Mathematics 12 Make Up Exam 2024-2025 PDF

ÖĞRETİM YILI & DÖNEM / 2024-2025 / 1 ACADEMIC YEAR & TERM SEVİYE(LER) / LEVEL(S) 12 DERS / COURSE MATHEMATICS 12 Make Up(Scenario No 1) TAR...

ÖĞRETİM YILI & DÖNEM / 2024-2025 / 1 ACADEMIC YEAR & TERM SEVİYE(LER) / LEVEL(S) 12 DERS / COURSE MATHEMATICS 12 Make Up(Scenario No 1) TARİH / DATE 13.01.2024 SÜRE / BAŞLANGIÇ BİTİŞ / END 40 min 09:20 10:00 DURATION / START ÖĞRENCİ ADI & SOYADI / STUDENT NAME & SURNAME ÖĞRENCİNİN SINIFI / STUDENT CLASS SINAV ODASI / EXAM ROOM ÖĞRETMEN ADI & SOYADI / TEACHER NAME & SURNAME SINAV DUYURULARI / EXAM NOTIFICATIONS 1) Students are not allowed to borrow, lend, or share anything during the exam. 2) Show your work for questions 3) Students are not allowed to talk and ask questions to teachers during the exam. Question 1 2 3 4 5 6 7 8 9 Total Marks 10 10 10 10 16 9 11 12 12 100 Marks Awarded Page 1 You will have 40 minutes to complete the exam. Show all your work. Clearly indicate the method you use, because you will be graded on the correctness of your method as well as the accuracy of your final answer. Be sure to write CLEARLY and LEGIBLY. Do not forget to give the correct units, if required, with your answers. Good Luck! QUESTIONS 4 1. Given tan x + cot x = , then find sin 2x (10 pts) 3 1 3π 2. If tan α = , where π < α < 2. Find the value of cos 2α. (10 pts) 2 2 sin 39∘ cos 39∘ 3. Evaluate sin 13∘ − cos 13∘ (10 pts) Page 2  2 4. Solve the equation sin x = − 2 for x ∈ [0,2π]. (10 pts) 5. Find the general solution of the following trigonometric equations. 1 a) cos(7x) = 2 (10 pts) b) tan(x − π4 ) = − 1 (6 pts) 3 Page 3 6. Evaluate the following limits by using the graph of the function f (x) shown below. If the limit does not exist, write DNE. If the value of the function f (x) undefined, write UND. (9 pts) a) f (−6) b) lim − f (x) x→−1 c) lim f (x) x→6+ d) lim f (x) x→−6 e) Write discontinuity points of the function f (x) on the interval (−9,9). 7. Evaluate the following limits −x 2 + 1 a) lim (7pts) x→−1 −x 2 + x + 2 | 2x − 3 | b) lim (4 pts) x→( 32 )− x − 32 Page 4 8. The function f (x) is continuous for all x ∈ ℝ ? Find the values of a and b. (12 pts) a x2 + 3 , if x < − 2 f (x) = −2 , if x = − 2 bx − 1 , if x > − 2 9. Find all values of k that would make the function f (x) continuous at x = − 9. Justify your result. (12 pts) x 2 + 7x − 18 , for x ≠ − 9 f (x) = x 2 + 8x − 9 k , for x = − 9 Polat CHARYYEV Erdal ŞEN Zeynep PEHLİVAN Zeynel KIZILELMA Math Teacher Math Teacher Math Teacher Head of Math Department Page 5