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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 an exterior angle of a triangle?
No matter how many angles there are - the sum around the point is 360°.
Their sum is 180°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

2. What are the sum - difference - products - and quotient of two numbers?
Shifted up 2 units.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

3. What is the relationship between a radius of a circle and a line that is tangent to the circle?
M = (y2 - y1)/(x2 - x1)
360°
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

4. What is true about the slopes of perpendicular lines?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The product of their slopes is -1 (negative reciprocal).
A fraction whose denominator is 100 i.e. 17% = 17/100
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

5. What is the Pythagorean theorem?
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)(x - y) = x^2 - y^2
For any right triangle - a^2 + b^2 = c^2.
Set x = 0 - and solve.

6. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Area = (x°/360)(pr^2) 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.
Their sum is 180°.

7. In a circle of radius r - what is the formula for the circumference?
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.
C = p2r
Shifted left 2 units.
(n - 2)(180°)

8. 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°.
All positive and negative whole numbers - and zero.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
In the expression x^b - x is the base and b is the exponent.

9. What is the area of a square?
An equation that states that two ratios are equivalent. 4/6 = 10/15
0 is a multiple of every integer.
A = s^2 or A =d^2/2 where d is the diagonal
A fraction whose denominator is 100 i.e. 17% = 17/100

10. What is true about the measures of the three angles in a triangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(b^m)^n = b^mn
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.
Their sum is 180°.

11. What is an even and an odd number?
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°.
B^m/b^n = b^m-n
Even numbers are divisible by 2 and odd numbers are not.
(x + y)(x - y) = x^2 - y^2

12. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Then the quotient y/x is a constant.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

13. If the product of two or more numbers is 0 - what do you know about the numbers?
(Circumference/diameter) of a circle - or approximately 3.14.
At least one of the factors is 0.
A = s^2 or A =d^2/2 where d is the diagonal
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

14. What is the formula for the area of a parallelogram?
For any number n: x^-n means 1/x^n.
A = bh
Arc = (x°/360)(2pr) where x is the central angle.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

15. What are similar triangles?
B^m*b^n = b^m+n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
B^m/b^n = b^m-n
V = l^3

16. What is the distance formula?
Arc = (x°/360)(2pr) where x is the central angle.
For any number b: b = -b if and only if b = 0.
Then the quotient y/x is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

17. What is a proportion?
How steep the line is. Horizontal line = 0 - vertical has no slope.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted right 2 units.
Avg = sum of n numbers/n

18. Properties of zero 3
M = (y2 - y1)/(x2 - x1)
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.
0 is a multiple of every integer.
Shifted down 2 units.

19. In a circle of radius r - what is the formula for the diameter?
Shifted up 2 units.
D = 2r
Their sum is 180°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

20. What is the volume of a cube?
V = l^3
0 is the only number that is neither positive nor negative.
V = pr^2h
1 is the smallest positive odd integer.

21. What are the important properties of a 45-45 - 90 triangle?
Write the percent as a decimal - and multiply.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

22. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
1 is the smallest positive odd integer.
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted right 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

23. How do you find the area of a sector of a circle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = s^2 or A =d^2/2 where d is the diagonal
Area = (x°/360)(pr^2) where x is the central angle.
The product of their slopes is -1 (negative reciprocal).

24. What are the properties of a parallelogram?
Write the percent as a decimal - and multiply.
Divide - then multiply by 100.
(Circumference/diameter) of a circle - or approximately 3.14.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

25. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
(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.
Set x = 0 - and solve.
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°.

26. Properties of square roots
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = bh

27. How do you find a percent of a number?
Area = (x°/360)(pr^2) where x is the central angle.
Write the percent as a decimal - and multiply.
(b^m)^n = b^mn
Shifted up 2 units.

28. What is the formula for the surface area of a cube?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted down 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]
A = 6(l^2)

29. What does it mean if y is directly proportional to x?
Their sum is 90°.
Set y = 0 - and solve.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Then the quotient y/x is a constant.

30. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted left 2 units.
Shifted up 2 units.
Arc = (x°/360)(2pr) where x is the central angle.

31. What is an exterior angle of a polygon?
C = p2r
An angle formed by extending the side of the polygon.
At least one of the factors is 0.
Is a right triangle with a ratio of sides x:xv3:2x.

32. 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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Their sum is 180°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

33. How do you calculate percent increases and decreases?
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.
M = (y2 - y1)/(x2 - x1)
For any right triangle - a^2 + b^2 = c^2.

34. What is true about the measures of the four angles formed by two intersecting lines?
Avg = sum of n numbers/n
The two pairs of opposite angles formed are equal to each other.
V = pr^2h
The product of their slopes is -1 (negative reciprocal).

35. What is a composite number?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An integer greater than one that is not prime.
1 is a divisor (or factor) of every integer.
For any integer n: 1^n = 1.

36. How do you find the y-intercept of a graph?
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.
(x + y)(x - y) = x^2 - y^2
Set x = 0 - and solve.
360°

37. Properties of zero 4
Set x = 0 - and solve.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.

38. What is an integer?
In the expression x^b - x is the base and b is the exponent.
All positive and negative whole numbers - and zero.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

39. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
(b^m)^n = b^mn
Shifted up 2 units.
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.
For any number a: a * 1 = a and a / 1 = a.

40. What is true about the slopes of parallel lines?
M = (y2 - y1)/(x2 - x1)
Equal slopes.
Write the percent as a decimal - and multiply.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

41. Law of exponents 4
A^m*b^m = (ab)^m
For any right triangle - a^2 + b^2 = c^2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
An angle formed by extending the side of the polygon.

42. Properties of zero 5
(Circumference/diameter) of a circle - or approximately 3.14.
For any number b: b = -b if and only if b = 0.
[(x1 + x2)/2] -[(y1 + y2)/2]
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

43. Important binomial 2
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = lw

44. Law of exponents 5
(x + y)(x - y) = x^2 - y^2
A^m/b^m = (a/b)^m
They are both the same. A divisor or factor of an integer leaves no remainder.
An integer greater than one that is not prime.

45. What are the properties of a rectangle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = 6(l^2)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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 probability of an event that cannot occur? That must occur?
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 quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Cannot is 0 - must is 1 - all others are in between.
A = s^2 or A =d^2/2 where d is the diagonal

47. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Write the percent as a decimal - and multiply.
A = lw
0 is a multiple of every integer.

48. Important binomial 1
M = (y2 - y1)/(x2 - x1)
Their sum is 90°.
A = s^2 or A =d^2/2 where d is the diagonal
(x + y)(x - y) = x^2 - y^2

49. What is the formula for the area of a rectangle?
Write the percent as a decimal - and multiply.
A = lw
A = bh
For any right triangle - a^2 + b^2 = c^2.

50. Properties of one 4
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
1 is the smallest positive odd integer.
A = 6(l^2)