IM 9 Advanced Problem Sets Problem Set 12: Probability, Pythagorean Theorem, Angles in Circles
1) What obtuse angle is formed by the hands of a clock at 7:00?
2) Solve the Diamond
Problems on the right.
3) Find the EXACT (simple radical form) values of the side length labeled x in the right triangles below.
a)
6 b)
x p x r 10 4) Two fair number cubes are rolled. Find the probability of rolling:
a) A sum of 6
b) Two prime numbers
5) Find the values of x and y in the diagram on the right.
c) Two of the same number
IM 9 Advanced Problem Sets Problem Set 13: Systems of Equations, Foundations for Factoring
1) Expand: (𝑥 − 2)!
2) Find the value of 𝑥 and y given the diagram to the right.
3) Solve the following diamond problems
4) Consider the expression (𝑥 − 2)(𝑥 + 4).
a) Expand and simplify (𝑥 − 2)(𝑥 + 4).
b) Where does the 2 come from in your answer? Where does the - 8 come from?
5) Consider the expression (𝑥 + 6)(𝑥 + 3).
a) Expand and simplify (𝑥 + 6)(𝑥 + 3).
b) Where does the 9 come from in your answer? Where does the 18 come from?
6) Create diamond problems that illustrate your explanations to both 3b and 4b.
IM 9 Advanced Problem Sets Problem Set 14: Special Segments in Triangles, Domain and Range, Simple
Probability
1) In the diagram on the right A(2,2), B(4,6) and C(10,4) form a
triangle. D and E are the midpoints of AB and BC, respectively.
a) Find the coordinates of D and E.
b) Show that AC is twice as long as DE.
c) Show AC and DE are parallel.
2) Simplify the following radical expressions WITHOUT USING YOUR CALCULATOR.
a)
48
b) 50 75
c) 72 + 128
3) For each of the graphs shown below state the domain and range.
4) A standard deck of cards has 52 cards divided equally into 4 suits (hearts, clubs, diamonds, spades), each
of which has 13 cards, ace through king. Find the following probabilities.
a)
b)
c)
d)
Drawing a king and then a queen with replacement.
Drawing a king and then a queen without replacement.
Drawing three hearts with replacement.
Drawing 3 of the same card without replacement.
IM 9 Advanced Problem Sets Problem Set 15: Simplifying Exponents, Diamond Problems
1) Use the diagram on the right to find
the value of x and y.
2) Consider the expression (𝑥 + 5)(𝑥 + 4).
a) Expand and simplify (𝑥 + 5)(𝑥 + 4).
b) Where does the 9 come from in your answer? Where does the 20 come from?
c) Create a diamond problem that illustrates your explanation to part b.
3) With your solution to 3c in mind, make and complete Diamond Problems for the following:
a) (𝑥 + 5)(𝑥 − 2)
b) (𝑥 − 7)(𝑥 + 3)
c) (𝑥 + 9)(𝑥 + 7)
4) Again thinking about problem 3, make and complete Diamond Problems for the following:
a) 𝑥 ! + 3𝑥 − 10
b) 𝑥 ! − 4𝑥 − 21
c) 𝑥 ! + 16𝑥 + 63
5) Notice that the diamond problems you set up for 4a and 5a are the same! What does this tell you
about the expressions in 4a and 5a? Answer the same question for parts b) and c) by creating a valid
equation.
IM 9 Advanced Problem Sets Answers!
Problem Set 12
1) 150°
2)
3) a) 𝑥 = 2 34
b) 𝑥 = 𝑝! − 𝑟 !
!
!
!
4) a) !" b) !
c) !
5) a) 𝐷: 𝑥 𝑥 ∈ ℝ , 𝑅: 𝑦 𝑦 ≤ 1}
b) 𝐷: 𝑥 −5 ≤ 𝑥 ≤ 5 , 𝑅: { 𝑦 | − 3 ≤ 𝑥 ≤ 3}
Problem Set 13
1) x3 – 6x2 – 12x - 8
2) 𝑥 = 4, 𝑦 = 12
3) on right
4) a) 𝑥 ! + 2𝑥 − 8
5) a) 𝑥 ! + 9𝑥 + 18
6) on right
b) -2 + 4 = 2, (-2)(4) = -8
b) 3 + 6 = 9, (3)(6) = 18
Problem Set 14
1) a) D(3,4) E(7,5)
b) AC = 8 2 + 2 2 = 68 = 2 17 , DE = 4 2 +12 = 17
2 1
1
c) SlopeAC = = , SlopeDE =
8 4
4
2) a) 4 3
b) 25 6
c) 14 2
€ 3) a) D :{x | −3 ≤ x ≤ 4} €
R :{y | −3 ≤ y ≤ 2}
b) D :{x | −4 ≤ x ≤ 4} R :{y |1 ≤ y ≤ 4}
€
€
c) D :{x | −4 ≤ x ≤ −2, −1 ≤ x ≤ 5} R :{y | −2 ≤ y ≤ 3}
d) D :{x | −4, − 3 ≤ x ≤ −2, 2 ≤ x} R :{y | −4 ≤ y}
€
4 4
1
4 4
13 13 13
€ 4) a)
⋅
=
≈ .59% b)
⋅
≈ .60% c)
⋅ ⋅
≈ 1.56%
52 52 169
52 51
52 52 52
€
€
Problem
Set 15
1) x = 17, y = 8
€ 2) a) x2 + 9x + 20
3)
€
b)€4 + 5 = 9, (4)(5) = 20
c)
d)
4 3 2
⋅ ⋅ ⋅ 13 ≈ .235%
52 51 50
€
4)
5) The answers are the same!
x2 + 9x + 20 = (x + 5)(x - 2),
x2 - 4x - 2 = (x + 3)(x - 7), x2 + 16x + 63 = (x + 9)(x + 7)