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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. What are the properties of a parallelogram?
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
B^m*b^n = b^m+n

2. What is a percent?
A = pr^2
Then the product xy is a constant.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A fraction whose denominator is 100 i.e. 17% = 17/100

3. What does it mean if y is directly proportional to x?
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted up 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Then the quotient y/x is a constant.

4. Properties of square roots
For any number n: x^-n means 1/x^n.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Is a right triangle with a ratio of sides x:xv3:2x.
Corresponding sides of similar triangles are in proportion.

5. What is an even and an odd number?
A = lw
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Even numbers are divisible by 2 and odd numbers are not.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

6. What is the formula for the area of a rectangle?
A = lw
For any number n: x^-n means 1/x^n.
1 is the smallest positive odd integer.
Shifted left 2 units.

7. How do you find the probability that an event will occur?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A fraction whose denominator is 100 i.e. 17% = 17/100
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

8. What does it mean if y is inversely proportional to x?
B^m*b^n = b^m+n
Cannot is 0 - must is 1 - all others are in between.
Then the product xy is a constant.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

9. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Arc = (x°/360)(2pr) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100
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°.

10. How do you calculate a weighted average?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
360°
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

11. What is true about the measures of the four angles formed by two intersecting lines?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = s^2 or A =d^2/2 where d is the diagonal
The two pairs of opposite angles formed are equal to each other.
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.

12. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The two pairs of opposite angles formed are equal to each other.
360°
V = pr^2h

13. What is the probability of an event that cannot occur? That must occur?
Divide - then multiply by 100.
Set y = 0 - and solve.
Cannot is 0 - must is 1 - all others are in between.
Arc = (x°/360)(2pr) where x is the central angle.

14. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
V = lwh
For any number b: b = -b if and only if b = 0.

15. For what values of a function is the function undefined?
A = s^2 or A =d^2/2 where d is the diagonal
Shifted up 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

16. What is true about the measures of the three angles in a triangle?
For any right triangle - a^2 + b^2 = c^2.
Their sum is 180°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Shifted right 2 units.

17. What is an integer?
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.
All positive and negative whole numbers - and zero.
A fraction whose denominator is 100 i.e. 17% = 17/100
360°

18. What is the formula for the surface area of a cube?
A = 6(l^2)
If a is negative and b is positive - then a < 0 < b.
For any number n: x^-n means 1/x^n.
Their sum is 180°.

19. What is the relationship between a radius of a circle and a line that is tangent to the circle?
M = (y2 - y1)/(x2 - x1)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

20. What are the median and the mode of a set of data?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
360°
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

21. What is a composite number?
An integer greater than one that is not prime.
The product of their slopes is -1 (negative reciprocal).
Is a right triangle with a ratio of sides x:xv3:2x.
A^m*b^m = (ab)^m

22. Law of exponents 1
B^m*b^n = b^m+n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A fraction whose denominator is 100 i.e. 17% = 17/100
Avg = sum of n numbers/n

23. How you convert a fraction or a decimal to a percent?
0 is a multiple of every integer.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = (1/2)bh.
Divide - then multiply by 100.

24. Properties of one 2
For any number a: a * 1 = a and a / 1 = a.
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any integer n: 1^n = 1.

25. Important binomial 2
A = lw
(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.
A = (1/2)bh.

26. What is an exterior angle of a polygon?
Divide - then multiply by 100.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
An angle formed by extending the side of the polygon.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

27. What is a negative exponent?
No matter how many angles there are - the sum around the point is 360°.
For any number n: x^-n means 1/x^n.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A fraction whose denominator is 100 i.e. 17% = 17/100

28. What is special formula for the area of an equilateral triangle?
All positive and negative whole numbers - and zero.
B^m/b^n = b^m-n
A = [(s^2*v3)/4]
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

29. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = (1/2)bh.
How steep the line is. Horizontal line = 0 - vertical has no slope.
(Circumference/diameter) of a circle - or approximately 3.14.

30. What are the quotient and the remainder?

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31. What is the formula for the area of a parallelogram?
A = bh
The ratio of corresponding sides of similar triangles.
A = 2(lw + lh + hw)
C = p2r

32. What is an exponent?
Set x = 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.
For any number n: x^-n means 1/x^n.
In the expression x^b - x is the base and b is the exponent.

33. What is a divisor and a factor of an integer?
For any number a: a * 1 = a and a / 1 = a.
All positive and negative whole numbers - and zero.
For any number n: x^-n means 1/x^n.
They are both the same. A divisor or factor of an integer leaves no remainder.

34. Law of exponents 3
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.
(b^m)^n = b^mn
0 is the only number that is neither positive nor negative.

35. Law of exponents 4
For any right triangle - a^2 + b^2 = c^2.
The set of all ordered pairs (x -y) such that y = f(x).
A^m*b^m = (ab)^m
Then the product xy is a constant.

36. Properties of zero 1
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Arc = (x°/360)(2pr) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
0 is the only number that is neither positive nor negative.

37. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = s^2 or A =d^2/2 where d is the diagonal
360°

38. What is the midpoint formula?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A^m*b^m = (ab)^m
Shifted left 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]

39. In a circle of radius r - what is the formula for the circumference?
Even numbers are divisible by 2 and odd numbers are not.
C = p2r
For any number n: x^-n means 1/x^n.
A = bh

40. 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.
Equal slopes.
Their sum is 180°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

41. What are the important properties of a 45-45 - 90 triangle?
[(x1 + x2)/2] -[(y1 + y2)/2]
A^m/b^m = (a/b)^m
Is a right triangle with a ratio of sides x:xv3:2x.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

42. Properties of zero 3
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Shifted right 2 units.
1 is a divisor (or factor) of every integer.
0 is a multiple of every integer.

43. What are the sum - difference - products - and quotient of two numbers?
A = lw
Equal slopes.
(x + y)(x - y) = x^2 - y^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

44. What is the sum of the measures of the n angles of a polygon with n sides?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(n - 2)(180°)
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

45. What is true about the slopes of perpendicular lines?
No matter how many angles there are - the sum around the point is 360°.
Shifted down 2 units.
The product of their slopes is -1 (negative reciprocal).
A = 2(lw + lh + hw)

46. Law of exponents 2
At least one of the factors is 0.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
B^m/b^n = b^m-n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

47. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
Even numbers are divisible by 2 and odd numbers are not.
All positive and negative whole numbers - and zero.
A^m/b^m = (a/b)^m

48. What are the important properties of 30-60-90 triangle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number a: a * 1 = a and a / 1 = a.
Is a right triangle with a ratio of sides x:xv3:2x.

49. What is the formula for the volume of a rectangular solid?
Then the product xy is a constant.
(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.
V = lwh

50. What is the volume of a cube?
V = l^3
Area = (x°/360)(pr^2) where x is the central angle.
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°.
360°