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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. What are the properties of a rectangle?
Their sum is 90°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A^m/b^m = (a/b)^m

2. How do you find the area of a sector of a circle?
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.
The product of their slopes is -1 (negative reciprocal).
B^m*b^n = b^m+n
Area = (x°/360)(pr^2) where x is the central angle.

3. What is the area of a square?
[(x1 + x2)/2] -[(y1 + y2)/2]
C = p2r
A = s^2 or A =d^2/2 where d is the diagonal
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

4. What is the measure of a straight 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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
180°. If two or more angles form a straight angle - their sum is 180°.
An integer greater than one that is not prime.

5. 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 whose denominator is 100 i.e. 17% = 17/100
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.

6. What is an exterior angle of a polygon?
Their sum is 90°.
An angle formed by extending the side of the polygon.
360°
No matter how many angles there are - the sum around the point is 360°.

7. What is the formula for the area of a rectangle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
360°
A = lw

8. Properties of zero 1
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any number n: x^-n means 1/x^n.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
0 is the only number that is neither positive nor negative.

9. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
Shifted left 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.
The two pairs of opposite angles formed are equal to each other.

10. What is special formula for the area of an equilateral triangle?
The ratio of corresponding sides of similar triangles.
Shifted down 2 units.
A = [(s^2*v3)/4]
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

11. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
[(x1 + x2)/2] -[(y1 + y2)/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.
Cannot is 0 - must is 1 - all others are in between.

12. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.
Equal slopes.
B^m/b^n = b^m-n

13. In a circle of radius r - what is the formula for the circumference?
The ratio of corresponding sides of similar triangles.
M = (y2 - y1)/(x2 - x1)
C = p2r
Avg = sum of n numbers/n

14. How do we write the equation of a line?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Cannot is 0 - must is 1 - all others are in between.
[(x1 + x2)/2] -[(y1 + y2)/2]

15. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Equal slopes.
Shifted right 2 units.
Arc = (x°/360)(2pr) where x is the central angle.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

16. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(b^m)^n = b^mn
Is a right triangle with a ratio of sides x:xv3:2x.

17. Properties of one 3
1 is a divisor (or factor) of every 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.
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.

18. Properties of one 1
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.
For any number a: a * 1 = a and a / 1 = a.
A^m*b^m = (ab)^m
(Circumference/diameter) of a circle - or approximately 3.14.

19. What is the triangle inequality?
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.
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.

20. In a circle of radius r - what is the formula for the area?
A = pr^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.

21. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted left 2 units.
Divide - then multiply by 100.
The two pairs of opposite angles formed are equal to each other.

22. What are the sum - difference - products - and quotient of two numbers?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Set y = 0 - and solve.
They are both the same. A divisor or factor of an integer leaves no remainder.

23. What is the formula for the volume of a cylinder?
Set y = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.
V = pr^2h
An equation that states that two ratios are equivalent. 4/6 = 10/15

24. Law of exponents 5
A^m/b^m = (a/b)^m
Divide - then multiply by 100.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = 2(lw + lh + hw)

25. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
1 is a divisor (or factor) of every integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted up 2 units.

26. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
Set x = 0 - and solve.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

27. For what values of a function is the function undefined?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Avg = sum of n numbers/n
For any number b: b = -b if and only if b = 0.

28. What is an exponent?
Their sum is 180°.
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.
In the expression x^b - x is the base and b is the exponent.
At least one of the factors is 0.

29. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
Write the percent as a decimal - and multiply.
Their sum is 90°.
For any integer n: 1^n = 1.

30. What is true about the measures of the four angles formed by two intersecting lines?
The product of their slopes is -1 (negative reciprocal).
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The two pairs of opposite angles formed are equal to each other.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

31. What is the volume of a cube?
An angle formed by extending the side of the polygon.
Write the percent as a decimal - and multiply.
How steep the line is. Horizontal line = 0 - vertical has no slope.
V = l^3

32. Properties of zero 5
Shifted down 2 units.
For any number b: b = -b if and only if b = 0.
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.

33. What is the sum of the measures of the four angles in a quadrilateral?
Corresponding sides of similar triangles are in proportion.
In the expression x^b - x is the base and b is the exponent.
360°
A = 6(l^2)

34. What is the formula for the area of a triangle?
For any number n: x^-n means 1/x^n.
Area = (x°/360)(pr^2) where x is the central angle.
A = (1/2)bh.
D = 2r

35. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/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
A^m/b^m = (a/b)^m

36. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
0 is a multiple of every integer.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.

37. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
An integer greater than one that is not prime.
M = (y2 - y1)/(x2 - x1)
B^m*b^n = b^m+n

38. Important binomial 1
(x + y)(x - y) = x^2 - y^2
D = 2r
A^m*b^m = (ab)^m
Cannot is 0 - must is 1 - all others are in between.

39. Properties of square roots
Set y = 0 - and solve.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = s^2 or A =d^2/2 where d is the diagonal

40. What are similar triangles?
For any number n: x^-n means 1/x^n.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
1 is the smallest positive odd integer.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

41. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
Cannot is 0 - must is 1 - all others are in between.
Write the percent over 100 and reduce.
How steep the line is. Horizontal line = 0 - vertical has no slope.

42. 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.
Shifted down 2 units.
Even numbers are divisible by 2 and odd numbers are not.
They are both the same. A divisor or factor of an integer leaves no remainder.

43. What do we mean by the slope of the line?
0 is a multiple of every integer.
How steep the line is. Horizontal line = 0 - vertical has no slope.
In the expression x^b - x is the base and b is the exponent.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

44. What is the formula for the surface area of a cube?
A = 6(l^2)
Divide - then multiply by 100.
1 is a divisor (or factor) of every integer.
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 a fractional exponent?
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

46. What is the distributive law?
(b^m)^n = b^mn
A = lw
A^m/b^m = (a/b)^m
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

47. What is an even and an odd number?
Avg = sum of n numbers/n
Even numbers are divisible by 2 and odd numbers are not.
An equation that states that two ratios are equivalent. 4/6 = 10/15
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

48. Law of exponents 2
360°
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m/b^n = b^m-n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

49. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
The ratio of corresponding sides of similar triangles.
Shifted left 2 units.
1 is the smallest positive odd integer.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

50. What is a divisor and a factor of an integer?
(x + y)(x - y) = x^2 - y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
B^m*b^n = b^m+n
They are both the same. A divisor or factor of an integer leaves no remainder.