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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

2. What is the sum of the measures of the four angles in a quadrilateral?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any right triangle - a^2 + b^2 = c^2.
A = s^2 or A =d^2/2 where d is the diagonal
360°

3. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

4. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A^m/b^m = (a/b)^m
C = p2r
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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°.

5. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If a is negative and b is positive - then a < 0 < b.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = 6(l^2)

6. Properties of zero 5
The set of all ordered pairs (x -y) such that y = f(x).
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
360°
For any number b: b = -b if and only if b = 0.

7. Properties of zero 4
A = [(s^2*v3)/4]
Then the quotient y/x is a constant.
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.

8. What is the formula for the surface area of a rectangular solid?
Set x = 0 - and solve.
1 is a divisor (or factor) of every integer.
360°
A = 2(lw + lh + hw)

9. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
For any number a: a * 1 = a and a / 1 = a.
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.
Shifted left 2 units.
A = pr^2

10. 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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If a is negative and b is positive - then a < 0 < b.
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.

11. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
V = lwh
For any integer n: 1^n = 1.
Shifted down 2 units.

12. How do you find the length of an arc of a circle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Arc = (x°/360)(2pr) where x is the central angle.
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.
Set y = 0 - and solve.

13. What are the properties of a parallelogram?
A^m*b^m = (ab)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
1 is the smallest positive odd integer.
Their sum is 180°.

14. Law of exponents 1
B^m*b^n = b^m+n
How steep the line is. Horizontal line = 0 - vertical has no slope.
B^m/b^n = b^m-n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

15. What do we mean by the slope of the line?
0 is the only number that is neither positive nor negative.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
How steep the line is. Horizontal line = 0 - vertical has no slope.

16. What is true about the measures of the two acute angles in a right triangle?
The ratio of corresponding sides of similar triangles.
For any number n: x^-n means 1/x^n.
Set y = 0 - and solve.
Their sum is 90°.

17. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
In the expression x^b - x is the base and b is the exponent.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
At least one of the factors is 0.

18. Important binomial 3
An angle formed by extending the side of the polygon.
Their sum is 180°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

19. 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.
A^m/b^m = (a/b)^m
The ratio of corresponding sides of similar triangles.
The set of all ordered pairs (x -y) such that y = f(x).

20. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
A^m*b^m = (ab)^m
1 is a divisor (or factor) of every integer.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

21. What is a Venn diagram?
V = pr^2h
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

22. How do you calculate a weighted average?
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.
1 is a divisor (or factor) of every integer.
0 is a multiple of every integer.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

23. What is true about the measures of the three angles in a triangle?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Their sum is 180°.
A = (1/2)bh.
A = [(s^2*v3)/4]

24. What is the formula for the area of a parallelogram?
A = bh
For any number n: x^-n means 1/x^n.
The two pairs of opposite angles formed are equal to each other.
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.

25. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
D = 2r
(Circumference/diameter) of a circle - or approximately 3.14.
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°.
Shifted up 2 units.

26. What is the measure of a straight angle?
Divide - then multiply by 100.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted up 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.

27. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Is a right triangle with a ratio of sides x:xv3:2x.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = lw

28. What are the important properties of 30-60-90 triangle?
B^m/b^n = b^m-n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Is a right triangle with a ratio of sides x:xv3:2x.
A = pr^2

29. Law of exponents 5
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A^m/b^m = (a/b)^m

30. 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.
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°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
C = p2r

31. What is true about the areas of similar triangles?
They are both the same. A divisor or factor of an integer leaves no remainder.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
B^m*b^n = b^m+n
M = (y2 - y1)/(x2 - x1)

32. How do you find the x-intercept of a graph?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Set y = 0 - and solve.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Write the percent over 100 and reduce.

33. What is the triangle inequality?
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.
In the expression x^b - x is the base and b is the exponent.
Their sum is 180°.
For any number n: x^-n means 1/x^n.

34. Properties of zero 1
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
0 is the only number that is neither positive nor negative.
Their sum is 180°.
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.

35. What is a prime number?
D = 2r
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.
A = lw

36. What is an exponent?
A = bh
Then the quotient y/x is a constant.
In the expression x^b - x is the base and b is the exponent.
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.

37. What are the properties of a rectangle?
The product of their slopes is -1 (negative reciprocal).
Equal slopes.
D = 2r
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

38. What is the formula for the volume of a cylinder?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
C = p2r
For any number a: a * 1 = a and a / 1 = a.
V = pr^2h

39. Properties of one 2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The set of all ordered pairs (x -y) such that y = f(x).
For any integer n: 1^n = 1.

40. For what values of a function is the function undefined?
Then the quotient y/x is a constant.
An integer greater than one that is not prime.
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 the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

41. What formula is used for an average?
No matter how many angles there are - the sum around the point is 360°.
Avg = sum of n numbers/n
A fraction whose denominator is 100 i.e. 17% = 17/100
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

42. How do we write the equation of a line?
An equation that states that two ratios are equivalent. 4/6 = 10/15
At least one of the factors is 0.
Shifted up 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

43. 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.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
B^m/b^n = b^m-n
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°.

44. What are the quotient and the remainder?

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45. What is true about the slopes of perpendicular lines?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The product of their slopes is -1 (negative reciprocal).
At least one of the factors is 0.

46. What are the properties of a square?
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.
Cannot is 0 - must is 1 - all others are in between.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
The set of all ordered pairs (x -y) such that y = f(x).

47. What does it mean if y is directly proportional to x?
A = bh
The ratio of corresponding sides of similar triangles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the quotient y/x is a constant.

48. What is an integer?
(n - 2)(180°)
A = (1/2)bh.
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.
All positive and negative whole numbers - and zero.

49. What is p?
A = [(s^2*v3)/4]
1 is the smallest positive odd integer.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(Circumference/diameter) of a circle - or approximately 3.14.

50. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
A = pr^2
Area = (x°/360)(pr^2) where x is the central angle.
[(x1 + x2)/2] -[(y1 + y2)/2]