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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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1. What is true about the measures of the three angles in a triangle?
0 is a multiple of every integer.
Their sum is 180°.
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°.
Their sum is 90°.

2. How do you find the y-intercept of a graph?
0 is the only number that is neither positive nor negative.
The ratio of corresponding sides of similar triangles.
Set x = 0 - and solve.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

3. Properties of one 4
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.
1 is the smallest positive odd integer.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
V = pr^2h

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

5. What is the midpoint formula?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Even numbers are divisible by 2 and odd numbers are not.
[(x1 + x2)/2] -[(y1 + y2)/2]
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

6. What is an integer?
Write the percent as a decimal - and multiply.
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.
V = pr^2h

7. How do we write the equation of a line?
Avg = sum of n numbers/n
Then the product xy is a constant.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

8. How you convert a fraction or a decimal to a percent?
A^m/b^m = (a/b)^m
Divide - then multiply by 100.
A = lw
B^m*b^n = b^m+n

9. What do we mean by the slope of the line?
Set y = 0 - and solve.
Set x = 0 - and solve.
Shifted right 2 units.
How steep the line is. Horizontal line = 0 - vertical has no slope.

10. What is the formula for the volume of a cylinder?
V = pr^2h
360°
Set x = 0 - and solve.
Shifted down 2 units.

11. Law of exponents 4
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^m*b^m = (ab)^m
D = 2r
(b^m)^n = b^mn

12. How do you find the probability that an event will occur?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A^m*b^m = (ab)^m
P(e) = (# of favorable outcomes)/(# of possible outcomes)

13. What is an exterior angle of a polygon?
Corresponding sides of similar triangles are in proportion.
An angle formed by extending the side of the polygon.
The product of their slopes is -1 (negative reciprocal).
B^m*b^n = b^m+n

14. 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.
Set x = 0 - and solve.
For any right triangle - a^2 + b^2 = c^2.
An angle formed by extending the side of the polygon.

15. 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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An integer greater than one that is not prime.
A = (1/2)bh.

16. How do you find a percent of a number?
1 is a divisor (or factor) of every integer.
Write the percent as a decimal - and multiply.
In the expression x^b - x is the base and b is the exponent.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

17. How do you find the length of an arc of a circle?
D = 2r
Write the percent over 100 and reduce.
Arc = (x°/360)(2pr) where x is the central angle.
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.

18. What are the quotient and the remainder?

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19. What is a divisor and a factor of an integer?
A fraction whose denominator is 100 i.e. 17% = 17/100
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted down 2 units.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

20. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
(n - 2)(180°)
Then the product xy is a constant.
Shifted down 2 units.
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.

21. In a circle of radius r - what is the formula for the area?
V = lwh
A = pr^2
1 is the smallest positive odd integer.
(n - 2)(180°)

22. What is the formula for the area of a rectangle?
Corresponding sides of similar triangles are in proportion.
A = lw
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.
If a is negative and b is positive - then a < 0 < b.

23. What are the important properties of a 45-45 - 90 triangle?
Then the quotient y/x is a constant.
M = (y2 - y1)/(x2 - x1)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Even numbers are divisible by 2 and odd numbers are not.

24. For what values of a function is the function undefined?
For any integer n: 1^n = 1.
The ratio of corresponding sides of similar triangles.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Even numbers are divisible by 2 and odd numbers are not.

25. Properties of square roots
A = (1/2)bh.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Area = (x°/360)(pr^2) where x is the central angle.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

26. What is an even and an odd number?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = l^3
V = lwh
Even numbers are divisible by 2 and odd numbers are not.

27. What are the properties of a parallelogram?
The set of all ordered pairs (x -y) such that y = f(x).
0 is the only number that is neither positive nor negative.
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

28. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Even numbers are divisible by 2 and odd numbers are not.
Shifted left 2 units.
Divide - then multiply by 100.

29. What is the distance formula?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = lwh
V = l^3

30. Properties of zero 4
A = [(s^2*v3)/4]
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Area = (x°/360)(pr^2) where x is the central angle.
B^m*b^n = b^m+n

31. What is p?
A = bh
0 is the only number that is neither positive nor negative.
Corresponding sides of similar triangles are in proportion.
(Circumference/diameter) of a circle - or approximately 3.14.

32. What is the sum of the measures of the four angles in a quadrilateral?
Even numbers are divisible by 2 and odd numbers are not.
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.
C = p2r
360°

33. Properties of one 3
1 is a divisor (or factor) of every integer.
A = 6(l^2)
An equation that states that two ratios are equivalent. 4/6 = 10/15
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

34. What are the sum - difference - products - and quotient of two numbers?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
C = p2r
The ratio of corresponding sides of similar triangles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

35. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
A = bh
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Set y = 0 - and solve.

36. What is a percent?
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.
A fraction whose denominator is 100 i.e. 17% = 17/100
At least one of the factors is 0.
An angle formed by extending the side of the polygon.

37. How do you find the area of a sector of a circle?
All positive and negative whole numbers - and zero.
Area = (x°/360)(pr^2) where x is the central angle.
M = (y2 - y1)/(x2 - x1)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

38. What is true about the slopes of parallel lines?
A = (1/2)bh.
A fraction whose denominator is 100 i.e. 17% = 17/100
Equal slopes.
In the expression x^b - x is the base and b is the exponent.

39. 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.
V = lwh
Corresponding sides of similar triangles are in proportion.
Write the percent over 100 and reduce.

40. What are the properties of a square?
D = 2r
1 is the smallest positive odd integer.
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.
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.

41. Important binomial 2
Set y = 0 - and solve.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Shifted up 2 units.

42. What is the sum of the measures of the n angles of a polygon with n sides?
C = p2r
Equal slopes.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(n - 2)(180°)

43. How do you convert a percent to a fraction or a decimal?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent over 100 and reduce.
Shifted up 2 units.
For any integer n: 1^n = 1.

44. What is the probability of an event that cannot occur? That must occur?
360°
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.
V = lwh

45. What is true about the slopes of perpendicular lines?
Corresponding sides of similar triangles are in proportion.
Even numbers are divisible by 2 and odd numbers are not.
Shifted right 2 units.
The product of their slopes is -1 (negative reciprocal).

46. Important binomial 1
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A fraction whose denominator is 100 i.e. 17% = 17/100
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)(x - y) = x^2 - y^2

47. What is special formula for the area of an equilateral triangle?
For any integer n: 1^n = 1.
A = 2(lw + lh + hw)
A = [(s^2*v3)/4]
Their sum is 90°.

48. Law of exponents 5
Area = (x°/360)(pr^2) where x is the central angle.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A^m/b^m = (a/b)^m

49. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Write the percent over 100 and reduce.
Set y = 0 - and solve.
(n - 2)(180°)

50. What are similar triangles?
If a is negative and b is positive - then a < 0 < b.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Corresponding sides of similar triangles are in proportion.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

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