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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. Properties of square roots
(b^m)^n = b^mn
(x + y)(x - y) = x^2 - y^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any number n: x^-n means 1/x^n.

2. What is true about the slopes of perpendicular lines?
Then the product xy is a constant.
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.
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.

3. How do you find the slope of a line?
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any right triangle - a^2 + b^2 = c^2.
M = (y2 - y1)/(x2 - x1)
C = p2r

4. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
A = lw
Then the product xy is a constant.
(x + y)(x - y) = x^2 - y^2

5. What is a ratio?

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6. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = pr^2

7. How do you find the x-intercept of a graph?
A = bh
Set y = 0 - and solve.
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

8. 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.
A = 6(l^2)
Their sum is 90°.
For any right triangle - a^2 + b^2 = c^2.

9. What important property do similar triangles have?
180°. If two or more angles form a straight angle - their sum is 180°.
Corresponding sides of similar triangles are in proportion.
(b^m)^n = b^mn
A = bh

10. What are the quotient and the remainder?

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11. Properties of one 2
If a is negative and b is positive - then a < 0 < b.
For any integer n: 1^n = 1.
B^m*b^n = b^m+n
(b^m)^n = b^mn

12. How do you calculate percent increases and decreases?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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

13. Properties of one 3
1 is a divisor (or factor) of every integer.
They are both the same. A divisor or factor of an integer leaves no remainder.
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted right 2 units.

14. What are the properties of a square?
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.
360°
Is a right triangle with a ratio of sides x:xv3:2x.

15. 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 every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.
Avg = sum of n numbers/n

16. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Write the percent over 100 and reduce.
The two pairs of opposite angles formed are equal to each other.

17. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Arc = (x°/360)(2pr) where x is the central angle.
All positive and negative whole numbers - and zero.
V = lwh

18. What is a composite number?
How steep the line is. Horizontal line = 0 - vertical has no slope.
The two pairs of opposite angles formed are equal to each other.
An integer greater than one that is not prime.
360°

19. What formula is used for an average?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
360°
C = p2r
Avg = sum of n numbers/n

20. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
In the expression x^b - x is the base and b is the exponent.
A = 6(l^2)
Corresponding sides of similar triangles are in proportion.
Shifted right 2 units.

21. 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.
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°.
M = (y2 - y1)/(x2 - x1)
0 is the only number that is neither positive nor negative.

22. How do you calculate a weighted average?
Shifted left 2 units.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The two pairs of opposite angles formed are equal to each other.
For any number a: a * 1 = a and a / 1 = a.

23. If the product of two or more numbers is 0 - what do you know about the numbers?
M = (y2 - y1)/(x2 - x1)
D = 2r
At least one of the factors is 0.
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.

24. In a circle of radius r - what is the formula for the diameter?
360°
D = 2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(b^m)^n = b^mn

25. For what values of a function is the function undefined?
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

26. What is the sum of the measures of the n angles of a polygon with n sides?
Shifted down 2 units.
0 is the only number that is neither positive nor negative.
(n - 2)(180°)
An integer greater than one that is not prime.

27. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
A = (1/2)bh.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

28. What is true about the measures of the three angles in a triangle?
Then the product xy is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any number a: a * 1 = a and a / 1 = a.
Their sum is 180°.

29. Law of exponents 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.
Corresponding sides of similar triangles are in proportion.
B^m/b^n = b^m-n
Shifted right 2 units.

30. What is an exterior angle of a polygon?
[(x1 + x2)/2] -[(y1 + y2)/2]
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An angle formed by extending the side of the polygon.
Set x = 0 - and solve.

31. What is a Venn diagram?
Then the quotient y/x is a constant.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any number n: x^-n means 1/x^n.

32. What is the formula for the area of a triangle?
Their sum is 180°.
A = (1/2)bh.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
D = 2r

33. What is the midpoint formula?
B^m*b^n = b^m+n
[(x1 + x2)/2] -[(y1 + y2)/2]
Cannot is 0 - must is 1 - all others are in between.
A fraction whose denominator is 100 i.e. 17% = 17/100

34. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted right 2 units.

35. How do you find the probability that an event will occur?
Write the percent as a decimal - and multiply.
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)
How steep the line is. Horizontal line = 0 - vertical has no slope.

36. What are the properties of a rectangle?
Area = (x°/360)(pr^2) where x is the central angle.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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°.

37. In a circle of radius r - what is the formula for the area?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The two pairs of opposite angles formed are equal to each other.
A = pr^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

38. What is the square root of a number?
Their sum is 180°.
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.
1 is the smallest positive odd integer.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

39. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.

40. How do you find the area of a sector of a circle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Area = (x°/360)(pr^2) where x is the central angle.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = 2(lw + lh + hw)

41. Properties of zero 4
Shifted down 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Then the quotient y/x is a constant.

42. Properties of zero 3
A = s^2 or A =d^2/2 where d is the diagonal
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The set of all ordered pairs (x -y) such that y = f(x).
0 is a multiple of every integer.

43. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Shifted up 2 units.
A = lw
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

44. Law of exponents 4
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A^m*b^m = (ab)^m
No matter how many angles there are - the sum around the point is 360°.
The product of their slopes is -1 (negative reciprocal).

45. What is an exterior angle of a triangle?
C = p2r
V = l^3
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
1 is the smallest positive odd integer.

46. In a circle of radius r - what is the formula for the circumference?
(Circumference/diameter) of a circle - or approximately 3.14.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
C = p2r

47. What is the formula for the surface area of a rectangular solid?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Even numbers are divisible by 2 and odd numbers are not.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = 2(lw + lh + hw)

48. What are similar triangles?
Is a right triangle with a ratio of sides x:xv3:2x.
In the expression x^b - x is the base and b is the exponent.
A = s^2 or A =d^2/2 where d is the diagonal
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

49. What is true about the measures of the two acute angles in a right triangle?
Area = (x°/360)(pr^2) where x is the central angle.
A = bh
Their sum is 90°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

50. Law of exponents 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = lw
Set x = 0 - and solve.
(b^m)^n = b^mn