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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 is the relationship between the graph of f(x) the graph of y = f(x - 2)?
A = 6(l^2)
Shifted right 2 units.
A = pr^2
An integer greater than one that is not prime.

2. What is true about the slopes of perpendicular lines?
In the expression x^b - x is the base and b is the exponent.
360°
The set of all ordered pairs (x -y) such that y = f(x).
The product of their slopes is -1 (negative reciprocal).

3. How do you find the probability that an event will occur?
Divide - then multiply by 100.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If a is negative and b is positive - then a < 0 < b.

4. Law of exponents 4
Cannot is 0 - must is 1 - all others are in between.
If a is negative and b is positive - then a < 0 < b.
A^m*b^m = (ab)^m
For any number b: b = -b if and only if b = 0.

5. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
A = bh
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

6. What formula is used for an average?
(x + y)(x - y) = x^2 - y^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Avg = sum of n numbers/n
For any number n: x^-n means 1/x^n.

7. 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.
In the expression x^b - x is the base and b is the exponent.
A = s^2 or A =d^2/2 where d is the diagonal
A fraction whose denominator is 100 i.e. 17% = 17/100

8. Properties of zero 3
B^m/b^n = b^m-n
V = l^3
V = pr^2h
0 is a multiple of every integer.

9. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
V = pr^2h
An equation that states that two ratios are equivalent. 4/6 = 10/15
360°
A = s^2 or A =d^2/2 where d is the diagonal

10. If the product of two or more numbers is 0 - what do you know about the numbers?
For any right triangle - a^2 + b^2 = c^2.
At least one of the factors is 0.
(Circumference/diameter) of a circle - or approximately 3.14.
360°

11. What is a percent?
1 is the smallest positive odd integer.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = s^2 or A =d^2/2 where d is the diagonal
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

12. For what values of a function is the function undefined?
Write the percent as a decimal - and multiply.
M = (y2 - y1)/(x2 - x1)
0 is the only number that is neither positive nor negative.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

13. Law of exponents 3
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Avg = sum of n numbers/n
Arc = (x°/360)(2pr) where x is the central angle.
(b^m)^n = b^mn

14. What is a ratio?

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15. Properties of one 4
Arc = (x°/360)(2pr) where x is the central angle.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
1 is the smallest positive odd integer.
A^m*b^m = (ab)^m

16. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Their sum is 90°.
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.

17. Properties of one 3
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

18. How do you convert a percent to a fraction or a decimal?
For any integer n: 1^n = 1.
The ratio of corresponding sides of similar triangles.
Write the percent over 100 and reduce.
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.

19. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
[(x1 + x2)/2] -[(y1 + y2)/2]
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The set of all ordered pairs (x -y) such that y = f(x).

20. Law of exponents 2
B^m/b^n = b^m-n
D = 2r
Shifted down 2 units.
A = pr^2

21. What is the area of a square?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = s^2 or A =d^2/2 where d is the diagonal
180°. If two or more angles form a straight angle - their sum is 180°.

22. What is an integer?
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.
All positive and negative whole numbers - and zero.
360°
180°. If two or more angles form a straight angle - their sum is 180°.

23. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
C = p2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If a is negative and b is positive - then a < 0 < b.

24. What is the Pythagorean theorem?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
In the expression x^b - x is the base and b is the exponent.
For any right triangle - a^2 + b^2 = c^2.

25. Properties of one 2
The product of their slopes is -1 (negative reciprocal).
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any integer n: 1^n = 1.

26. What are the properties of a parallelogram?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
No matter how many angles there are - the sum around the point is 360°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
360°

27. What is the formula for the surface area of a cube?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Then the product xy is a constant.
A = 6(l^2)

28. Important binomial 3
M = (y2 - y1)/(x2 - x1)
A = (1/2)bh.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

29. Law of exponents 1
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any number n: x^-n means 1/x^n.
B^m*b^n = b^m+n
Their sum is 180°.

30. What is the formula for the area of a triangle?
B^m/b^n = b^m-n
(x + y)(x - y) = x^2 - y^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = (1/2)bh.

31. What is a composite number?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
An integer greater than one that is not prime.
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.
No matter how many angles there are - the sum around the point is 360°.

32. What is the formula for the surface area of a rectangular solid?
Write the percent over 100 and reduce.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = 2(lw + lh + hw)
1 is the smallest positive odd integer.

33. What is the square root of a number?
M = (y2 - y1)/(x2 - x1)
At least one of the factors is 0.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(x + y)(x - y) = x^2 - y^2

34. What important property do similar triangles have?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
180°. If two or more angles form a straight angle - their sum is 180°.
Corresponding sides of similar triangles are in proportion.

35. What is a Venn diagram?
Area = (x°/360)(pr^2) where x is the central angle.
They are both the same. A divisor or factor of an integer leaves no remainder.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = l^3

36. What is the measure of a straight angle?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.
180°. If two or more angles form a straight angle - their sum is 180°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

37. Properties of one 1
An integer greater than one that is not prime.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The set of all ordered pairs (x -y) such that y = f(x).
For any number a: a * 1 = a and a / 1 = a.

38. Important binomial 2
For any number b: b = -b if and only if b = 0.
The two pairs of opposite angles formed are equal to each other.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = 2(lw + lh + hw)

39. What is the midpoint formula?
B^m/b^n = b^m-n
For any right triangle - a^2 + b^2 = c^2.
[(x1 + x2)/2] -[(y1 + y2)/2]
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

40. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A^m*b^m = (ab)^m
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An angle formed by extending the side of the polygon.

41. What are similar triangles?
A = 2(lw + lh + hw)
The ratio of corresponding sides of similar triangles.
360°
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

42. What is an exponent?
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
In the expression x^b - x is the base and b is the exponent.
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.

43. What is the volume of a cube?
V = l^3
Is a right triangle with a ratio of sides x:xv3:2x.
For any number n: x^-n means 1/x^n.
Cannot is 0 - must is 1 - all others are in between.

44. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
For any number n: x^-n means 1/x^n.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.
Cannot is 0 - must is 1 - all others are in between.

45. What is the formula for the volume of a cylinder?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = pr^2h
A = (1/2)bh.

46. What is the relationship between a radius of a circle and a line that is tangent to the circle?
1 is the smallest positive odd integer.
V = l^3
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.

47. In a circle of radius r - what is the formula for the circumference?
At least one of the factors is 0.
Their sum is 90°.
C = p2r
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

48. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
C = p2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
B^m*b^n = b^m+n

49. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
B^m/b^n = b^m-n
Then the quotient y/x is a constant.
The product of their slopes is -1 (negative reciprocal).

50. How do we write the equation of a line?
A^m/b^m = (a/b)^m
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Corresponding sides of similar triangles are in proportion.
How steep the line is. Horizontal line = 0 - vertical has no slope.