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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 are the important properties of 30-60-90 triangle?
Then the product xy is a constant.
Is a right triangle with a ratio of sides x:xv3:2x.
Cannot is 0 - must is 1 - all others are in between.
For any number b: b = -b if and only if b = 0.

2. What is true about the areas of similar triangles?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

3. What is a divisor and a factor of an integer?
V = lwh
They are both the same. A divisor or factor of an integer leaves no remainder.
A = lw
Equal slopes.

4. 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.
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
Avg = sum of n numbers/n
(Circumference/diameter) of a circle - or approximately 3.14.

5. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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.
1 is the smallest positive odd integer.
0 is the only number that is neither positive nor negative.

6. Law of exponents 2
B^m/b^n = b^m-n
A = [(s^2*v3)/4]
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.

7. Properties of one 2
For any integer n: 1^n = 1.
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.
Then the product xy is a constant.
A^m/b^m = (a/b)^m

8. In a circle of radius r - what is the formula for the area?
D = 2r
A = pr^2
Equal slopes.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

9. 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.
1 is a divisor (or factor) of every integer.
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.

10. What is a Venn diagram?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any number n: x^-n means 1/x^n.

11. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
An integer greater than one that is not prime.
A = pr^2
Shifted up 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.

12. What are the important properties of a 45-45 - 90 triangle?
The ratio of corresponding sides of similar triangles.
A = 6(l^2)
V = lwh
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

13. Law of exponents 4
A^m*b^m = (ab)^m
P(e) = (# of favorable outcomes)/(# of possible outcomes)
V = l^3
Shifted right 2 units.

14. What are the quotient and the remainder?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted left 2 units.

15. What is the formula for the surface area of a cube?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = 6(l^2)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
B^m/b^n = b^m-n

16. What is the formula for the volume of a rectangular solid?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any integer n: 1^n = 1.
B^m*b^n = b^m+n
V = lwh

17. What is the distance formula?
Equal slopes.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
1 is the smallest positive odd integer.

18. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
Even numbers are divisible by 2 and odd numbers are not.
Avg = sum of n numbers/n
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.

19. What is the formula for the area of a rectangle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = lw
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.

20. Important binomial 1
(x + y)(x - y) = x^2 - y^2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

21. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
(Circumference/diameter) of a circle - or approximately 3.14.
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.
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.

22. What is the Pythagorean theorem?
A = 6(l^2)
(b^m)^n = b^mn
For any right triangle - a^2 + b^2 = c^2.
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.

23. What is an exponent?
Arc = (x/360)(2pr) where x is the central angle.
0 is a multiple of every integer.
In the expression x^b - x is the base and b is the exponent.
The set of all ordered pairs (x -y) such that y = f(x).

24. What are the sum - difference - products - and quotient of two numbers?
A = pr^2
(n - 2)(180)
D = 2r
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

25. What is the volume of a cube?
Corresponding sides of similar triangles are in proportion.
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.
V = l^3
A = 6(l^2)

26. In a circle of radius r - what is the formula for the diameter?
Equal slopes.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Avg = sum of n numbers/n
D = 2r

27. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Area = (x/360)(pr^2) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100
A^m*b^m = (ab)^m

28. Properties of zero 3
Their sum is 180.
D = 2r
For any integer n: 1^n = 1.
0 is a multiple of every integer.

29. What do we mean by the slope of the line?
Their sum is 180.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An equation that states that two ratios are equivalent. 4/6 = 10/15
How steep the line is. Horizontal line = 0 - vertical has no slope.

30. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
For any number a: a * 1 = a and a / 1 = a.
A^m/b^m = (a/b)^m
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

31. Properties of zero 2
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
If a is negative and b is positive - then a < 0 < b.
A = 2(lw + lh + hw)
0 is a multiple of every integer.

32. How do you convert a percent to a fraction or a decimal?
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.
Write the percent over 100 and reduce.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

33. What is a proportion?
Is a right triangle with a ratio of sides x:xv3:2x.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted left 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

34. What is a composite number?
Their sum is 180.
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.
B^m/b^n = b^m-n

35. What is the ratio of similitude?
(x + y)(x - y) = x^2 - y^2
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 ratio of corresponding sides of similar triangles.
360

36. What is a ratio?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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 expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

37. What is true about the slopes of perpendicular lines?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Avg = sum of n numbers/n
The product of their slopes is -1 (negative reciprocal).
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

38. How do you find a percent of a number?
Then the quotient y/x is a constant.
Write the percent as a decimal - and multiply.
D = 2r
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.

39. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted right 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

40. What are the median and the mode of a set of data?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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 n: x^-n means 1/x^n.

41. What are the properties of a parallelogram?
Cannot is 0 - must is 1 - all others are in between.
B^m*b^n = b^m+n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.

42. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = pr^2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

43. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
For any number b: b = -b if and only if b = 0.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

44. How you convert a fraction or a decimal to a percent?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A^m/b^m = (a/b)^m
Divide - then multiply by 100.
At least one of the factors is 0.

45. How do you calculate percent increases and decreases?
A = 6(l^2)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = lw
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

46. Properties of one 1
Set x = 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.
For any number a: a * 1 = a and a / 1 = a.
They are both the same. A divisor or factor of an integer leaves no remainder.

47. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360
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.
1 is the smallest positive odd integer.

48. Properties of one 4
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.
Shifted right 2 units.
1 is the smallest positive odd integer.
Is a right triangle with a ratio of sides x:xv3:2x.

49. Properties of zero 4
1 is the smallest positive odd integer.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
All positive and negative whole numbers - and zero.

50. What is the distributive law?
An integer greater than one that is not prime.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any number a: a * 1 = a and a / 1 = a.
(b^m)^n = b^mn

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