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GRE Math: Facts

Subjects : gre, math

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 true about the slopes of perpendicular lines?
For any integer n: 1^n = 1.
(n - 2)(180°)
The product of their slopes is -1 (negative reciprocal).
A = bh

2. Properties of one 4
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
1 is the smallest positive odd integer.
A^m*b^m = (ab)^m
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.

3. What is the triangle inequality?
C = p2r
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.
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.

4. In a circle of radius r - what is the formula for the area?
360°
A = pr^2
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any integer n: 1^n = 1.

5. What is a percent?
The set of all ordered pairs (x -y) such that y = f(x).
A fraction whose denominator is 100 i.e. 17% = 17/100
B^m/b^n = b^m-n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

6. What are the important properties of 30-60-90 triangle?
The set of all ordered pairs (x -y) such that y = f(x).
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Is a right triangle with a ratio of sides x:xv3:2x.
Then the quotient y/x is a constant.

7. How do we write the equation of a line?
A = 6(l^2)
Equal slopes.
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.

8. What is the measure of a straight 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°.
D = 2r
180°. If two or more angles form a straight angle - their sum is 180°.
1 is the smallest positive odd integer.

9. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
An angle formed by extending the side of the polygon.
The two pairs of opposite angles formed are equal to each other.
Avg = sum of n numbers/n

10. What is the volume of a cube?
For any right triangle - a^2 + b^2 = c^2.
V = l^3
Area = (x°/360)(pr^2) where x is the central angle.
360°

11. What are the important properties of a 45-45 - 90 triangle?
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = 2(lw + lh + hw)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = s^2 or A =d^2/2 where d is the diagonal

12. What is a negative exponent?
For any number n: x^-n means 1/x^n.
For any right triangle - a^2 + b^2 = c^2.
[(x1 + x2)/2] -[(y1 + y2)/2]
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

13. Properties of one 2
For any integer n: 1^n = 1.
A = 2(lw + lh + hw)
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°.
0 is a multiple of every integer.

14. Law of exponents 3
(b^m)^n = b^mn
Corresponding sides of similar triangles are in proportion.
B^m*b^n = b^m+n
Their sum is 90°.

15. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
An angle formed by extending the side of the polygon.
(b^m)^n = b^mn
V = lwh

16. Law of exponents 2
An angle formed by extending the side of the polygon.
For any number a: a * 1 = a and a / 1 = a.
[(x1 + x2)/2] -[(y1 + y2)/2]
B^m/b^n = b^m-n

17. Properties of square roots
Then the product xy is a constant.
A fraction whose denominator is 100 i.e. 17% = 17/100
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = bh

18. How do you convert a percent to a fraction or a decimal?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Write the percent over 100 and reduce.
0 is a multiple of every integer.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

19. Law of exponents 4
V = l^3
A^m*b^m = (ab)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted left 2 units.

20. What is the distance formula?
In the expression x^b - x is the base and b is the exponent.
Set x = 0 - and solve.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

21. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
Is a right triangle with a ratio of sides x:xv3:2x.
Their sum is 180°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

22. What is the probability of an event that cannot occur? That must occur?
Is a right triangle with a ratio of sides x:xv3:2x.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Cannot is 0 - must is 1 - all others are in between.
Then the quotient y/x is a constant.

23. What is true about the measures of the three angles in a triangle?
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.
In the expression x^b - x is the base and b is the exponent.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Their sum is 180°.

24. Properties of zero 3
Set x = 0 - and solve.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Avg = sum of n numbers/n
0 is a multiple of every integer.

25. What is true about the measures of the four angles formed by two intersecting lines?
Shifted right 2 units.
The two pairs of opposite angles formed are equal to each other.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

26. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(n - 2)(180°)
The two pairs of opposite angles formed are equal to each other.
Arc = (x°/360)(2pr) where x is the central angle.

27. What is a divisor and a factor of an integer?
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 - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = bh

28. What is the distributive law?
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.
0 is the only number that is neither positive nor negative.
A^m/b^m = (a/b)^m

29. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
C = p2r
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

30. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(Circumference/diameter) of a circle - or approximately 3.14.
If a is negative and b is positive - then a < 0 < b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

31. How do you find the x-intercept of a graph?
An integer greater than one that is not prime.
A = 2(lw + lh + hw)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Set y = 0 - and solve.

32. What do we mean by the slope of the line?
B^m*b^n = b^m+n
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
How steep the line is. Horizontal line = 0 - vertical has no slope.

33. What is the formula for the area of a rectangle?
Arc = (x°/360)(2pr) where x is the central angle.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = lw
0 is the only number that is neither positive nor negative.

34. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Even numbers are divisible by 2 and odd numbers are not.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

35. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The set of all ordered pairs (x -y) such that y = f(x).
An angle formed by extending the side of the polygon.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

36. What is an exponent?
360°
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A fraction whose denominator is 100 i.e. 17% = 17/100
In the expression x^b - x is the base and b is the exponent.

37. What is an integer?
Their sum is 180°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A^m*b^m = (ab)^m
All positive and negative whole numbers - and zero.

38. What formula is used for an average?
C = p2r
Avg = sum of n numbers/n
Their sum is 180°.
In the expression x^b - x is the base and b is the exponent.

39. What is the square root of a number?
D = 2r
A = pr^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any number a: a * 1 = a and a / 1 = a.

40. What is the formula for the volume of a rectangular solid?
A = [(s^2*v3)/4]
V = lwh
Cannot is 0 - must is 1 - all others are in between.
Write the percent as a decimal - and multiply.

41. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
An integer greater than one that is not prime.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.
Then the quotient y/x is a constant.

42. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted up 2 units.
For any integer n: 1^n = 1.

43. What does it mean if y is inversely proportional to x?
C = p2r
(b^m)^n = b^mn
A = 2(lw + lh + hw)
Then the product xy is a constant.

44. What is true about the measures of the two acute angles in a right triangle?
Then the quotient y/x is a constant.
Write the percent over 100 and reduce.
Their sum is 90°.
(Circumference/diameter) of a circle - or approximately 3.14.

45. What is the Pythagorean theorem?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

46. In a circle of radius r - what is the formula for the circumference?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
1 is the smallest positive odd integer.
C = p2r
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

47. Important binomial 1
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
They are both the same. A divisor or factor of an integer leaves no remainder.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x + y)(x - y) = x^2 - y^2

48. How do you find the y-intercept of a graph?
If a is negative and b is positive - then a < 0 < b.
Divide - then multiply by 100.
Set x = 0 - and solve.
B^m/b^n = b^m-n

49. What is special formula for the area of an equilateral triangle?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
C = p2r
A = [(s^2*v3)/4]
1 is the smallest positive odd integer.

50. Important binomial 3
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(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.
An integer greater than one that is not prime.

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