Sudoku Puzzle – Precalculus Topics
Name:______________________________Per_____
Adapted from a puzzle by David Pleacher
Solve the 35 multiple-choice problems below.
The choices are integers from 1 to 9 inclusive.
Place the answer in the corresponding cell (labeled A, B, C, … Y, Z, a, b,…h, i).
Then solve the resulting SUDOKU puzzle.
The rules of Sudoku are simple.
Enter digits from 1 to 9 into the blank spaces.
Every row must contain one of each digit.
So must every column, and so must every 3x3 square.
Each Sudoku has a unique solution that can be reached logically without guessing.
3
4
_______A. If cos 𝜃 = − 5 and tan 𝜃 = − 3 then sin 𝜃 =
3
3
(1)4
4
(2) − 4
4
(3) 5
(4) − 5
_______B. Which of the following is correct?
(1) 𝑡𝑎𝑛2 𝑥 = 𝑠𝑒𝑐 2 𝑥 + 1
(2) 𝑠𝑖𝑛2 𝑥 = 𝑐𝑜𝑠 2 𝑥 − 1
(3)𝑡𝑎𝑛2 𝑥 = 𝑐𝑠𝑐 2 𝑥 + 1
(4) 𝑡𝑎𝑛2 𝑥 = 𝑠𝑒𝑐 2 𝑥 − 1
_______C. The inverse function of 𝑦 = 3𝑥 + 12
(1) 𝑦 =
𝑥−12
(2) 𝑦 =
3
(3)𝑦 = 3𝑥 − 12
𝑥+12
3
(4) 𝑦 = −3𝑥 − 12
_______D. The inverse secant of −2 is
(6)−60°
(7) 30°
(8) 60°
(9) 120°
_______E. Use the graph to solve the inequality 𝑓(𝑥) ≤ 0. Write the answer in interval
notation.
(5) 𝑥 ∈ (−∞, −3) ∪ (1, 5)
(6) 𝑥 ∈ (−3, 1) ∪ (5, ∞)
(7) 𝑥 ∈ [−3, 1] ∪ [5, ∞)
(8) 𝑥 ∈ (−∞, −3] ∪ [1, 5]
_______F. Choose the correct right-hand side to make the equation an identity.
1 − sin 𝑥
=
1 + sin 𝑥
(4) (sec 𝑥 − cot 𝑥)2
(5) (sec 𝑥 − tan 𝑥)2
(6) (sec 𝑥 + cot 𝑥)2
(7) (sec 𝑥 + tan 𝑥)2
_______G. Which of the following statements is true?
𝐴
(1) 𝑙𝑜𝑔 (𝐵) = 𝑙𝑜𝑔(𝐴) − 𝑙𝑜𝑔(𝐵)
𝐴
log 𝐴
(2) 𝑙𝑜𝑔 (𝐵) = log 𝐵
(3) log(𝐴 − 𝐵) = log(𝐴) − log(𝐵)
𝐴
(4) log(𝐴 − 𝐵) = log (𝐵)
_______H. Simplify the expression without using a calculator.
4𝜋
𝑠𝑖𝑛−1 [cos ( )]
3
(4)
5𝜋
3
𝜋
(5) − 3
(6)
2𝜋
3
𝜋
(7) − 6
_______I. The range of 𝑦 = 𝑠𝑖𝑛−1 𝑥 is
𝜋 𝜋
(4) [0, 𝜋]
(5) [− 4 , 4 ]
𝜋 𝜋
𝜋 5𝜋
(6) [− 2 , 2 ]
(7) [2,
4
]
_______J. Which of the following is a graph of 𝑦 = 2𝑥+2
(6)
(7)
(8)
(9)
_______K. If 𝑓(𝑥) = 3𝑥 + 1 and 𝑔(𝑥) = √𝑥, determine 𝑔(𝑓(5))
(1) 3√5 + 1
(2) 4
(3) 16
(4) √5
_______L. If the graph of 𝑦 = 2−𝑥 − 1 is reflected in the x-axis, then an equation of the
reflection is
(1) 𝑦 = 2𝑥 − 1
(4) 𝑦 = 𝑙𝑜𝑔2 (𝑥 + 1)
(2) 𝑦 = −2𝑥 + 1
(3) 𝑦 = −2−𝑥 + 1
(5) 𝑦 = 𝑙𝑜𝑔2 (1 − 𝑥)
_______M. What is the domain of the function in interval notation. 𝑓(𝑥) =
(3) [−2, 2]
(4) (−∞, 3) ∪ (3, ∞)
(6) (−∞, −2] ∪ [2, 3) ∪ (3, ∞)
√𝑥 2 −4
𝑥−3
(5) (−∞, 2] ∪ [2, ∞)
(7) [2, 3) ∪ (3, ∞)
1
_______N. Find the value of cos 𝜃, given 𝑃 (− 6 , −
with 𝜃 in standard position.
