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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. How do you find the x-intercept of a graph?
D = 2r
Set y = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.

2. Properties of zero 1
0 is the only number that is neither positive nor negative.
Then the product xy is a constant.
Their sum is 180°.
Equal slopes.

3. What is the area of a square?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = s^2 or A =d^2/2 where d is the diagonal
Their sum is 180°.

4. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = pr^2
V = l^3
V = lwh

5. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(b^m)^n = b^mn
A = 2(lw + lh + hw)

6. 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.
All positive and negative whole numbers - and zero.
The product of their slopes is -1 (negative reciprocal).
[(x1 + x2)/2] -[(y1 + y2)/2]

7. What is an integer?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
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.
C = p2r
All positive and negative whole numbers - and zero.

8. What is a proportion?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Set x = 0 - and solve.
(n - 2)(180°)

9. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted right 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

10. What is an exponent?
V = pr^2h
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
In the expression x^b - x is the base and b is the exponent.
Shifted left 2 units.

11. What is a function?
All positive and negative whole numbers - and zero.
C = p2r
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

12. Important binomial 2
A^m*b^m = (ab)^m
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Then the product xy is a constant.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

13. Properties of zero 3
(Circumference/diameter) of a circle - or approximately 3.14.
0 is a multiple of every integer.
(x + y)(x - y) = x^2 - y^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

14. What does it mean if y is inversely proportional to x?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Even numbers are divisible by 2 and odd numbers are not.
Then the product xy is a constant.
The set of all ordered pairs (x -y) such that y = f(x).

15. 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.
Area = (x°/360)(pr^2) where x is the central angle.
B^m/b^n = b^m-n
The two pairs of opposite angles formed are equal to each other.

16. What formula is used for an average?
Avg = sum of n numbers/n
Write the percent as a decimal - and multiply.
0 is the only number that is neither positive nor negative.
A = [(s^2*v3)/4]

17. What is a negative exponent?
0 is the only number that is neither positive nor negative.
Write the percent as a decimal - and multiply.
For any number n: x^-n means 1/x^n.
A = bh

18. What is true about the slopes of parallel lines?
0 is a multiple of every integer.
Equal slopes.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = bh

19. In a circle of radius r - what is the formula for the area?
No matter how many angles there are - the sum around the point is 360°.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = pr^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.

20. What is the formula for the area of a triangle?
A = (1/2)bh.
360°
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
360°

21. What are the properties of a square?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
C = p2r
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.

22. How do we write the equation of a line?
A fraction whose denominator is 100 i.e. 17% = 17/100
[(x1 + x2)/2] -[(y1 + y2)/2]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

23. In a circle of radius r - what is the formula for the circumference?
Arc = (x°/360)(2pr) where x is the central angle.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
C = p2r
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.

24. What is a percent?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The product of their slopes is -1 (negative reciprocal).
A = 6(l^2)
A fraction whose denominator is 100 i.e. 17% = 17/100

25. What is a prime number?
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.
In the expression x^b - x is the base and b is the exponent.
Equal slopes.
For any number n: x^-n means 1/x^n.

26. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
Set y = 0 - and solve.
Then the product xy is a constant.
Is a right triangle with a ratio of sides x:xv3:2x.

27. What do we mean by the slope of the line?
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.
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
An integer greater than one that is not prime.

28. How do you find the y-intercept of a graph?
Equal slopes.
Set x = 0 - and solve.
Shifted left 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

29. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
M = (y2 - y1)/(x2 - x1)
Shifted up 2 units.
Shifted down 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

30. 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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted down 2 units.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

31. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
1 is a divisor (or factor) of every integer.
A = 6(l^2)
For any number b: b = -b if and only if b = 0.

32. What are the important properties of a 45-45 - 90 triangle?
At least one of the factors is 0.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Avg = sum of n numbers/n

33. What is the midpoint formula?
1 is the smallest positive odd integer.
A = [(s^2*v3)/4]
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
[(x1 + x2)/2] -[(y1 + y2)/2]

34. How do you find a percent of a number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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°.
Shifted left 2 units.
Write the percent as a decimal - and multiply.

35. What is a Venn diagram?
For any right triangle - a^2 + b^2 = c^2.
(n - 2)(180°)
A = 6(l^2)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

36. What are the important properties of 30-60-90 triangle?
C = p2r
Then the product xy is a constant.
If a is negative and b is positive - then a < 0 < b.
Is a right triangle with a ratio of sides x:xv3:2x.

37. What is p?
A fraction whose denominator is 100 i.e. 17% = 17/100
(Circumference/diameter) of a circle - or approximately 3.14.
Write the percent as a decimal - and multiply.
A = [(s^2*v3)/4]

38. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
1 is the smallest positive odd integer.
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.

39. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

40. 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.
They are both the same. A divisor or factor of an integer leaves no remainder.
An integer greater than one that is not prime.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

41. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
B^m/b^n = b^m-n
(x + y)(x - y) = x^2 - y^2
Area = (x°/360)(pr^2) where x is the central angle.

42. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(b^m)^n = b^mn
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.

43. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
[(x1 + x2)/2] -[(y1 + y2)/2]
D = 2r
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

44. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
A^m*b^m = (ab)^m
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.
180°. If two or more angles form a straight angle - their sum is 180°.

45. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
The product of their slopes is -1 (negative reciprocal).
Equal slopes.
360°
(n - 2)(180°)

46. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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°.

47. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
The product of their slopes is -1 (negative reciprocal).
A = 6(l^2)
[(x1 + x2)/2] -[(y1 + y2)/2]

48. What are the quotient and the remainder?

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49. Properties of one 1
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.
Shifted down 2 units.
For any number a: a * 1 = a and a / 1 = a.

50. What is the probability of an event that cannot occur? That must occur?
The set of all ordered pairs (x -y) such that y = f(x).
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°.
180°. If two or more angles form a straight angle - their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.