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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. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
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 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.

2. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(n - 2)(180°)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

3. What is a fractional exponent?
For any integer n: 1^n = 1.
In the expression x^b - x is the base and b is the exponent.
(x + y)(x - y) = x^2 - y^2
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

4. How do you calculate a weighted average?
A = lw
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
D = 2r
1 is the smallest positive odd integer.

5. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
At least one of the factors is 0.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any number n: x^-n means 1/x^n.

6. Law of exponents 5
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A^m/b^m = (a/b)^m
They are both the same. A divisor or factor of an integer leaves no remainder.
The set of all ordered pairs (x -y) such that y = f(x).

7. Properties of zero 5
A = 2(lw + lh + hw)
For any number b: b = -b if and only if b = 0.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
0 is the only number that is neither positive nor negative.

8. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
An angle formed by extending the side of the polygon.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.

9. What is the formula for the area of a parallelogram?
Avg = sum of n numbers/n
(n - 2)(180°)
A^m/b^m = (a/b)^m
A = bh

10. How you convert a fraction or a decimal to a percent?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A^m/b^m = (a/b)^m
Set x = 0 - and solve.
Divide - then multiply by 100.

11. In a circle of radius r - what is the formula for the area?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = pr^2
(Circumference/diameter) of a circle - or approximately 3.14.
M = (y2 - y1)/(x2 - x1)

12. What is a percent?
(Circumference/diameter) of a circle - or approximately 3.14.
No matter how many angles there are - the sum around the point is 360°.
Shifted left 2 units.
A fraction whose denominator is 100 i.e. 17% = 17/100

13. What is the formula for the surface area of a rectangular solid?
0 is a multiple of every integer.
(n - 2)(180°)
A = 2(lw + lh + hw)
360°

14. What is a multiple of an integer?
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = pr^2
For any right triangle - a^2 + b^2 = c^2.

15. What is the relationship between a radius of a circle and a line that is tangent to the circle?
B^m/b^n = b^m-n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = (1/2)bh.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

16. What are the important properties of 30-60-90 triangle?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Is a right triangle with a ratio of sides x:xv3:2x.
A = pr^2
For any number n: x^-n means 1/x^n.

17. What is a proportion?
Cannot is 0 - must is 1 - all others are in between.
Then the product xy is a constant.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Area = (x°/360)(pr^2) where x is the central angle.

18. What is the area of a square?
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.
A = s^2 or A =d^2/2 where d is the diagonal
For any right triangle - a^2 + b^2 = c^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.

19. Law of exponents 3
(b^m)^n = b^mn
Their sum is 180°.
For any integer n: 1^n = 1.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

20. How do you find the slope of a line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
The ratio of corresponding sides of similar triangles.
M = (y2 - y1)/(x2 - x1)
A = bh

21. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Then the product xy is a constant.

22. If you were given the graph of y = f(x) - what does f(a) represent?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A fraction whose denominator is 100 i.e. 17% = 17/100

23. What are the properties of a square?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^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.
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 = bh

24. What is a prime number?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.
A = s^2 or A =d^2/2 where d is the diagonal

25. What is true about the measures of the three angles in a triangle?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Cannot is 0 - must is 1 - all others are in between.
Their sum is 180°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

26. How do you find the x-intercept of a graph?
D = 2r
Set y = 0 - and solve.
Arc = (x°/360)(2pr) where x is the central angle.
Then the product xy is a constant.

27. Properties of one 4
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted up 2 units.
1 is the smallest positive odd integer.
A = (1/2)bh.

28. What is the Pythagorean theorem?
180°. If two or more angles form a straight angle - their sum is 180°.
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.
For any right triangle - a^2 + b^2 = c^2.
The product of their slopes is -1 (negative reciprocal).

29. What is the sum of the measures of the four angles in a quadrilateral?
A = (1/2)bh.
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.
(x + y)(x - y) = x^2 - y^2
360°

30. What is true about the measures of the two acute angles in a right triangle?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Their sum is 90°.
(x + y)(x - y) = x^2 - y^2
(n - 2)(180°)

31. What is the distance formula?
C = p2r
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°.
0 is a multiple of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

32. What is an integer?
A = pr^2
All positive and negative whole numbers - and zero.
B^m/b^n = b^m-n
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

33. How do you find the probability that an event will occur?
M = (y2 - y1)/(x2 - x1)
Then the quotient y/x is a constant.
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

34. In a circle of radius r - what is the formula for the circumference?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
C = p2r
Their sum is 90°.
V = l^3

35. Law of exponents 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.
A = (1/2)bh.
B^m/b^n = b^m-n
(x + y)(x - y) = x^2 - y^2

36. What is a composite number?
Is a right triangle with a ratio of sides x:xv3:2x.
An integer greater than one that is not prime.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted left 2 units.

37. What are the sum - difference - products - and quotient of two numbers?
A = lw
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
0 is a multiple of every integer.

38. Properties of zero 1
Divide - then multiply by 100.
Set x = 0 - and solve.
V = lwh
0 is the only number that is neither positive nor negative.

39. What is the volume of a cube?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
1 is the smallest positive odd integer.
V = l^3
Area = (x°/360)(pr^2) where x is the central angle.

40. What is the formula for the area of a triangle?
(Circumference/diameter) of a circle - or approximately 3.14.
V = l^3
A = (1/2)bh.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

41. What is a negative exponent?
An integer greater than one that is not prime.
Shifted right 2 units.
For any integer n: 1^n = 1.
For any number n: x^-n means 1/x^n.

42. What is a ratio?

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43. What are the properties of a parallelogram?
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 any number a: a * 1 = a and a / 1 = a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

44. What does it mean if y is directly proportional to x?
0 is a multiple of every integer.
Shifted left 2 units.
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.

45. 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.
Shifted down 2 units.
An angle formed by extending the side of the polygon.
(b^m)^n = b^mn

46. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
A = [(s^2*v3)/4]
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.
Cannot is 0 - must is 1 - all others are in between.

47. What is true about the slopes of parallel lines?
Equal slopes.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Cannot is 0 - must is 1 - all others are in between.

48. Properties of one 2
An angle formed by extending the side of the polygon.
For any integer n: 1^n = 1.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(b^m)^n = b^mn

49. What formula is used for an average?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
If a is negative and b is positive - then a < 0 < b.
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°.
Avg = sum of n numbers/n

50. 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 = [(s^2*v3)/4]
No matter how many angles there are - the sum around the point is 360°.
A = 6(l^2)

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