither positive nor negative.
A = [(s^2*v3)/4]
V = lwh

13. 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.
All positive and negative whole numbers - and zero.
Then the product xy is a constant.
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 triangle inequality?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A^m*b^m = (ab)^m
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.

15. What is an exterior angle of a polygon?
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 quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
An angle formed by extending the side of the polygon.
360°

16. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A^m*b^m = (ab)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

17. What is true about the measures of the two acute angles in a right triangle?
Set x = 0 - and solve.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Their sum is 90°.
Arc = (x°/360)(2pr) where x is the central angle.

18. In a circle of radius r - what is the formula for the circumference?
C = p2r
180°. If two or more angles form a straight angle - their sum is 180°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Then the product xy is a constant.

19. In a circle of radius r - what is the formula for the diameter?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any right triangle - a^2 + b^2 = c^2.
D = 2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

20. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.
Set y = 0 - and solve.
For any number a: a * 1 = a and a / 1 = a.

21. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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 as a decimal - and multiply.

22. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Shifted left 2 units.
0 is the only number that is neither positive nor negative.
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°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

23. What is the sum of the measures of the n angles of a polygon with n sides?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The set of all ordered pairs (x -y) such that y = f(x).
(n - 2)(180°)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

24. Important binomial 3
Avg = sum of n numbers/n
A = lw
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
0 is a multiple of every integer.

25. What do we mean by the slope of the line?
0 is the only number that is neither positive nor negative.
The set of all ordered pairs (x -y) such that y = f(x).
How steep the line is. Horizontal line = 0 - vertical has no slope.
[(x1 + x2)/2] -[(y1 + y2)/2]

26. What is p?
A = (1/2)bh.
Set x = 0 - and solve.
V = lwh
(Circumference/diameter) of a circle - or approximately 3.14.

27. What is the formula for the surface area of a cube?
A = 6(l^2)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
[(x1 + x2)/2] -[(y1 + y2)/2]

28. What is the graph of a function?
The product of their slopes is -1 (negative reciprocal).
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = 2(lw + lh + hw)
The set of all ordered pairs (x -y) such that y = f(x).

29. What is the formula for the area of a triangle?
A = (1/2)bh.
A = lw
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

30. In a circle of radius r - what is the formula for the area?
A = pr^2
For any number a: a * 1 = a and a / 1 = a.
Write the percent as a decimal - and multiply.
(n - 2)(180°)

31. What are the sum - difference - products - and quotient of two numbers?
A^m/b^m = (a/b)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Write the percent as a decimal - and multiply.
A = 6(l^2)

32. What is true about the measures of the four angles formed by two intersecting lines?
A = pr^2
The two pairs of opposite angles formed are equal to each other.
Is a right triangle with a ratio of sides x:xv3:2x.
Then the quotient y/x is a constant.

33. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any number n: x^-n means 1/x^n.
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.
Their sum is 90°.

34. What is an exponent?
An equation that states that two ratios are equivalent. 4/6 = 10/15
[(x1 + x2)/2] -[(y1 + y2)/2]
No matter how many angles there are - the sum around the point is 360°.
In the expression x^b - x is the base and b is the exponent.

35. Law of exponents 1
Write the percent over 100 and reduce.
0 is a multiple of every integer.
B^m*b^n = b^m+n
Their sum is 180°.

36. Law of exponents 5
A^m/b^m = (a/b)^m
If a is negative and b is positive - then a < 0 < b.
In the expression x^b - x is the base and b is the exponent.
Set y = 0 - and solve.

37. How do you find the x-intercept of a graph?
0 is the only number that is neither positive nor negative.
1 is a divisor (or factor) of every integer.
Set y = 0 - and solve.
An angle formed by extending the side of the polygon.

38. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Divide - then multiply by 100.
Shifted right 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

39. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
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.
The two pairs of opposite angles formed are equal to each other.
B^m/b^n = b^m-n
Shifted up 2 units.

40. What is a multiple of an integer?
A = lw
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted left 2 units.

41. How do you find a percent of a number?
For any number n: x^-n means 1/x^n.
Corresponding sides of similar triangles are in proportion.
Write the percent as a decimal - and multiply.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

42. What are the median and the mode of a set of data?
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted down 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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

43. Properties of zero 5
For any number b: b = -b if and only if b = 0.
The set of all ordered pairs (x -y) such that y = f(x).
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any integer n: 1^n = 1.

44. What is the square root of a number?
Set y = 0 - and solve.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
1 is a divisor (or factor) of every integer.

45. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
C = p2r
Divide - then multiply by 100.
V = l^3

46. What is the sum of the measures of all angles around a point?
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
No matter how many angles there are - the sum around the point is 360°.

47. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Shifted right 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Arc = (x°/360)(2pr) where x is the central angle.
V = l^3

48. How do you calculate a weighted average?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Write the percent over 100 and reduce.

49. Properties of one 1
At least one of the factors is 0.
B^m/b^n = b^m-n
For any number a: a * 1 = a and a / 1 = a.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

50. What are the properties of a square?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = 6(l^2)

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