Al- Hussan Model Private
Secondary School in Dammam
Academic Year 2022-2023
Second
Trimester – Midterm
Exam
Midterm-Worksheet
- G11
Student’s Name: ___________________________________ Class : 11/A
Grade : 10
11
Date: 08.01.2023
Score:
Subject: Precalculus
Duration: 40 minutes
20
Teacher: Mr.Mostafa Fawzy
Notice: In this test you are supposed to answer ( 15 ) questions on the following 4 pages.
Question 1 : Choose the correct answer :
(1) Find the value of x. Round to the nearest tenth, if necessary.
(a) 4.6
(b) 8.1
(c) 9.3
(d) 10.7
(2) Use a trigonometric function to find the measure of θ. Round to the nearest degree, if necessary.
(a) 50°
(3)
(c) 40°
(d) 32°
Write 150o in radians as a multiple of π.
(a)
(4)
(b) 58°
𝝅
(b)
𝟒
𝟐𝝅
(c)
𝟑
𝟓𝝅
(d)
𝟔
𝟒𝝅
𝟑
Which of the following functions represent the given graph?
(a) y = sin x
(b) y = cos x
(c) y = tan x
(d) y = sec x
(5) State the amplitude, period, frequency, and phase shift of 𝒚 = 𝟒 𝐜𝐨𝐬
(a) amplitude: 4 , period:
𝟑
𝟐𝝅
𝟏
(b) amplitude: , period: 3
(c) amplitude: 4 , period: 6π , frequency:
𝟐𝝅
𝟑
𝟑
𝟏
, frequency:
𝟒
(d) amplitude: -4, period:
𝟐𝝅
, frequency:
, frequency:
𝟑
𝟏
𝟔𝝅
𝟑
𝟐𝝅
,phase shift:
,phase shift:
𝟑
+
𝝅
𝟔
𝝅
,phase shift:
,phase shift:
𝒙
𝟔
𝝅
𝟏𝟖
𝝅
𝟐
𝝅
𝟐
(6) Find the exact value of sin–1 0
(a) 𝒛𝒆𝒓𝒐
𝝅
(b) 𝟐
𝝅
(c) 𝟒
(d) 𝝅
(7) Find the exact value of 𝒂𝒓𝒄𝒔𝒊𝒏 𝐬𝐢𝐧 𝟕𝝅
𝟔
(a)
𝝅
𝟔
(b)
𝟕𝝅
𝟔
(c)
𝟏𝟏𝝅
𝟔
(d)
√𝟑
𝟐
(8) Solve ΔXYZ. Round side lengths to the nearest tenth and angle measures to the nearest degree.
(a) y ≈ 11.8, z ≈ 8.0, Y = 75°
(b) y ≈ 8.0, z ≈ 5.3, Y = 85°
(c) y ≈ 28.7, z ≈ 18.9, Y = 95°
(d) y ≈ 14.6, z ≈ 9.9, Y = 75°
(9) Find all solutions for ΔABC where a = 18, b = 13, and A = 126o, if possible. If no
solution exists, write no solution. Round side lengths to the nearest tenth and angle
measures to the nearest degree.
(a) B ≈ 42°, C ≈ 12°, c ≈ 4.6
(c) B ≈ 36°, C ≈ 18°, c ≈ 6.9
(b) B ≈ 28°, C ≈ 26°, c ≈ 9.8
(d) no solution
(10) Find the area of ΔGHJ.
(a) 2790.1 ft2
(c) 191.6 ft2
(b) 678.0 ft2
(d) 31.9 ft2
Question 2 : Solve the following questions ( Show your steps ):
(I) Find the exact values of the six trigonometric functions of θ.
________________________________________
________________________________________
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(II) Find the area of the sector of the circle.
______________________________________________________________________
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(III) Find the area of ΔABC to the nearest tenth.
_______________________________________________
_______________________________________________
(IV) Solve ΔABC.Round side lengths to the nearest tenth and angle measures to the nearest degree.
_____________________________________________
_____________________________________________
_____________________________________________
(V) Find and draw one positive and one negative angle coterminal with 80°.
_________________________________________________________
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