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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.
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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 a fractional exponent?
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.
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

2. In a circle of radius r - what is the formula for the area?
At least one of the factors is 0.
A = pr^2
Corresponding sides of similar triangles are in proportion.
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.

3. What is a ratio?

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4. What formula is used for an average?
Then the quotient y/x is a constant.
Write the percent over 100 and reduce.
Avg = sum of n numbers/n
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.

5. What is special formula for the area of an equilateral triangle?
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°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = [(s^2*v3)/4]
0 is a multiple of every integer.

6. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
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.
A = s^2 or A =d^2/2 where d is the diagonal

7. What is the ratio of similitude?
Arc = (x°/360)(2pr) where x is the central angle.
The ratio of corresponding sides of similar triangles.
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.
For any integer n: 1^n = 1.

8. How you convert a fraction or a decimal to a percent?
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted up 2 units.
A fraction whose denominator is 100 i.e. 17% = 17/100
Divide - then multiply by 100.

9. What is the formula for the area of a parallelogram?
A = bh
B^m*b^n = b^m+n
Shifted down 2 units.
V = lwh

10. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Their sum is 90°.
The ratio of corresponding sides of similar triangles.
Shifted up 2 units.
A = [(s^2*v3)/4]

11. What is the square root of a 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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
V = pr^2h
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

12. What is an exterior angle of a triangle?
Avg = sum of n numbers/n
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = pr^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

13. In a circle of radius r - what is the formula for the diameter?
360°
D = 2r
Even numbers are divisible by 2 and odd numbers are not.
A = [(s^2*v3)/4]

14. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
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.
A = [(s^2*v3)/4]
If a is negative and b is positive - then a < 0 < b.

15. What is the Pythagorean theorem?
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any right triangle - a^2 + b^2 = c^2.
A = 2(lw + lh + hw)
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.

16. What are the quotient and the remainder?

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17. What do we mean by the slope of the line?
(b^m)^n = b^mn
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = s^2 or A =d^2/2 where d is the diagonal
For any number a: a * 1 = a and a / 1 = a.

18. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Set x = 0 - and solve.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

19. Properties of one 4
Equal slopes.
Then the product xy is a constant.
Write the percent over 100 and reduce.
1 is the smallest positive odd integer.

20. What is true about the measures of the four angles formed by two intersecting lines?
Set x = 0 - and solve.
The product of their slopes is -1 (negative reciprocal).
The two pairs of opposite angles formed are equal to each other.
An equation that states that two ratios are equivalent. 4/6 = 10/15

21. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
An integer greater than one that is not prime.
(n - 2)(180°)

22. How do you calculate a weighted average?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
[(x1 + x2)/2] -[(y1 + y2)/2]
In the expression x^b - x is the base and b is the exponent.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

23. What is a function?
Their sum is 90°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Divide - then multiply by 100.
B^m*b^n = b^m+n

24. What is an integer?
D = 2r
A^m/b^m = (a/b)^m
0 is a multiple of every integer.
All positive and negative whole numbers - and zero.

25. What is the area of a square?
For any number a: a * 1 = a and a / 1 = a.
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 = s^2 or A =d^2/2 where d is the diagonal
The two pairs of opposite angles formed are equal to each other.

26. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
All positive and negative whole numbers - and zero.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
1 is a divisor (or factor) of every integer.

27. What are the important properties of a 45-45 - 90 triangle?
Arc = (x°/360)(2pr) where x is the central angle.
Set x = 0 - and solve.
0 is the only number that is neither positive nor negative.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

28. What is the formula for the volume of a cylinder?
V = pr^2h
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
They are both the same. A divisor or factor of an integer leaves no remainder.
C = p2r

29. What is true about the measures of the three angles in a triangle?
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.
Even numbers are divisible by 2 and odd numbers are not.
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.

30. Important binomial 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = (1/2)bh.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

31. What is an exponent?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Equal slopes.
Shifted right 2 units.
In the expression x^b - x is the base and b is the exponent.

32. What is the distance formula?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
At least one of the factors is 0.
Shifted down 2 units.

33. Properties of zero 5
For any number b: b = -b if and only if b = 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Arc = (x°/360)(2pr) where x is the central angle.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

34. What is the sum of the measures of all angles around a point?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Their sum is 180°.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
No matter how many angles there are - the sum around the point is 360°.

35. What is the sum of the measures of the four angles in a quadrilateral?
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.
360°
B^m*b^n = b^m+n
M = (y2 - y1)/(x2 - x1)

36. What is a prime number?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
C = p2r
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.
Shifted left 2 units.

37. How do you find the y-intercept of a graph?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Set x = 0 - and solve.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.

38. What is the volume of a cube?
A fraction whose denominator is 100 i.e. 17% = 17/100
V = l^3
They are both the same. A divisor or factor of an integer leaves no remainder.
The set of all ordered pairs (x -y) such that y = f(x).

39. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(n - 2)(180°)
Shifted down 2 units.
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.

40. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = lw
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

41. What is a multiple of an integer?
Write the percent as a decimal - and multiply.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.

42. What are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = s^2 or A =d^2/2 where d is the diagonal
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

43. Properties of one 3
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Their sum is 90°.
1 is a divisor (or factor) of every integer.
Corresponding sides of similar triangles are in proportion.

44. How do you find the x-intercept of a graph?
360°
For any right triangle - a^2 + b^2 = c^2.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Set y = 0 - and solve.

45. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A fraction whose denominator is 100 i.e. 17% = 17/100
360°
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

46. How do you find the area of a sector of a circle?
Corresponding sides of similar triangles are in proportion.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Area = (x°/360)(pr^2) where x is the central angle.
An integer greater than one that is not prime.

47. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Avg = sum of n numbers/n
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.
1 is a divisor (or factor) of every integer.
D = 2r

48. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
An angle formed by extending the side of the polygon.
C = p2r
How steep the line is. Horizontal line = 0 - vertical has no slope.

49. What is a composite number?
1 is a divisor (or factor) of every integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = lw
An integer greater than one that is not prime.

50. What is an even and an odd number?
Equal slopes.
Area = (x°/360)(pr^2) where x is the central angle.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Even numbers are divisible by 2 and odd numbers are not.