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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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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 relationship between the graph of f(x) the graph of y = f(x) + 2?
Write the percent over 100 and reduce.
Shifted up 2 units.
The ratio of corresponding sides of similar triangles.
Their sum is 180°.

2. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
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°.
V = lwh
Their sum is 90°.

3. Law of exponents 5
A^m/b^m = (a/b)^m
180°. If two or more angles form a straight angle - their sum is 180°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
They are both the same. A divisor or factor of an integer leaves no remainder.

4. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the 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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Area = (x°/360)(pr^2) where x is the central angle.
Then the product xy is a constant.

5. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
If a is negative and b is positive - then a < 0 < b.
Cannot is 0 - must is 1 - all others are in between.
A^m*b^m = (ab)^m

6. What is a Venn diagram?
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
The two pairs of opposite angles formed are equal to each other.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

7. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
For any right triangle - a^2 + b^2 = c^2.
(b^m)^n = b^mn
For any integer n: 1^n = 1.

8. What is the sum of the measures of the four angles in a quadrilateral?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
An angle formed by extending the side of the polygon.
360°
[(x1 + x2)/2] -[(y1 + y2)/2]

9. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
B^m*b^n = b^m+n
M = (y2 - y1)/(x2 - x1)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

10. Law of exponents 1
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
D = 2r
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
B^m*b^n = b^m+n

11. In a circle of radius r - what is the formula for the area?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Write the percent over 100 and reduce.
Shifted up 2 units.
A = pr^2

12. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
C = p2r
In the expression x^b - x is the base and b is the exponent.
Even numbers are divisible by 2 and odd numbers are not.

13. What is a percent?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A fraction whose denominator is 100 i.e. 17% = 17/100

14. What is the distributive law?
A = (1/2)bh.
How steep the line is. Horizontal line = 0 - vertical has no slope.
They are both the same. A divisor or factor of an integer leaves no remainder.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

15. What is the triangle inequality?
Write the percent as a decimal - and multiply.
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

16. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
How steep the line is. Horizontal line = 0 - vertical has no slope.
360°
0 is the only number that is neither positive nor negative.

17. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Is a right triangle with a ratio of sides x:xv3:2x.
Their sum is 90°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
In the expression x^b - x is the base and b is the exponent.

18. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
In the expression x^b - x is the base and b is the exponent.
Shifted down 2 units.
A = pr^2

19. What is the measure of a straight angle?
Shifted left 2 units.
1 is the smallest positive odd integer.
180°. If two or more angles form a straight angle - their sum is 180°.
Even numbers are divisible by 2 and odd numbers are not.

20. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
B^m/b^n = b^m-n
180°. If two or more angles form a straight angle - their sum is 180°.

21. What is the formula for the volume of a cylinder?
V = pr^2h
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

22. Important binomial 1
In the expression x^b - x is the base and b is the exponent.
Area = (x°/360)(pr^2) where x is the central angle.
(x + y)(x - y) = x^2 - y^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

23. What are the properties of a parallelogram?
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.
1 is a divisor (or factor) of every integer.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
C = p2r

24. In a circle of radius r - what is the formula for the diameter?
D = 2r
Divide - then multiply by 100.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The set of all ordered pairs (x -y) such that y = f(x).

25. 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.
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.
Arc = (x°/360)(2pr) where x is the central angle.
1 is a divisor (or factor) of every integer.

26. How do you calculate a weighted average?
Arc = (x°/360)(2pr) where x is the central angle.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = lwh
The set of all ordered pairs (x -y) such that y = f(x).

27. Law of exponents 4
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
An angle formed by extending the side of the polygon.
The set of all ordered pairs (x -y) such that y = f(x).
A^m*b^m = (ab)^m

28. What is a prime number?
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
All positive and negative whole numbers - and zero.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

29. Properties of zero 5
360°
The set of all ordered pairs (x -y) such that y = f(x).
The two pairs of opposite angles formed are equal to each other.
For any number b: b = -b if and only if b = 0.

30. What is a negative exponent?
An equation that states that two ratios are equivalent. 4/6 = 10/15
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 = [(s^2*v3)/4]
For any number n: x^-n means 1/x^n.

31. What does it mean if y is inversely proportional to x?
A = (1/2)bh.
Then the product xy is a constant.
B^m/b^n = b^m-n
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

32. What are the important properties of a 45-45 - 90 triangle?
A^m/b^m = (a/b)^m
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
In the expression x^b - x is the base and b is the exponent.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

33. Law of exponents 2
A = lw
An integer greater than one that is not prime.
B^m/b^n = b^m-n
Their sum is 180°.

34. What is a composite number?
An integer greater than one that is not prime.
0 is the only number that is neither positive nor negative.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

35. How do you find the length of an arc of a circle?
Shifted down 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = 2(lw + lh + hw)
Arc = (x°/360)(2pr) where x is the central angle.

36. 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.
For any integer n: 1^n = 1.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

37. What is an exponent?
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
1 is a divisor (or factor) of every integer.
A^m/b^m = (a/b)^m

38. What are the median and the mode of a set of data?
All positive and negative whole numbers - and zero.
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°.
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.
Shifted right 2 units.

39. What are the quotient and the remainder?

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40. What are the properties of a square?
V = l^3
M = (y2 - y1)/(x2 - x1)
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

41. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
V = l^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.
(b^m)^n = b^mn

42. What is the formula for the surface area of a cube?
360°
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Then the quotient y/x is a constant.
A = 6(l^2)

43. How do you find the area of a sector of a circle?
Their sum is 90°.
Area = (x°/360)(pr^2) where x is the central angle.
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.
Their sum is 180°.

44. Properties of zero 3
Area = (x°/360)(pr^2) where x is the central angle.
An integer greater than one that is not prime.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
0 is a multiple of every integer.

45. What is a function?
Then the product xy is a constant.
Set x = 0 - and solve.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
All positive and negative whole numbers - and zero.

46. What is true about the slopes of perpendicular lines?
Is a right triangle with a ratio of sides x:xv3:2x.
A^m*b^m = (ab)^m
(x + y)(x - y) = x^2 - y^2
The product of their slopes is -1 (negative reciprocal).

47. How do you find the slope of a line?
V = lwh
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
M = (y2 - y1)/(x2 - x1)
0 is a multiple of every integer.

48. What is the formula for the volume of a rectangular solid?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = s^2 or A =d^2/2 where d is the diagonal
Equal slopes.
V = lwh

49. Law of exponents 3
(b^m)^n = b^mn
A = [(s^2*v3)/4]
(x + y)(x - y) = x^2 - y^2
V = lwh

50. What is the distance formula?
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.
(x + y)(x - y) = x^2 - y^2
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°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

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