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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 the formula for the surface area of a cube?
A = 6(l^2)
D = 2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

2. How do you calculate a weighted average?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An angle formed by extending the side of the polygon.
B^m/b^n = b^m-n
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

3. What are the quotient and the remainder?

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4. What are the properties of a square?
(b^m)^n = b^mn
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.
B^m*b^n = b^m+n
A = lw

5. What is special formula for the area of an equilateral triangle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = [(s^2*v3)/4]
Set x = 0 - and solve.

6. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
How steep the line is. Horizontal line = 0 - vertical has no slope.
An angle formed by extending the side of the polygon.
360°

7. What is the volume of a cube?
V = l^3
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted down 2 units.
Write the percent over 100 and reduce.

8. 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.
Their sum is 90°.
A = (1/2)bh.
A fraction whose denominator is 100 i.e. 17% = 17/100

9. What is the area of a square?
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = s^2 or A =d^2/2 where d is the diagonal
V = l^3

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

11. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
0 is the only number that is neither positive nor negative.
How steep the line is. Horizontal line = 0 - vertical has no slope.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
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°.

12. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
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.
360°

13. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Arc = (x°/360)(2pr) where x is the central angle.
Shifted left 2 units.
A = (1/2)bh.

14. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
The two pairs of opposite angles formed are equal to each other.
The ratio of corresponding sides of similar triangles.
(Circumference/diameter) of a circle - or approximately 3.14.

15. What is a Venn diagram?
A = bh
Divide - then multiply by 100.
The two pairs of opposite angles formed are equal to each other.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

16. What is the graph of a function?
1 is a divisor (or factor) of every integer.
The set of all ordered pairs (x -y) such that y = f(x).
Shifted left 2 units.
The product of their slopes is -1 (negative reciprocal).

17. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A^m*b^m = (ab)^m
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

18. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
Corresponding sides of similar triangles are in proportion.

19. Law of exponents 4
A^m*b^m = (ab)^m
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.
Their sum is 90°.
They are both the same. A divisor or factor of an integer leaves no remainder.

20. What is the sum of the measures of the n angles of a polygon with n sides?
B^m*b^n = b^m+n
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
(n - 2)(180°)

21. What is the formula for the volume of a rectangular solid?
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
V = lwh

22. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The ratio of corresponding sides of similar triangles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

23. What is true about the slopes of parallel lines?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Equal slopes.
Cannot is 0 - must is 1 - all others are in between.
A = bh

24. What is the measure of a straight angle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any number n: x^-n means 1/x^n.
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.

25. What are similar triangles?
The product of their slopes is -1 (negative reciprocal).
All positive and negative whole numbers - and zero.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

26. What is true about the measures of the three angles in a triangle?
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.
Their sum is 180°.
M = (y2 - y1)/(x2 - x1)

27. What is the triangle inequality?
Divide - then multiply by 100.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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 b: b = -b if and only if b = 0.

28. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
360°
0 is the only number that is neither positive nor negative.
M = (y2 - y1)/(x2 - x1)

29. What is a proportion?
(Circumference/diameter) of a circle - or approximately 3.14.
If a is negative and b is positive - then a < 0 < b.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
An equation that states that two ratios are equivalent. 4/6 = 10/15

30. What are the sum - difference - products - and quotient of two numbers?
An integer greater than one that is not prime.
1 is a divisor (or factor) of every integer.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.

31. How do you find the y-intercept of a graph?
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.
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.

32. What does it mean if y is inversely proportional to x?
A = s^2 or A =d^2/2 where d is the diagonal
Then the product xy is a constant.
M = (y2 - y1)/(x2 - x1)
A = [(s^2*v3)/4]

33. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
C = p2r
0 is the only number that is neither positive nor negative.
Area = (x°/360)(pr^2) where x is the central angle.

34. What is the formula for the area of a parallelogram?
A = bh
The product of their slopes is -1 (negative reciprocal).
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A^m*b^m = (ab)^m

35. What is true about the measures of the two acute angles in a right triangle?
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 fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Their sum is 90°.
The set of all ordered pairs (x -y) such that y = f(x).

36. How do you calculate percent increases and decreases?
Cannot is 0 - must is 1 - all others are in between.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Even numbers are divisible by 2 and odd numbers are not.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

37. What is the sum of the measures of all angles around a point?
1 is a divisor (or factor) of every integer.
Corresponding sides of similar triangles are in proportion.
No matter how many angles there are - the sum around the point is 360°.
How steep the line is. Horizontal line = 0 - vertical has no slope.

38. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
M = (y2 - y1)/(x2 - x1)
In the expression x^b - x is the base and b is the exponent.
All positive and negative whole numbers - and zero.

39. What is the midpoint formula?
A = 2(lw + lh + hw)
[(x1 + x2)/2] -[(y1 + y2)/2]
The product of their slopes is -1 (negative reciprocal).
360°

40. If you were given the graph of y = f(x) - what does f(a) represent?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
360°
An angle formed by extending the side of the polygon.

41. 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.
For any integer n: 1^n = 1.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.

42. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
V = lwh
A^m*b^m = (ab)^m
M = (y2 - y1)/(x2 - x1)
Shifted right 2 units.

43. What is the formula for the surface area of a rectangular solid?
In the expression x^b - x is the base and b is the exponent.
A = 2(lw + lh + hw)
Is a right triangle with a ratio of sides x:xv3:2x.
A^m/b^m = (a/b)^m

44. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = lwh
The set of all ordered pairs (x -y) such that y = f(x).
Corresponding sides of similar triangles are in proportion.

45. Properties of one 4
D = 2r
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
No matter how many angles there are - the sum around the point is 360°.
1 is the smallest positive odd integer.

46. What is the relationship between a radius of a circle and a line that is tangent to the circle?
A = 2(lw + lh + hw)
The set of all ordered pairs (x -y) such that y = f(x).
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
No matter how many angles there are - the sum around the point is 360°.

47. Properties of zero 3
An equation that states that two ratios are equivalent. 4/6 = 10/15
360°
A = s^2 or A =d^2/2 where d is the diagonal
0 is a multiple of every integer.

48. What is a composite number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = lw
An integer greater than one that is not prime.
A = (1/2)bh.

49. What is an exponent?
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
360°
In the expression x^b - x is the base and b is the exponent.

50. What is the square root of a number?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Is a right triangle with a ratio of sides x:xv3:2x.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

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