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GRE Math: Facts

Subjects : gre, math

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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. Important binomial 1
(x + y)(x - y) = x^2 - y^2
Arc = (x°/360)(2pr) where x is the central angle.
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

2. In a circle of radius r - what is the formula for the diameter?
(n - 2)(180°)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
D = 2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

3. What is true about the slopes of perpendicular lines?
The ratio of corresponding sides of similar triangles.
Shifted down 2 units.
The product of their slopes is -1 (negative reciprocal).
A = (1/2)bh.

4. What is an even and an odd number?
V = pr^2h
Corresponding sides of similar triangles are in proportion.
Even numbers are divisible by 2 and odd numbers are not.
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.

5. What is a function?
B^m*b^n = b^m+n
How steep the line is. Horizontal line = 0 - vertical has no slope.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted right 2 units.

6. How do you convert a percent to a fraction or a decimal?
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.
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.
An angle formed by extending the side of the polygon.
Write the percent over 100 and reduce.

7. What is the measure of a straight angle?
Shifted down 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Then the quotient y/x is a constant.

8. What is the relationship between a radius of a circle and a line that is tangent to the circle?
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 point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
[(x1 + x2)/2] -[(y1 + y2)/2]
The product of their slopes is -1 (negative reciprocal).

9. How do you find the length of an arc of a circle?
The ratio of corresponding sides of similar triangles.
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Arc = (x°/360)(2pr) where x is the central angle.

10. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
An integer greater than one that is not prime.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

11. Properties of one 2
Shifted right 2 units.
At least one of the factors is 0.
For any integer n: 1^n = 1.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

12. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = s^2 or A =d^2/2 where d is the diagonal
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°.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = [(s^2*v3)/4]

13. What is a multiple of an integer?
A = pr^2
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

14. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
360°
Their sum is 90°.
(n - 2)(180°)

15. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(b^m)^n = b^mn
Avg = sum of n numbers/n

16. What is a negative exponent?
Is a right triangle with a ratio of sides x:xv3:2x.
Then the product xy is a constant.
For any number n: x^-n means 1/x^n.
Write the percent over 100 and reduce.

17. If you were given the graph of y = f(x) - what does f(a) represent?
V = l^3
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Avg = sum of n numbers/n
At least one of the factors is 0.

18. What are the properties of a parallelogram?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

19. What is an exterior angle of a polygon?
They are both the same. A divisor or factor of an integer leaves no remainder.
An angle formed by extending the side of the polygon.
An equation that states that two ratios are equivalent. 4/6 = 10/15
0 is the only number that is neither positive nor negative.

20. How do you calculate a weighted average?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
They are both the same. A divisor or factor of an integer leaves no remainder.
For any number b: b = -b if and only if b = 0.

21. What is a composite number?
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.
An integer greater than one that is not prime.
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.

22. What is a Venn diagram?
An angle formed by extending the side of the polygon.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Divide - then multiply by 100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

23. What is the distributive law?
For any number n: x^-n means 1/x^n.
Avg = sum of n numbers/n
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.

24. How you convert a fraction or a decimal to a percent?
They are both the same. A divisor or factor of an integer leaves no remainder.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Divide - then multiply by 100.
Cannot is 0 - must is 1 - all others are in between.

25. What is p?
360°
(Circumference/diameter) of a circle - or approximately 3.14.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
1 is a divisor (or factor) of every integer.

26. What do we mean by the slope of the 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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = pr^2
An integer greater than one that is not prime.

27. What is special formula for the area of an equilateral triangle?
A = pr^2
An integer greater than one that is not prime.
No matter how many angles there are - the sum around the point is 360°.
A = [(s^2*v3)/4]

28. What is the Pythagorean theorem?
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
0 is the only number that is neither positive nor negative.

29. What are the important properties of 30-60-90 triangle?
Area = (x°/360)(pr^2) where x is the central angle.
Avg = sum of n numbers/n
Equal slopes.
Is a right triangle with a ratio of sides x:xv3:2x.

30. What are similar triangles?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted up 2 units.
B^m*b^n = b^m+n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

31. What is the sum of the measures of the n angles of a polygon with n sides?
B^m*b^n = b^m+n
D = 2r
Divide - then multiply by 100.
(n - 2)(180°)

32. What does it mean if y is inversely proportional to x?
Avg = sum of n numbers/n
The product of their slopes is -1 (negative reciprocal).
V = l^3
Then the product xy is a constant.

33. 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.
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.
Arc = (x°/360)(2pr) where x is the central angle.

34. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
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.
Divide - then multiply by 100.
An integer greater than one that is not prime.

35. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
B^m*b^n = b^m+n
Shifted up 2 units.
(b^m)^n = b^mn
Shifted left 2 units.

36. Properties of zero 5
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any number b: b = -b if and only if b = 0.
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.
Equal slopes.

37. What is the formula for the area of a parallelogram?
A = bh
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Write the percent over 100 and reduce.
A = s^2 or A =d^2/2 where d is the diagonal

38. What is the formula for the area of a triangle?
No matter how many angles there are - the sum around the point is 360°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = 2(lw + lh + hw)
A = (1/2)bh.

39. In a circle of radius r - what is the formula for the area?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
V = pr^2h
For any number b: b = -b if and only if b = 0.
A = pr^2

40. What is a ratio?

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41. What is the area of a square?
360°
The product of their slopes is -1 (negative reciprocal).
A = s^2 or A =d^2/2 where d is the diagonal
Cannot is 0 - must is 1 - all others are in between.

42. What is the formula for the surface area of a cube?
A = 6(l^2)
No matter how many angles there are - the sum around the point is 360°.
The product of their slopes is -1 (negative reciprocal).
A = 2(lw + lh + hw)

43. Law of exponents 5
B^m*b^n = b^m+n
A = pr^2
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m

44. What is true about the measures of the four angles formed by two intersecting lines?
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.
0 is the only number that is neither positive nor negative.
The two pairs of opposite angles formed are equal to each other.

45. What formula is used for an average?
A^m/b^m = (a/b)^m
(x + y)(x - y) = x^2 - y^2
A fraction whose denominator is 100 i.e. 17% = 17/100
Avg = sum of n numbers/n

46. Law of exponents 2
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
Then the quotient y/x is a constant.

47. What is the triangle inequality?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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°.
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.

48. What is true about the measures of the three angles in a triangle?
A fraction whose denominator is 100 i.e. 17% = 17/100
A = [(s^2*v3)/4]
The product of their slopes is -1 (negative reciprocal).
Their sum is 180°.

49. What are the properties of a rectangle?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number a: a * 1 = a and a / 1 = a.

50. How do you find the area of a sector of a circle?
A = pr^2
At least one of the factors is 0.
Area = (x°/360)(pr^2) where x is the central angle.
B^m/b^n = b^m-n

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