1
(5) − 3
(6) −3
(7) −
√2
) is
3
on the terminal side of angle 𝜃,
2√2
3
3
(8) − 2√2
_______O. Determine the solution of log 5 𝑥 + log 5 (𝑥 + 4) = 1
(1) 𝑥 = 1 and 𝑥 = −5
(2) 𝑥 = −2 ± √3
(3) 𝑥 = 1 and 𝑥 = −5 is extraneous
(4) 𝑥 = −5
_______P. Determine the constant 𝑘 if 𝑥 − 3 is a linear factor of 3𝑥 3 − 9𝑥 2 + 𝑘𝑥 − 12
(1) 𝑘 = 3
(2) 𝑘 = 4
(3) 𝑘 = 5
(4) 𝑘 = 6
_______Q. Find the equation of all lines parallel to 5𝑥 − 3𝑦 + 4 = 0
(6) 5𝑥 + 3𝑦 + 𝑘 = 0
(7) 3𝑥 − 5𝑦 + 𝑘 = 0
(8) 5𝑥 − 3𝑦 + 𝑘 = 0
(9) 3𝑥 + 5𝑦 + 𝑘 = 0
_______R. Determine the domain of 𝑔(𝑥) = log √16 − 𝑥 2
(1) 𝑥 ∈ [−4, 4]
(2) 𝑥 ∈ (−∞, −4) ∪ ( 4, ∞)
(3) 𝑥 ∈ (−∞, +∞)
(4) 𝑥 ∈ (−4, 4)
______S. Determine the solution of log(−𝑥 − 1) = log(5𝑥) + log(𝑥)
(6) 𝑥 =
1±2√5
(7) 𝑥 =
10
_______T. If 𝑓(𝑥) =
𝑥
𝑥−1
𝑥
−𝑥
(6) 1−𝑥
(7) 1−𝑥
1±√21
10
1
(8) 𝑥 = 5 and 𝑥 = −1
(9) No solution
and 𝑔(𝑥) = 1 − 𝑥 then 𝑓(𝑔(𝑥)) =
1
(8) 𝑥
(9)
𝑥−1
𝑥
_______U. Determine the solution of log 3 ( 𝑥 − 4) + log 3 ( 7) = 2
(1) 𝑥 =
37
7
(2) 𝑥 =
−19
7
(3) 𝑥 = 67
(4) 𝑥 =
13
7
√2
_______V. Simplify the expression without using a calculator: csc[sin−1 ( 2 )]
(1) −
√2
2
(2) −
1
√3
2
(3) 2
(4)
√2
2
(5) √2
_______W. The inverse function for 𝑦 = 2𝑥 − 5 is
1
(3) 𝑦 = −2𝑥 + 5
(5) 𝑦 =
(4)𝑦 = 2𝑥−5
𝑥+5
(6)𝑦 =
2
𝑥−5
2
_______X. Complete the square of the following to write in standard form. What is the
length of the major axis? 4𝑥 2 + 9𝑦 2 − 16𝑥 + 18𝑦 − 11 = 0
(1) 10
(2) 2
(3) 4
(4) 6
_______Y. Solve the triangle. Find sides to the nearest tenth.
𝑎 = 16𝑚, 𝐴 = 37° , 𝐵 = 44°
(1) 𝐶 = 99° , 𝑏 ≈ 17.8𝑚, 𝑐 ≈ 25.7𝑚
(2) 𝐶 = 99° , 𝑏 ≈ 18.3𝑚, 𝑐 ≈ 26.7𝑚
(3) 𝐶 = 99° , 𝑏 ≈ 18.5𝑚, 𝑐 ≈ 26.3𝑚
(4)𝐶 = 99° , 𝑏 ≈ 19.0𝑚, 𝑐 ≈ 26.1𝑚
_______Z. Which of the following equations has a graph that is symmetric with respect to
the origin?
(5) 𝑦 =
𝑥−1
(6) 𝑦 = 2𝑥 4 + 1
𝑥
𝑥
(8) 𝑦 = 𝑥 3 +1
(7) 𝑦 = 𝑥 3 + 2
(9) 𝑦 = 𝑥 3 + 2
_______a. A pilot wishes to fly from Pleasant Hills to Sheldon. She calculates the distances
shown using a map, with York for reference since it is due east from Pleasant Hills. What is
the measure of angle P?
S
Sheldon
852 miles
105 miles
Y
Pleasant Hills
York
P
784 miles
(1) 4.7°
(2) 5.6°
(3) 6.8°
(4) 7.5°
_______b. Which of the following equations has a graph that is symmetric with respect to
the y-axis?
(5) 𝑦 =
𝑥−1
(6) 𝑦 = 𝑥 3 + 2𝑥
𝑥
(7) 𝑦 = 2𝑥 4 + 1
𝑥
(8) 𝑦 = 𝑥 3 + 2
(9) 𝑦 = 𝑥 3 +1
________c. Solve using an appropriate method. ln(𝑥 + 3) + ln 10 = 2
(4) 𝑥 = 𝑒 2 − 13
(5) 𝑥 = ln 2 − 13
(6) 𝑥 =
𝑒 2 −30
10
(7) 𝑥 =
ln 2−30
10
_______d. Solve the exponential equation. 27𝑥+2 = 3
5
2
(5)3
2
(6) 3
5
(7)− 3
(8) − 3
_______e. The range of 𝑦 = 𝑐𝑜𝑠 −1 𝑥 is
𝜋
𝜋 𝜋
(1) [0, 2 ]
(2) [− 2, , 2 ]
𝜋 3𝜋
(3) [ 2 ,
2
]
(4) [0, 𝜋]
5𝑥+1
_______f. The domain of 𝑦 = 𝑥 2 −2𝑥 is
1
1
(6) 𝑥 ∈ (−∞, − 5) ∪ (− 5 , ∞)
(7) 𝑥 ∈ (2, ∞)
1
(8) 𝑥 ∈ (− 5 , ∞)
(9) 𝑥 ∈ (−∞, 0) ∪ (0, 2) ∪ (2, ∞)
_______g. Convert 75° to radians
𝜋
(1) 12
_______h. Convert
(1) 29°
(2)
2𝜋
9
2𝜋
5
(3)
3𝜋
5
5𝜋
(4) 12
to degrees.
(2) 33°
(3) 40°
(4) 50°
_______i. (−
(5) −
4√5
5
√5 √11
, 4 ) is
4
a point on the unit circle corresponding to angle 𝑡. Find sin 𝑡.
(6)
4√11
11
(7)−
√5
4
(8)
√11
4
Here is a blank Sudoku for you to use.