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### Final exam g7 2015

• 1. Page 1 of 3 CCS Mathematics June 2015 Class ofG7 Exam of 𝟑 𝒕𝒉 semester Duration : 120 min Name :………………………………….. I. (2 points) In the following table, one answer is correct. Choose that answer and justify your choice. Nb Questions Answers A B C 1 5² × 25² × (5²)⁴ 5¹² × 5² 5¹⁶ 5¹² 2 The GCD of 16 and 48 3 48 16 3 The scientific notation of 37.05 × 10⁵ is 0.3705 × 10⁷ 3.705 × 10⁶ 3.705 × 10⁴ 4 𝐴 = ( 2 3 − 5 2 ) × 9 4 + 1 2 = 𝐴 = − 29 8 𝐴 = 29 8 𝐴 = 29 7 II. (4 points) Given 𝐴( 𝑥) = (2𝑥 − 3)( 𝑥 − 1) − (2𝑥 − 3)(4 − 𝑥) 1) Factorize 𝐴(𝑥). 2) Develop and reduce 𝐴(𝑥). 3) Calculate 𝐴(0), 𝐴(−1). 4) Solve the equation 𝐴( 𝑥) = 4𝑥² + 8𝑥 + 4 III. (4 points) 1) Three cars out of 75 have an accident. What is the percentage of those ? 2) With 3.5 𝑙 of pain, we can paint 14 m². a) What is the area can we paint with 12 𝑙 of paint ? b) What is the quantity needed to paint 23 m² ? 3) A shop bought three packets of tissues of measures 30 m, 25 m and 40 m respectively. If the first packet costs 600000 LL. Find the price of the other two packets. IV. (2 points) B and C are two fixed points such that BC= 3 cm. 1) Find the locus of the variable point M such that BM= 7 cm. 2) Find the locus of the point N such that (CN) and (BC) are perpendicular.
• 2. Page 2 of 3 V. (4 points) Look at the following figure, then answer the following questions: 1 1) Find the measure of the angle 𝐴𝐻̂ 𝐵. 2) Prove that (EI) is parallel to (KL). 3) The lines (JE) and (BH) are parallel ? Justify 4) Find x and y. VI. (6 points) 1) Construct the angle 𝑋𝑂̂ 𝑌 = 120°, then construct the bisector of that angle, [OZ). 2) Place the point A on [Oz) such that OA= 6cm. 3) B and C are the orthogonal projections of A respectively on [Ox) and [Oy). 4) Place the points S and T the symmetric of A with B and C respectively. 5) Prove that the triangles OAC and OAB are congruent. 6) Prove that OS= OT. 7) Prove that BOS and COT are congruent. 8) Find the measure of the angles 𝑂𝐴̂ 𝐵, 𝑂𝐴̂ 𝐶, 𝐴𝑆̂ 𝑂 𝑎𝑛𝑑 𝐴𝑇̂ 𝑂.
• 3. Page 3 of 3 VII. (3 points) In the adjacent figure, ABC is a triangle such that : EFHG, FEHI, GHJB, HICK, EFCK and GHKJ are parallelograms. 1) What is the translate of G by translation taken B to G ? 2) What is translate of G by translation taken E to F ? 3) Determine the translation taken the triangle HIK to the triangle GHJ. 4) Determine the translation of the triangle HIK by translation taken I to H. GOOD WORK. Best wishes for a happy summer and a bright and a successful future.
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