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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
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Avg = sum of n numbers/n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

2. Properties of zero 3
0 is a multiple of every integer.
An angle formed by extending the side of the polygon.
A = lw
D = 2r

3. What is an integer?
The ratio of corresponding sides of similar triangles.
Write the percent over 100 and reduce.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
All positive and negative whole numbers - and zero.

4. What are the sum - difference - products - and quotient of two numbers?
Even numbers are divisible by 2 and odd numbers are not.
V = pr^2h
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

5. Important binomial 3
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
1 is the smallest positive odd integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

6. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
0 is the only number that is neither positive nor negative.
A = lw
Their sum is 90°.

7. Important binomial 2
A = pr^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Area = (x°/360)(pr^2) where x is the central angle.

8. Important binomial 1
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(x + y)(x - y) = x^2 - y^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted up 2 units.

9. What is the triangle inequality?
A = 6(l^2)
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

10. What are the median and the mode of a set of data?
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.
Shifted up 2 units.
Then the quotient y/x is a constant.
A^m*b^m = (ab)^m

11. What are the quotient and the remainder?

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12. What is the sum of the measures of all angles around a point?
They are both the same. A divisor or factor of an integer leaves no remainder.
The ratio of corresponding sides of similar triangles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
No matter how many angles there are - the sum around the point is 360°.

13. What is the formula for the area of a triangle?
A = 2(lw + lh + hw)
360°
A = (1/2)bh.
A = lw

14. Law of exponents 1
B^m*b^n = b^m+n
A = lw
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Set y = 0 - and solve.

15. Law of exponents 2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
B^m/b^n = b^m-n
All positive and negative whole numbers - and zero.
The product of their slopes is -1 (negative reciprocal).

16. What is the distance formula?
All positive and negative whole numbers - and zero.
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

17. What is the square root of a number?
Arc = (x°/360)(2pr) where x is the central angle.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
M = (y2 - y1)/(x2 - x1)
An integer greater than one that is not prime.

18. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
Set x = 0 - and solve.
V = lwh
Their sum is 180°.

19. How do you find the area of a sector of a circle?
0 is the only number that is neither positive nor negative.
Area = (x°/360)(pr^2) where x is the central angle.
For any number a: a * 1 = a and a / 1 = a.
(n - 2)(180°)

20. Properties of one 3
Shifted left 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.
1 is a divisor (or factor) of every integer.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

21. Properties of one 2
For any integer n: 1^n = 1.
Then the product xy is a constant.
(Circumference/diameter) of a circle - or approximately 3.14.
All positive and negative whole numbers - and zero.

22. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
A^m/b^m = (a/b)^m
Shifted up 2 units.
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.

23. Properties of zero 1
0 is the only number that is neither positive nor negative.
Arc = (x°/360)(2pr) where x is the central angle.
A = 6(l^2)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

24. For what values of a function is the function undefined?
D = 2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = 6(l^2)
Then the quotient y/x is a constant.

25. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(b^m)^n = b^mn
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

26. How do you find the y-intercept of a graph?
Then the quotient y/x is a constant.
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°.
Set x = 0 - and solve.
Their sum is 90°.

27. Law of exponents 3
(b^m)^n = b^mn
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
B^m*b^n = b^m+n

28. Properties of one 1
A = 2(lw + lh + hw)
For any number a: a * 1 = a and a / 1 = a.
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.
(n - 2)(180°)

29. What is the formula for the surface area of a cube?
For any number a: a * 1 = a and a / 1 = a.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
All positive and negative whole numbers - and zero.
A = 6(l^2)

30. What is a ratio?

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31. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
A = (1/2)bh.
A^m*b^m = (ab)^m
C = p2r

32. How do you find the probability that an event will occur?
The two pairs of opposite angles formed are equal to each other.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.

33. What is the formula for the area of a parallelogram?
A = bh
V = lwh
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

34. What is p?
For any right triangle - a^2 + b^2 = c^2.
(Circumference/diameter) of a circle - or approximately 3.14.
A = s^2 or A =d^2/2 where d is the diagonal
1 is the smallest positive odd integer.

35. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 90°.
A fraction whose denominator is 100 i.e. 17% = 17/100
D = 2r

36. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
B^m/b^n = b^m-n
Shifted right 2 units.
An integer greater than one that is not prime.
No matter how many angles there are - the sum around the point is 360°.

37. What is an exterior angle of a polygon?
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.
An angle formed by extending the side of the polygon.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

38. What is special formula for the area of an equilateral triangle?
V = pr^2h
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = [(s^2*v3)/4]
Cannot is 0 - must is 1 - all others are in between.

39. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = bh
360°
Area = (x°/360)(pr^2) where x is the central angle.

40. What is the probability of an event that cannot occur? That must occur?
Set y = 0 - and solve.
The two pairs of opposite angles formed are equal to each other.
Cannot is 0 - must is 1 - all others are in between.
Corresponding sides of similar triangles are in proportion.

41. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.
[(x1 + x2)/2] -[(y1 + y2)/2]

42. What is true about the measures of the four angles formed by two intersecting lines?
1 is the smallest positive odd integer.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The two pairs of opposite angles formed are equal to each other.
A = bh

43. Properties of zero 5
For any number b: b = -b if and only if b = 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.
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.
No matter how many angles there are - the sum around the point is 360°.

44. What is a percent?
Set y = 0 - and solve.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A fraction whose denominator is 100 i.e. 17% = 17/100

45. What is the ratio of similitude?
B^m/b^n = b^m-n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
All positive and negative whole numbers - and zero.
The ratio of corresponding sides of similar triangles.

46. Properties of one 4
1 is the smallest positive odd integer.
Shifted right 2 units.
A^m/b^m = (a/b)^m
A = pr^2

47. How do we write the equation of a line?
(b^m)^n = b^mn
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

48. What formula is used for an average?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Avg = sum of n numbers/n
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

49. What is a divisor and a factor of an 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.
They are both the same. A divisor or factor of an integer leaves no remainder.
For any number a: a * 1 = a and a / 1 = a.
360°

50. What is the relationship between a radius of a circle and a line that is tangent to the circle?
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°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
1 is the smallest positive odd integer.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.