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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 relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
A = (1/2)bh.
Corresponding sides of similar triangles are in proportion.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.

2. What is the sum of the measures of the n angles of a polygon with n sides?
Divide - then multiply by 100.
Avg = sum of n numbers/n
(n - 2)(180°)
The set of all ordered pairs (x -y) such that y = f(x).

3. Properties of zero 5
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The product of their slopes is -1 (negative reciprocal).
For any number b: b = -b if and only if b = 0.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

4. In a circle of radius r - what is the formula for the circumference?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Write the percent over 100 and reduce.
C = p2r
Arc = (x°/360)(2pr) where x is the central angle.

5. Properties of zero 1
No matter how many angles there are - the sum around the point is 360°.
360°
0 is the only number that is neither positive nor negative.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

6. How do you find the area of a sector of a circle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Write the percent over 100 and reduce.
Area = (x°/360)(pr^2) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.

7. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

8. What is the formula for the area of a triangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = (1/2)bh.
(Circumference/diameter) of a circle - or approximately 3.14.
Is a right triangle with a ratio of sides x:xv3:2x.

9. Properties of zero 2
V = l^3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted left 2 units.
If a is negative and b is positive - then a < 0 < b.

10. What is true about the slopes of parallel lines?
Equal slopes.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
B^m*b^n = b^m+n

11. What does it mean if y is directly proportional to x?
An integer greater than one that is not prime.
Then the quotient y/x is a constant.
All positive and negative whole numbers - and zero.
The product of their slopes is -1 (negative reciprocal).

12. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
V = lwh
They are both the same. A divisor or factor of an integer leaves no remainder.
An equation that states that two ratios are equivalent. 4/6 = 10/15

13. What is the sum of the measures of all angles around a point?
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
D = 2r

14. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
1 is a divisor (or factor) of every integer.
Shifted right 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The set of all ordered pairs (x -y) such that y = f(x).

15. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Cannot is 0 - must is 1 - all others are in between.
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.
Shifted left 2 units.

16. What is the graph of a function?
A fraction whose denominator is 100 i.e. 17% = 17/100
A = 6(l^2)
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The set of all ordered pairs (x -y) such that y = f(x).

17. How do you find the length of an arc of a circle?
Set x = 0 - and solve.
Arc = (x°/360)(2pr) where x is the central angle.
Shifted left 2 units.
For any integer n: 1^n = 1.

18. Properties of zero 4
[(x1 + x2)/2] -[(y1 + y2)/2]
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.
B^m*b^n = b^m+n

19. What do we mean by the slope of the line?
M = (y2 - y1)/(x2 - x1)
How steep the line is. Horizontal line = 0 - vertical has no slope.
Then the quotient y/x is a constant.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

20. What is the formula for the volume of a cylinder?
V = pr^2h
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Write the percent as a decimal - and multiply.

21. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
M = (y2 - y1)/(x2 - x1)
A^m/b^m = (a/b)^m
For any number n: x^-n means 1/x^n.

22. Law of exponents 3
For any number b: b = -b if and only if b = 0.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(b^m)^n = b^mn

23. What is true about the areas of similar triangles?
Write the percent as a decimal - and multiply.
V = pr^2h
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any number a: a * 1 = a and a / 1 = a.

24. What is the Pythagorean theorem?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any right triangle - a^2 + b^2 = c^2.
V = lwh
Cannot is 0 - must is 1 - all others are in between.

25. What important property do similar triangles have?
A fraction whose denominator is 100 i.e. 17% = 17/100
B^m*b^n = b^m+n
Corresponding sides of similar triangles are in proportion.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

26. In a circle of radius r - what is the formula for the area?
0 is the only number that is neither positive nor negative.
A = pr^2
In the expression x^b - x is the base and b is the exponent.
1 is the smallest positive odd integer.

27. What is a prime number?
They are both the same. A divisor or factor of an integer leaves no remainder.
Set y = 0 - and solve.
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.
Even numbers are divisible by 2 and odd numbers are not.

28. What are the important properties of 30-60-90 triangle?
For any right triangle - a^2 + b^2 = c^2.
Is a right triangle with a ratio of sides x:xv3:2x.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.

29. What are similar triangles?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
1 is the smallest positive odd integer.
All positive and negative whole numbers - and zero.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

30. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The product of their slopes is -1 (negative reciprocal).
Shifted left 2 units.
B^m/b^n = b^m-n

31. What is an even and an odd number?
(b^m)^n = b^mn
Their sum is 90°.
Even numbers are divisible by 2 and odd numbers are not.
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. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
They are both the same. A divisor or factor of an integer leaves no remainder.
A = 6(l^2)
An angle formed by extending the side of the polygon.

33. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
A = [(s^2*v3)/4]
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted up 2 units.

34. Properties of zero 3
A = 2(lw + lh + hw)
0 is a multiple of every integer.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
360°

35. What are the properties of a square?
(n - 2)(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.
A fraction whose denominator is 100 i.e. 17% = 17/100
C = p2r

36. What is an exterior angle of a polygon?
360°
An angle formed by extending the side of the polygon.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

37. If you were given the graph of y = f(x) - what does f(a) represent?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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°.

38. What is true about the measures of the three angles in a triangle?
(Circumference/diameter) of a circle - or approximately 3.14.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 180°.
For any right triangle - a^2 + b^2 = c^2.

39. What is a ratio?

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40. What is the ratio of similitude?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The ratio of corresponding sides of similar triangles.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The set of all ordered pairs (x -y) such that y = f(x).

41. What is the distributive law?
A = 2(lw + lh + hw)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
B^m/b^n = b^m-n

42. How you convert a fraction or a decimal to a percent?
Their sum is 90°.
A = 2(lw + lh + hw)
Their sum is 180°.
Divide - then multiply by 100.

43. What is the square root of a number?
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.
If a is negative and b is positive - then a < 0 < b.

44. What is true about the measures of the two acute angles in a right triangle?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = lwh
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Their sum is 90°.

45. What is a negative exponent?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Then the product xy is a constant.
For any number n: x^-n means 1/x^n.
Even numbers are divisible by 2 and odd numbers are not.

46. What is the distance formula?
Their sum is 180°.
An angle formed by extending the side of the polygon.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = [(s^2*v3)/4]

47. What is p?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Set y = 0 - and solve.
The product of their slopes is -1 (negative reciprocal).
(Circumference/diameter) of a circle - or approximately 3.14.

48. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Arc = (x°/360)(2pr) where x is the central angle.
For any integer n: 1^n = 1.
Then the product xy is a constant.

49. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(n - 2)(180°)
Shifted right 2 units.

50. Law of exponents 5
Set y = 0 - and solve.
Corresponding sides of similar triangles are in proportion.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A^m/b^m = (a/b)^m

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