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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Properties of one 3
Their sum is 180°.
1 is a divisor (or factor) of every integer.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A^m*b^m = (ab)^m

2. Important binomial 2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
180°. If two or more angles form a straight angle - their sum is 180°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

3. What is a Venn diagram?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
360°
Their sum is 180°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

4. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
In the expression x^b - x is the base and b is the exponent.
Shifted right 2 units.
A^m/b^m = (a/b)^m

5. What are the properties of a rectangle?
1 is a divisor (or factor) of every integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
All positive and negative whole numbers - and zero.

6. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any right triangle - a^2 + b^2 = c^2.
For any number a: a * 1 = a and a / 1 = a.
Shifted left 2 units.

7. What is true about the slopes of parallel lines?
Equal slopes.
(n - 2)(180°)
Divide - then multiply by 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.

8. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Arc = (x°/360)(2pr) where x is the central angle.
Shifted up 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.

9. 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.
A = s^2 or A =d^2/2 where d is the diagonal
A = 2(lw + lh + hw)

10. What is the graph of a function?
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 left 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
A = pr^2

11. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
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.
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 = s^2 or A =d^2/2 where d is the diagonal
Shifted up 2 units.

12. What are the important properties of 30-60-90 triangle?
The two pairs of opposite angles formed are equal to each other.
Is a right triangle with a ratio of sides x:xv3:2x.
D = 2r
A = pr^2

13. Properties of one 4
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Area = (x°/360)(pr^2) where x is the central angle.
1 is the smallest positive odd integer.
The two pairs of opposite angles formed are equal to each other.

14. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Their sum is 90°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

15. Properties of zero 4
The product of their slopes is -1 (negative reciprocal).
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.

16. What is true about the measures of the three angles in a triangle?
All positive and negative whole numbers - and zero.
Shifted left 2 units.
360°
Their sum is 180°.

17. How do you calculate a weighted average?
No matter how many angles there are - the sum around the point is 360°.
Then the product xy is a constant.
Set y = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

18. What is the square root of a number?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
360°
All positive and negative whole numbers - and zero.

19. What is the area of a square?
For any number n: x^-n means 1/x^n.
Shifted up 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = s^2 or A =d^2/2 where d is the diagonal

20. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
A = lw
All positive and negative whole numbers - and zero.
(n - 2)(180°)

21. How do you convert a percent to a fraction or a decimal?
In the expression x^b - x is the base and b is the exponent.
A = lw
Write the percent over 100 and reduce.
If a is negative and b is positive - then a < 0 < b.

22. What is a prime number?
Arc = (x°/360)(2pr) where x is the central angle.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
Then the product xy is a constant.

23. What is the probability of an event that cannot occur? That must occur?
Set y = 0 - and solve.
For any integer n: 1^n = 1.
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.
Cannot is 0 - must is 1 - all others are in between.

24. What is true about the measures of the two acute angles in a right triangle?
D = 2r
Their sum is 90°.
All positive and negative whole numbers - and zero.
The product of their slopes is -1 (negative reciprocal).

25. How do you find the area of a sector of a circle?
A = bh
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Then the product xy is a constant.
Area = (x°/360)(pr^2) where x is the central angle.

26. What is the formula for the area of a triangle?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = (1/2)bh.
The set of all ordered pairs (x -y) such that y = f(x).
The product of their slopes is -1 (negative reciprocal).

27. What is the distributive law?
For any number a: a * 1 = a and a / 1 = 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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

28. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
M = (y2 - y1)/(x2 - x1)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Avg = sum of n numbers/n
Shifted down 2 units.

29. Properties of zero 5
For any number b: b = -b if and only if b = 0.
A^m*b^m = (ab)^m
The set of all ordered pairs (x -y) such that y = f(x).
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°.

30. What is a composite number?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The ratio of corresponding sides of similar triangles.
An integer greater than one that is not prime.

31. What are the properties of a parallelogram?
V = lwh
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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 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.

32. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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
For any number b: b = -b if and only if b = 0.

33. What is the formula for the area of a rectangle?
A = lw
A = pr^2
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The ratio of corresponding sides of similar triangles.

34. What are the properties of a square?
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.
Arc = (x°/360)(2pr) where x is the central angle.
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.

35. Law of exponents 2
Corresponding sides of similar triangles are in proportion.
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted up 2 units.
B^m/b^n = b^m-n

36. What are the important properties of a 45-45 - 90 triangle?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.

37. 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°.
Shifted up 2 units.
A fraction whose denominator is 100 i.e. 17% = 17/100
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

38. What is a proportion?
Shifted right 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(x + y)(x - y) = x^2 - y^2
1 is the smallest positive odd integer.

39. What formula is used for an average?
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.
M = (y2 - y1)/(x2 - x1)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Avg = sum of n numbers/n

40. What are the sum - difference - products - and quotient of two numbers?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any integer n: 1^n = 1.
Cannot is 0 - must is 1 - all others are in between.

41. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
0 is a multiple of every integer.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An integer greater than one that is not prime.

42. How do you find the length of an arc of a circle?
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.
All positive and negative whole numbers - and zero.
Arc = (x°/360)(2pr) where x is the central angle.
For any number n: x^-n means 1/x^n.

43. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Write the percent over 100 and reduce.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Set y = 0 - and solve.

44. What is an exponent?
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.
180°. If two or more angles form a straight angle - their sum is 180°.
A = [(s^2*v3)/4]
In the expression x^b - x is the base and b is the exponent.

45. What is a function?
A = lw
A^m/b^m = (a/b)^m
In the expression x^b - x is the base and b is the exponent.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

46. What is true about the areas of similar triangles?
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).
Shifted left 2 units.
(x + y)(x - y) = x^2 - y^2

47. What is the formula for the area of a parallelogram?
(x + y)(x - y) = x^2 - y^2
A = bh
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Set x = 0 - and solve.

48. Properties of zero 3
0 is the only number that is neither positive nor negative.
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.
If a is negative and b is positive - then a < 0 < b.

49. Law of exponents 4
A = s^2 or A =d^2/2 where d is the diagonal
A^m*b^m = (ab)^m
Then the product xy is a constant.
A = 6(l^2)

50. What is true about the slopes of perpendicular lines?
Is a right triangle with a ratio of sides x:xv3:2x.
The product of their slopes is -1 (negative reciprocal).
A = (1/2)bh.
Arc = (x°/360)(2pr) where x is the central angle.