Vision: Our vision is to prepare and motivate our students through instilling in them critical thinking skills and a global perspective to help them take on the challenges of a rapidly changing world. Math revision Question 1: Circle the correct answer in each of the following. 1) The vertex of 𝑓(𝑥) = |𝑥 − 3| + 4 is: A) (-3, 4) B) (3, 4) C) (-3, -4) 2) The vertex of 𝑓(𝑥) = |𝑥 − 1| + 7 is: 3) (1, 7) B) (-1, 7) C) (-1, -7) D) (0, 0) D) (0, 0) 3) If 𝑓(𝑥) = |𝑥 + 1| − 6, the value -6 represents _____________. A) A vertical translation of 6 Places up. B) A vertical translation of 6 Places down. C) A horizontal translation of 6 Places to the right. D) A horizontal translation of 6 Places to the left. 4) If 𝑓(𝑥 ) = |𝑥 − 3| + 2, the value 2 represents _____________. A) A vertical translation of 2 Places up. B) A vertical translation of 2 Places down. C) A horizontal translation of 2 Places to the right. D) A horizontal translation of 2 Places to the left. 5) What are the possible solution(s) of |𝑥| = 5 A) 𝑥 = 5 B) 𝑥 = −5 C) 𝑥 = ±5 D) No solution. 6) What are the possible solution(s) of |𝑥| = 1 B) 𝑥 = ±1 B) 𝑥 = −1 C) 𝑥 = 1 D) No solution. Mission: We provide our students with a caring and culturally diverse environment where we make every student feel valued and welcomed. We encourage our students to become independent learners and motivate them to be creative, think critically, and communicate effectively. We also teach them the values of respect, honesty, and integrity. 1 Vision: Our vision is to prepare and motivate our students through instilling in them critical thinking skills and a global perspective to help them take on the challenges of a rapidly changing world. 7) What is the transformation of g(𝑥)=2|𝑥| compared to the Parent function 𝑓(𝑥) ? A) Shrinks vertically. B) Stretches vertically. C) Reflection over 𝑥 −Axis. D) Reflection over 𝑦 −Axis. 8) What is the transformation of g(𝑥)=0.5|𝑥| compared to the Parent function 𝑓(𝑥) ? B) Shrinks vertically. B) Stretches vertically. C) Reflection over 𝑥 −Axis. D) Reflection over 𝑦 −Axis. 9) What is the common ratio (r) of the sequence 5, 10, 20, 40, ....? A) 2 B) -2 C) 5 D) -5 The next term of the sequence 2, 6, 18, 54, …. is _______. 10) A) 162 11) 12) B) 174 C) 186 D) 198 𝑎𝑚 ∙ 𝑎𝑛 = ________. A) 𝑎𝑚𝑛 B) 𝑎𝑚+𝑛 C) 𝑎𝑚−𝑛 D) None of these. (𝑎𝑚 )𝑛 = ________. B) 𝑎𝑚𝑛 B) 𝑎𝑚+𝑛 C) 𝑎𝑚−𝑛 D) None of these. 1 2 13) What is the value of 2(64) ? A) 12 B) 16 C) 24 D) 36 C) 7 D) 0 14)If 9𝑥 = 97 , 𝑥 = _________. A) 9 B) 63 Mission: We provide our students with a caring and culturally diverse environment where we make every student feel valued and welcomed. We encourage our students to become independent learners and motivate them to be creative, think critically, and communicate effectively. We also teach them the values of respect, honesty, and integrity. 2 Vision: Our vision is to prepare and motivate our students through instilling in them critical thinking skills and a global perspective to help them take on the challenges of a rapidly changing world. 15) (4𝑦)(5𝑦 3 ) = _______________. A) 9𝑦 3 B) 20𝑦 4 D) 𝑦 4 + 9 C) 0 Question 2: Graph each function. A. 𝑓(𝑥 ) = |𝑥 | + 1 𝑦 𝑥 -2 -1 0 1 2 B. 𝑓(𝑥 ) = 0.6(3)𝑥 𝑥 𝑦 -1 0 1 2 Question 3: Solve each equation: A. |𝒙-3|=5 B. |𝒙-1|=6 Mission: We provide our students with a caring and culturally diverse environment where we make every student feel valued and welcomed. We encourage our students to become independent learners and motivate them to be creative, think critically, and communicate effectively. We also teach them the values of respect, honesty, and integrity. 3 Vision: Our vision is to prepare and motivate our students through instilling in them critical thinking skills and a global perspective to help them take on the challenges of a rapidly changing world. C. (3)𝑥 = 27 D. (2)𝑥 = 4 Question 4: A. Describe the translation(s) of the function g(𝑥), compared to the parent function, 𝑓(𝑥). 𝑓(𝑥 ) = (2)𝑥 , g(𝑥) = (2)𝑥 + 7 ________________________________________________________________ ________________________________________________________________ _______________________________________________________________ B. Describe the translation(s) of the function g(𝑥), compared to the parent function, 𝑓(𝑥). 𝑓(𝑥 ) = |𝑥 | , g(𝑥) = 4|𝑥 | ________________________________________________________________ ________________________________________________________________ _______________________________________________________________ Question 5: Classify the following polynomial by its degree and the number of terms. 5𝑥 6 − 3𝑥 3 + 9 The degree: ________________. The number of terms: _____________. Mission: We provide our students with a caring and culturally diverse environment where we make every student feel valued and welcomed. We encourage our students to become independent learners and motivate them to be creative, think critically, and communicate effectively. We also teach them the values of respect, honesty, and integrity. 4 Vision: Our vision is to prepare and motivate our students through instilling in them critical thinking skills and a global perspective to help them take on the challenges of a rapidly changing world. Question 6: A. Find the sum. (5𝑥 2 + 4) + (3𝑥 2 + 1) = B. Find the difference. (5𝑏 + 7) − (3𝑏 − 2) = Question 7: Find each product. A. (3𝑥)(4𝑥 3 ) B. 3𝑏(2𝑏 + 4) C. (𝑥 + 3)(𝑥 + 2) D. (𝑦 + 3)(𝑦 − 3) Question 8: Find the common ratio (r) and write an explicit rule for the following geometric sequence. 3, 9, 27, 81, …. 𝑟= ÷ = The explicit rule: 𝑎𝑛 = 𝑎1 ∙ 𝑟 𝑛−1 ________________________________________________________________ ________________________________________________________________ Mission: We provide our students with a caring and culturally diverse environment where we make every student feel valued and welcomed. We encourage our students to become independent learners and motivate them to be creative, think critically, and communicate effectively. We also teach them the values of respect, honesty, and integrity. 5 Vision: Our vision is to prepare and motivate our students through instilling in them critical thinking skills and a global perspective to help them take on the challenges of a rapidly changing world. Mission: We provide our students with a caring and culturally diverse environment where we make every student feel valued and welcomed. We encourage our students to become independent learners and motivate them to be creative, think critically, and communicate effectively. We also teach them the values of respect, honesty, and integrity. 6