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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 an exterior angle of a triangle?
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

2. What is a prime number?
Write the percent over 100 and reduce.
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 = (1/2)bh.
1 is the smallest positive odd integer.

3. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) 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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any number b: b = -b if and only if b = 0.

4. What is a proportion?
How steep the line is. Horizontal line = 0 - vertical has no slope.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

5. Properties of zero 2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any number n: x^-n means 1/x^n.
Set x = 0 - and solve.
If a is negative and b is positive - then a < 0 < b.

6. What is the triangle inequality?
B^m*b^n = b^m+n
(b^m)^n = b^mn
Set x = 0 - and solve.
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.

7. What are the sum - difference - products - and quotient of two numbers?
They are both the same. A divisor or factor of an integer leaves no remainder.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Corresponding sides of similar triangles are in proportion.

8. What is true about the areas of similar triangles?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = pr^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The set of all ordered pairs (x -y) such that y = f(x).

9. What formula is used for an average?
A = s^2 or A =d^2/2 where d is the diagonal
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = l^3
Avg = sum of n numbers/n

10. In a circle of radius r - what is the formula for the diameter?
D = 2r
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

11. What is a divisor and a factor of an integer?
Arc = (x°/360)(2pr) where x is the central angle.
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted right 2 units.
A = [(s^2*v3)/4]

12. How do you find the slope of a line?
A = bh
Write the percent as a decimal - and multiply.
M = (y2 - y1)/(x2 - x1)
A fraction whose denominator is 100 i.e. 17% = 17/100

13. How you convert a fraction or a decimal to a percent?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Divide - then multiply by 100.
The set of all ordered pairs (x -y) such that y = f(x).
D = 2r

14. Law of exponents 5
A^m/b^m = (a/b)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = (1/2)bh.
The ratio of corresponding sides of similar triangles.

15. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
No matter how many angles there are - the sum around the point is 360°.
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°.
An angle formed by extending the side of the polygon.
A = 6(l^2)

16. 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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
1 is the smallest positive odd integer.
Their sum is 180°.

17. Properties of one 2
The set of all ordered pairs (x -y) such that y = f(x).
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Cannot is 0 - must is 1 - all others are in between.
For any integer n: 1^n = 1.

18. In a circle of radius r - what is the formula for the circumference?
C = p2r
How steep the line is. Horizontal line = 0 - vertical has no slope.
Write the percent as a decimal - and multiply.
V = lwh

19. Properties of square roots
For any number b: b = -b if and only if b = 0.
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 positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = lw

20. What is the formula for the volume of a rectangular solid?
V = lwh
In the expression x^b - x is the base and b is the exponent.
If a is negative and b is positive - then a < 0 < b.
A = s^2 or A =d^2/2 where d is the diagonal

21. What is true about the slopes of parallel lines?
Divide - then multiply by 100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Equal slopes.
Shifted down 2 units.

22. How do we write the equation of a line?
Is a right triangle with a ratio of sides x:xv3:2x.
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
180°. If two or more angles form a straight angle - their sum is 180°.

23. What is the midpoint formula?
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.
(Circumference/diameter) of a circle - or approximately 3.14.
[(x1 + x2)/2] -[(y1 + y2)/2]
Corresponding sides of similar triangles are in proportion.

24. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Then the product xy is a constant.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

25. Properties of one 3
1 is a divisor (or factor) of every integer.
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
M = (y2 - y1)/(x2 - x1)

26. How do you find the x-intercept of a graph?
The ratio of corresponding sides of similar triangles.
Set y = 0 - and solve.
Even numbers are divisible by 2 and odd numbers are not.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

27. Properties of zero 5
The set of all ordered pairs (x -y) such that y = f(x).
A = s^2 or A =d^2/2 where d is the diagonal
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.

28. Important binomial 2
Arc = (x°/360)(2pr) where x is the central angle.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted up 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

29. What is the area of a square?
A^m/b^m = (a/b)^m
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
B^m/b^n = b^m-n
A = s^2 or A =d^2/2 where d is the diagonal

30. What is a ratio?

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31. What does it mean if y is directly proportional to x?
The set of all ordered pairs (x -y) such that y = f(x).
Then the quotient y/x is a constant.
An integer greater than one that is not prime.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

32. What is the formula for the area of a triangle?
A = (1/2)bh.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
B^m/b^n = b^m-n
An integer greater than one that is not prime.

33. What is the sum of the measures of the four angles in a quadrilateral?
0 is a multiple of every integer.
360°
A^m*b^m = (ab)^m
(Circumference/diameter) of a circle - or approximately 3.14.

34. What is the ratio of similitude?
Divide - then multiply by 100.
The ratio of corresponding sides of similar triangles.
For any right triangle - a^2 + b^2 = c^2.
360°

35. What is the Pythagorean theorem?
0 is the only number that is neither positive nor negative.
Then the quotient y/x is a constant.
For any number n: x^-n means 1/x^n.
For any right triangle - a^2 + b^2 = c^2.

36. 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°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted down 2 units.

37. What is the formula for the area of a parallelogram?
360°
Set y = 0 - and solve.
V = l^3
A = bh

38. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

39. What is the sum of the measures of the n angles of a polygon with n sides?
B^m/b^n = b^m-n
360°
For any number b: b = -b if and only if b = 0.
(n - 2)(180°)

40. How do you find a percent of a number?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Write the percent as a decimal - and multiply.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

41. What does it mean if y is inversely proportional to x?
In the expression x^b - x is the base and b is the exponent.
How steep the line is. Horizontal line = 0 - vertical has no slope.
No matter how many angles there are - the sum around the point is 360°.
Then the product xy is a constant.

42. What is special formula for the area of an equilateral triangle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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 = lwh
A = [(s^2*v3)/4]

43. What is an even and an odd number?
Their sum is 90°.
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.
A^m/b^m = (a/b)^m

44. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.

45. What is true about the measures of the four angles formed by two intersecting lines?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The two pairs of opposite angles formed are equal to each other.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
They are both the same. A divisor or factor of an integer leaves no remainder.

46. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
Arc = (x°/360)(2pr) where x is the central angle.
A = pr^2
Cannot is 0 - must is 1 - all others are in between.

47. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
A = (1/2)bh.
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°.
A^m/b^m = (a/b)^m

48. What is true about the measures of the three angles in a triangle?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
0 is the only number that is neither positive nor negative.
They are both the same. A divisor or factor of an integer leaves no remainder.
Their sum is 180°.

49. 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.
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°.
B^m/b^n = b^m-n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

50. How do you calculate percent increases and decreases?
0 is a multiple of every integer.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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^m/b^m = (a/b)^m

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