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Quiz, Answers and Solutions in 1st Quiz in Mathematics in preparation for UPCAT.docx

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  Welcome to our 1 st  Quiz in Mathematics for Preparation for UPCAT Made by: Jose Miguel Lopez A B C E D Grade 9 Level (Easy): Letters Only! 1.) (x -2)(x + 3) = ? a. x^2 + x  –   6 b. x^2  –   x  –   6 c. x^2 + x + 6 d. x^2 + 5x  –   6 2.) Complementary is to 90 degrees. Supplementary is to ___ degrees? a. 360 b. 90 c.180 d. 45 3.) What is the value of the discriminant in the equation f(x) = 2x^2 + 3x  –   7? a. -45 b.102 c. 42 d. none of the above 4.) What is the nature of the roots in the equation f(x) = x^2 + 6x + 9 a. Real, Rational, Equal b. Real, Irrational, Equal c. Real, Rational, Unequal d. Real, Irrational, Unequal 5.) What is the equation of the graph below? a. y = x^2 +7x + 12  b. y = x^2 + x  –   12 c. y = x^2 + 8x  –   12 d. y = x^2  –   x  –   12 6.) Point E and Point D are the Midpoints of the Line AB and Line AC, respectively. If DE = 8 cm, what is the length of Line CB? a. 8.5 cm b. 4 cm c. 12 cm d. 16 cm (Only for Number 6)  Welcome to our 1 st  Quiz in Mathematics for Preparation for UPCAT Made by: Jose Miguel Lopez A B Grade 9 Level (Average): Answer Only! 7.) Find the equation of a line that passes through the point (-2,3) and has a slope of 3. 8.) Triangle ABC is a right triangle at B. If m ∠ C = 45°, find the area of the triangle. 9.) x + 10, 4x + 5 and 5x + 13 turns out to be an Arithmetic Sequence. Find the numbers and their common difference. 10.) If tan θ  = 4/3, find cos^2 θ . 11.) y is inversely proportional to x. y = 15   when x = 3, find y if x = 31π  12.) Rationalize and Simplify: √ 2 √ 13√ 3+ √ 5  13.) Triangle ABC is similar to Triangle DEF if Line AB = 10, Line DE = 5, Line BC = 7 and Line EF = 3.5, find DF if AC = 30 Grade 9 Level (Hard): Answer with Solutions! 14.) Find the equation whose roots are half of the roots of the equation x^2 + 6x + 9 = 0. 15.) Triangle ABC is a right triangle at C. If ∠ A = 63° and a = 11 cm, find ∠ B, b and c. 16.) A tower is 15.24 m high. At a certain distance away from the tower, an observer determines the angle of elevation to the top of it is 41°. How far is the observer from the base of the tower? Express your answer in terms of tan. 17.) Find x on the equation:   ++=0   18.) Tomoya’s family is like a one big “Dango” family. Tomoya is the husband of Nagisa, and their daughter is Ushio. Tomoya is older than Nagisa by 13 years, and his wife is older than his daughter by 11 years. In 6 years, Tomoya’s age will be 4 times as the srcinal age of his daughter. Find the sum of their ages now and after 6 years. C (Only for Number 8)  Welcome to our 1 st  Quiz in Mathematics for Preparation for UPCAT Made by: Jose Miguel Lopez A B C D E F (x + 5) cm 3 cm 19.) Quad ABEF is a square and Quad BCDE is a rectangle. Find the area of the Triangle ABD. 20.) Yukihira Soma just had an examination. In Math Category, he stumble upon a question stated that “A McDo meal and a McDo Burger costs 270 pesos, and 9 McDo Meals and 8 McDo Burger cost 2,365 pesos. Find the cost of 2 McDo Meals and 5 McDo Burgers”. He found that the question given has 4 stars on it, indicating that the question is difficult to solve. Now, as a friend of his, you will solve the problem. Answer the Math exam question.  Welcome to our 1 st  Quiz in Mathematics for Preparation for UPCAT Made by: Jose Miguel Lopez Grade 10 (Easy): Letters Only! 1.) Which set of the numbers is an example of harmonic sequence? a. 1/2., -1/2, 1/3. -1/3 c. 2/3, 4/5, 6/7, 8/9  b. 1/3, 1/9, 1/27, 1/81 d. 3/10, 3/12, 3/14, 3/16 2.) If three arithmetic means are inserted between 11 and 39, find the second arithmetic mean. a. 8 b. 13 c. 21 d. 25 3.) If three geoemetric means are inserted between 2 and 32, find the sum of the three geometric means. a. 21 b. 24 c. 28 d.35 4.) 1, 8, 27, 64, 125, ___? a. 250 b. 353 c. 216 d. 275 5.) What is the leading coefficient of the polynomial function f(x) = x^3 + 2x^2 + 4x  –   10? a. 1 b. 2 c. 4 d. 10 6.) The Central Point of the circle is at point P. ∠ P = 50°. Find the angle of Arc FE. a. 50° b. 25° c. 5° d.10° Grade 10 (Average): Answers Only! 7.) C Find CE. Note that Point E is the intersection Point of the chords AB and CD. P F E A B D   (Only for Number 6) (Only for Number 7)
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