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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 formula for the area of a parallelogram?
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 = bh
(x + y)(x - y) = x^2 - y^2
360°

2. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

3. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
They are both the same. A divisor or factor of an integer leaves no remainder.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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 angle formed by extending the side of the polygon.

4. What is the measure of a straight angle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
0 is a multiple of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.
A = 6(l^2)

5. What is a percent?
360°
The product of their slopes is -1 (negative reciprocal).
A fraction whose denominator is 100 i.e. 17% = 17/100
(Circumference/diameter) of a circle - or approximately 3.14.

6. How do you calculate percent increases and decreases?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = lwh

7. Properties of zero 4
B^m/b^n = b^m-n
Area = (x°/360)(pr^2) where x is the central angle.
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.

8. What is a prime number?
The set of all ordered pairs (x -y) such that y = f(x).
A = (1/2)bh.
C = p2r
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.

9. Law of exponents 4
A^m*b^m = (ab)^m
The product of their slopes is -1 (negative reciprocal).
V = lwh
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

10. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Area = (x°/360)(pr^2) where x is the central angle.
0 is the only number that is neither positive nor negative.

11. What is the graph of a function?
A = s^2 or A =d^2/2 where d is the diagonal
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The set of all ordered pairs (x -y) such that y = f(x).

12. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
All positive and negative whole numbers - and zero.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = pr^2h

13. Properties of one 4
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
1 is the smallest positive odd integer.
No matter how many angles there are - the sum around the point is 360°.
[(x1 + x2)/2] -[(y1 + y2)/2]

14. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.

15. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
A = bh
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted up 2 units.
Then the quotient y/x is a constant.

16. What is the midpoint formula?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
0 is the only number that is neither positive nor negative.
[(x1 + x2)/2] -[(y1 + y2)/2]

17. Properties of zero 5
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any number b: b = -b if and only if b = 0.
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.

18. Important binomial 1
No matter how many angles there are - the sum around the point is 360°.
M = (y2 - y1)/(x2 - x1)
(x + y)(x - y) = x^2 - y^2
Divide - then multiply by 100.

19. What important property do similar triangles have?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The product of their slopes is -1 (negative reciprocal).
Cannot is 0 - must is 1 - all others are in between.
Corresponding sides of similar triangles are in proportion.

20. How do we write the equation of a line?
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

21. What is the Pythagorean theorem?
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.
(n - 2)(180°)
If a is negative and b is positive - then a < 0 < b.

22. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Then the quotient y/x is a constant.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x + y)(x - y) = x^2 - y^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 the distributive law?
Corresponding sides of similar triangles are in proportion.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted right 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

24. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

25. Properties of zero 1
Even numbers are divisible by 2 and odd numbers are not.
Shifted down 2 units.
0 is the only number that is neither positive nor negative.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

26. What are the properties of a square?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Avg = sum of n numbers/n
Equal slopes.
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.

27. What is a negative exponent?
Shifted down 2 units.
For any number n: x^-n means 1/x^n.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The two pairs of opposite angles formed are equal to each other.

28. What is an exterior angle of a triangle?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Divide - then multiply by 100.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

29. What is the formula for the volume of a rectangular solid?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = lwh
360°
V = l^3

30. 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.
Area = (x°/360)(pr^2) where x is the central angle.
Their sum is 180°.
C = p2r

31. What is true about the measures of the two acute angles in a right triangle?
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.
Arc = (x°/360)(2pr) where x is the central angle.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Their sum is 90°.

32. In a circle of radius r - what is the formula for the diameter?
For any integer n: 1^n = 1.
D = 2r
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
360°

33. Law of exponents 5
[(x1 + x2)/2] -[(y1 + y2)/2]
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A^m/b^m = (a/b)^m
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

34. What is a fractional exponent?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Equal slopes.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any integer n: 1^n = 1.

35. What is the formula for the area of a triangle?
D = 2r
A = 6(l^2)
All positive and negative whole numbers - and zero.
A = (1/2)bh.

36. What is special formula for the area of an equilateral triangle?
If a is negative and b is positive - then a < 0 < b.
A = [(s^2*v3)/4]
V = pr^2h
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

37. 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°.
Their sum is 180°.
[(x1 + x2)/2] -[(y1 + y2)/2]
A = [(s^2*v3)/4]

38. What do we mean by the slope of the line?
(x + y)(x - y) = x^2 - y^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted right 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

39. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Area = (x°/360)(pr^2) where x is the central angle.
A^m*b^m = (ab)^m

40. How you convert a fraction or a decimal to a percent?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
No matter how many angles there are - the sum around the point is 360°.
Divide - then multiply by 100.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

41. How do you find the slope of a line?
For any number a: a * 1 = a and a / 1 = a.
The ratio of corresponding sides of similar triangles.
0 is the only number that is neither positive nor negative.
M = (y2 - y1)/(x2 - x1)

42. What is the formula for the area of a rectangle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = [(s^2*v3)/4]
A = lw
Even numbers are divisible by 2 and odd numbers are not.

43. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
An angle formed by extending the side of the polygon.
Shifted right 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

44. What are the properties of a rectangle?
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.
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 positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

45. What does it mean if y is directly proportional to x?
The two pairs of opposite angles formed are equal to each other.
0 is a multiple of every integer.
1 is a divisor (or factor) of every integer.
Then the quotient y/x is a constant.

46. Important binomial 2
0 is the only number that is neither positive nor negative.
Write the percent over 100 and reduce.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = (1/2)bh.

47. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
360°
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

48. What is a ratio?

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49. What formula is used for an average?
A = s^2 or A =d^2/2 where d is the diagonal
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
V = lwh
Avg = sum of n numbers/n

50. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any right triangle - a^2 + b^2 = c^2.