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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 is the relationship between the graph of f(x) the graph of y = f(x - 2)?
For any right triangle - a^2 + b^2 = c^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Shifted right 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

2. Properties of zero 3
Corresponding sides of similar triangles are in proportion.
A = s^2 or A =d^2/2 where d is the diagonal
0 is a multiple of every integer.
M = (y2 - y1)/(x2 - x1)

3. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m/b^m = (a/b)^m
D = 2r

4. For what values of a function is the function undefined?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = (1/2)bh.
A = [(s^2*v3)/4]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

5. What is a proportion?
For any number b: b = -b if and only if b = 0.
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15

6. What is true about the measures of the two acute angles in a right triangle?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Their sum is 90°.
V = lwh
360°

7. Important binomial 2
Avg = sum of n numbers/n
V = lwh
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

8. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
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.
For any number b: b = -b if and only if b = 0.
0 is the only number that is neither positive nor negative.

9. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
Even numbers are divisible by 2 and odd numbers are not.
The set of all ordered pairs (x -y) such that y = f(x).
A = (1/2)bh.

10. What is a composite number?
An integer greater than one that is not prime.
For any right triangle - a^2 + b^2 = c^2.
A = lw
Arc = (x°/360)(2pr) where x is the central angle.

11. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
Their sum is 90°.
An integer greater than one that is not prime.
In the expression x^b - x is the base and b is the exponent.

12. How do you find the area of a sector of a circle?
C = p2r
D = 2r
Area = (x°/360)(pr^2) where x is the central angle.
1 is the smallest positive odd integer.

13. What is a Venn diagram?
Corresponding sides of similar triangles are in proportion.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
An equation that states that two ratios are equivalent. 4/6 = 10/15
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

14. Properties of zero 2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The product of their slopes is -1 (negative reciprocal).
If a is negative and b is positive - then a < 0 < b.

15. What is the sum of the measures of the n angles of a polygon with n sides?
Arc = (x°/360)(2pr) where x is the central angle.
V = lwh
(n - 2)(180°)
An equation that states that two ratios are equivalent. 4/6 = 10/15

16. In a circle of radius r - what is the formula for the circumference?
A = pr^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
C = p2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

17. What is the formula for the area of a rectangle?
For any integer n: 1^n = 1.
Write the percent over 100 and reduce.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = lw

18. 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.
0 is the only number that is neither positive nor negative.
Equal slopes.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

19. Properties of zero 1
Shifted up 2 units.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
0 is the only number that is neither positive nor negative.

20. Properties of one 3
Is a right triangle with a ratio of sides x:xv3:2x.
A fraction whose denominator is 100 i.e. 17% = 17/100
1 is a divisor (or factor) of every integer.
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.

21. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
1 is a divisor (or factor) of every integer.
B^m*b^n = b^m+n
A = lw

22. Properties of square roots
Then the product xy is a constant.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

23. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
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°.
(x + y)(x - y) = x^2 - y^2
A fraction whose denominator is 100 i.e. 17% = 17/100

24. What important property do similar triangles have?
A = 2(lw + lh + hw)
Area = (x°/360)(pr^2) where x is the central angle.
Corresponding sides of similar triangles are in proportion.
Shifted up 2 units.

25. What is the distributive law?
A = (1/2)bh.
A = 2(lw + lh + hw)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Write the percent over 100 and reduce.

26. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
Equal slopes.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = lwh

27. What is p?
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.
(Circumference/diameter) of a circle - or approximately 3.14.
A = bh

28. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
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.
(x + y)(x - y) = x^2 - y^2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

29. What is the formula for the volume of a cylinder?
Shifted right 2 units.
V = pr^2h
An integer greater than one that is not prime.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

30. What is the volume of a cube?
V = l^3
For any number a: a * 1 = a and a / 1 = a.
For any integer n: 1^n = 1.
In the expression x^b - x is the base and b is the exponent.

31. How do you find a percent of a number?
The set of all ordered pairs (x -y) such that y = f(x).
Write the percent as a decimal - and multiply.
Then the quotient y/x is a constant.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

32. What is an integer?
For any right triangle - a^2 + b^2 = c^2.
All positive and negative whole numbers - and zero.
No matter how many angles there are - the sum around the point is 360°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

33. Law of exponents 4
A^m*b^m = (ab)^m
0 is the only number that is neither positive nor negative.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
An angle formed by extending the side of the polygon.

34. What are the properties of a parallelogram?
Even numbers are divisible by 2 and odd numbers are not.
For any number a: a * 1 = a and a / 1 = a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Their sum is 90°.

35. How do you find the length of an arc of a circle?
In the expression x^b - x is the base and b is the exponent.
A = pr^2
Arc = (x°/360)(2pr) where x is the central angle.
At least one of the factors is 0.

36. What is the area of a square?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
No matter how many angles there are - the sum around the point is 360°.
A = (1/2)bh.
A = s^2 or A =d^2/2 where d is the diagonal

37. Properties of zero 5
For any number b: b = -b if and only if b = 0.
(b^m)^n = b^mn
Set x = 0 - and solve.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

38. What is a percent?
Their sum is 180°.
360°
[(x1 + x2)/2] -[(y1 + y2)/2]
A fraction whose denominator is 100 i.e. 17% = 17/100

39. What formula is used for an average?
Set y = 0 - and solve.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Avg = sum of n numbers/n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

40. What is the sum of the measures of the four angles in a quadrilateral?
A fraction whose denominator is 100 i.e. 17% = 17/100
V = lwh
360°
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

41. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number n: x^-n means 1/x^n.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

42. What is a prime number?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = lwh
An angle formed by extending the side of the polygon.
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.

43. What is the measure of a straight angle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
180°. If two or more angles form a straight angle - their sum is 180°.
1 is a divisor (or factor) of every integer.
Shifted left 2 units.

44. What is true about the measures of the four angles formed by two intersecting lines?
A = pr^2
The two pairs of opposite angles formed are equal to each other.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
C = p2r

45. In a circle of radius r - what is the formula for the diameter?
In the expression x^b - x is the base and b is the exponent.
D = 2r
They are both the same. A divisor or factor of an integer leaves no remainder.
Write the percent as a decimal - and multiply.

46. What is special formula for the area of an equilateral triangle?
An integer greater than one that is not prime.
Shifted right 2 units.
The two pairs of opposite angles formed are equal to each other.
A = [(s^2*v3)/4]

47. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

48. Properties of one 4
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
1 is the smallest positive odd integer.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

49. What are the properties of a square?
The product of their slopes is -1 (negative reciprocal).
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.
Set y = 0 - and solve.
Their sum is 90°.

50. 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.
A = (1/2)bh.
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted up 2 units.