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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 the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
360°
(Circumference/diameter) of a circle - or approximately 3.14.
A = (1/2)bh.

2. How do you calculate percent increases and decreases?
The product of their slopes is -1 (negative reciprocal).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Is a right triangle with a ratio of sides x:xv3:2x.
For any number n: x^-n means 1/x^n.

3. What are the important properties of 30-60-90 triangle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Is a right triangle with a ratio of sides x:xv3:2x.
A^m*b^m = (ab)^m

4. What is a negative exponent?
For any number n: x^-n means 1/x^n.
A fraction whose denominator is 100 i.e. 17% = 17/100
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any number a: a * 1 = a and a / 1 = a.

5. Important binomial 2
The ratio of corresponding sides of similar triangles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
B^m*b^n = b^m+n

6. What is the formula for the area of a triangle?
A = (1/2)bh.
A = bh
No matter how many angles there are - the sum around the point is 360°.
C = p2r

7. What are the properties of a square?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
A^m*b^m = (ab)^m
For any number a: a * 1 = a and a / 1 = a.

8. What is the formula for the volume of a cylinder?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = pr^2h
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

9. What is the formula for the volume of a rectangular solid?
V = lwh
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.
Set x = 0 - and solve.
360°

10. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
In the expression x^b - x is the base and b is the exponent.
M = (y2 - y1)/(x2 - x1)
(b^m)^n = b^mn

11. How do you convert a percent to a fraction or a decimal?
B^m/b^n = b^m-n
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
V = l^3
Write the percent over 100 and reduce.

12. Properties of zero 5
A = bh
360°
For any number n: x^-n means 1/x^n.
For any number b: b = -b if and only if b = 0.

13. For what values of a function is the function undefined?
1 is the smallest positive odd integer.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any integer n: 1^n = 1.
For any number b: b = -b if and only if b = 0.

14. What is the Pythagorean theorem?
Shifted right 2 units.
For any right triangle - a^2 + b^2 = c^2.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Corresponding sides of similar triangles are in proportion.

15. In a circle of radius r - what is the formula for the diameter?
D = 2r
The two pairs of opposite angles formed are equal to each other.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.

16. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
A = [(s^2*v3)/4]
If a is negative and b is positive - then a < 0 < b.
Cannot is 0 - must is 1 - all others are in between.

17. What does it mean if y is inversely proportional to x?
An equation that states that two ratios are equivalent. 4/6 = 10/15
B^m*b^n = b^m+n
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Then the product xy is a constant.

18. What is p?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(Circumference/diameter) of a circle - or approximately 3.14.
Is a right triangle with a ratio of sides x:xv3:2x.
An integer greater than one that is not prime.

19. What is the distance formula?
Then the quotient y/x is a constant.
(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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

20. What is the square root of a number?
For any number b: b = -b if and only if b = 0.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Their sum is 180°.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

21. In a circle of radius r - what is the formula for the circumference?
360°
For any number n: x^-n means 1/x^n.
C = p2r
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

22. What is true about the slopes of parallel lines?
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.
1 is a divisor (or factor) of every integer.
No matter how many angles there are - the sum around the point is 360°.
Equal slopes.

23. What is the formula for the area of a rectangle?
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°.
A = lw
Then the quotient y/x is a constant.
For any number n: x^-n means 1/x^n.

24. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
0 is a multiple of every integer.
Is a right triangle with a ratio of sides x:xv3:2x.
Corresponding sides of similar triangles are in proportion.

25. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
360°
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

26. Law of exponents 1
Is a right triangle with a ratio of sides x:xv3:2x.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
B^m*b^n = b^m+n

27. What is true about the measures of the two acute angles in a right triangle?
For any number a: a * 1 = a and a / 1 = a.
A = bh
Is a right triangle with a ratio of sides x:xv3:2x.
Their sum is 90°.

28. Properties of one 2
Corresponding sides of similar triangles are in proportion.
For any integer n: 1^n = 1.
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.

29. 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.
(Circumference/diameter) of a circle - or approximately 3.14.
0 is a multiple of every integer.
Cannot is 0 - must is 1 - all others are in between.

30. What is a composite number?
V = lwh
An integer greater than one that is not prime.
The product of their slopes is -1 (negative reciprocal).
Shifted up 2 units.

31. What are the properties of a parallelogram?
Cannot is 0 - must is 1 - all others are in between.
No matter how many angles there are - the sum around the point is 360°.
1 is a divisor (or factor) of every integer.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

32. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
For any number n: x^-n means 1/x^n.
Write the percent as a decimal - and multiply.
An equation that states that two ratios are equivalent. 4/6 = 10/15

33. What is the triangle inequality?
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.
V = pr^2h
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Then the quotient y/x is a constant.

34. 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.
Is a right triangle with a ratio of sides x:xv3:2x.
Area = (x°/360)(pr^2) where x is the central angle.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

35. Properties of one 3
Set x = 0 - and solve.
1 is a divisor (or factor) of every integer.
Area = (x°/360)(pr^2) where x is the central angle.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

36. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Equal slopes.
Shifted right 2 units.
V = pr^2h
Is a right triangle with a ratio of sides x:xv3:2x.

37. Law of exponents 5
A^m/b^m = (a/b)^m
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted left 2 units.

38. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Set x = 0 - and solve.
V = pr^2h
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.

39. What does it mean if y is directly proportional to x?
B^m*b^n = b^m+n
Then the quotient y/x is a constant.
(x + y)(x - y) = x^2 - y^2
1 is the smallest positive odd integer.

40. Properties of one 1
Then the quotient y/x is a constant.
Their sum is 180°.
For any number n: x^-n means 1/x^n.
For any number a: a * 1 = a and a / 1 = a.

41. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
The product of their slopes is -1 (negative reciprocal).
The ratio of corresponding sides of similar triangles.
Cannot is 0 - must is 1 - all others are in between.

42. What is the midpoint formula?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An equation that states that two ratios are equivalent. 4/6 = 10/15
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted left 2 units.

43. What is the formula for the surface area of a rectangular solid?
360°
A = 2(lw + lh + hw)
Avg = sum of n numbers/n
Corresponding sides of similar triangles are in proportion.

44. What is a ratio?

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45. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted up 2 units.
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.

46. How do you find the probability that an event will occur?
A^m*b^m = (ab)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

47. How do you find the area of a sector of a circle?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = pr^2
B^m/b^n = b^m-n
Area = (x°/360)(pr^2) where x is the central angle.

48. Properties of zero 4
A fraction whose denominator is 100 i.e. 17% = 17/100
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
360°

49. What is the distributive law?
A = 2(lw + lh + hw)
If a is negative and b is positive - then a < 0 < b.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
B^m*b^n = b^m+n

50. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted right 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

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