American College Of Sofia 8th Grade Final Exam Semester 2 2023-2024 PDF

Group A American College of Sofia Department of Mathematics Final Exam - S...

Group A American College of Sofia Department of Mathematics Final Exam - Semester 2 8th grade (2023-2024) Name: Part I: Multiple Choice 1 (2pts). Which of the following is not in simplest form? √ √ √ √ a) 2 5 b) 8 c) 15 d) 3 √ 2 (2pts). Simplify 99 √ √ √ a) 33 b) 99 c) 9 11 d) 3 11 √ √ √ √ 3 (2pts). Simplify the expression −3 5 − 25 + 20 + 10 √ √ √ √ √ √ a) 5 5 b) 5−5 c) 5+ 10 − 5 d) − 5 + 10 − 5 4 (2pts). Which of the following is not in simplest radical form?. √ √ 7 √ √ 21 a) 10 b) 3 c) 52 d) 7 5 (2pts). The sum of the sizes of internal angles of any n-sided polygon is: a) n × 180 b) (n + 2) × 180 c) (n − 2) × 180 d) (2 − n) × 180 6 (2pts). The sum of external angles of a 12-sided polygon is: a) 180◦ b) 360◦ c) 270◦ d) 90◦ 7 (2pts). Which of the following is a Pythagorean triple? a) {1, 5, 10} b) {3, 4, 5} c) {5, 2, 2} d) {2, 2, 2} 8 (2pts). Find the value of x: √ √ √ √ a) 2 5 b) 4 5 c) 2 3 d) 2 11 9 (2pts). Find the value of x: √ √ √ √ a) 2 11 b) 4 5 c) 2 3 d) 2 5 10 (2pts). Which of the following is the equation of a line that is perpendicular to the line y = 3x − 2 1 a) y = 3 b) y = − 31 x − 5 c) y = 31 x + 55 d) y = 3x + 4 11 (2pts). A line that is parallel to the x-axis (completely horizontal or ”flat”) has a slope equals to: a) Undefined b) m = 0 c) m = 1 d) m = −1 12 (2pts). Which of the following points is in the third quadrant?: a) (−1, 5) b) (3, 7.3) c) (3, −5) d) (−3, 0)) 13 (2pts). Select the only option that has enough information to find the equation of a line: a) The slope b) x-intercept c) One point d) y-intercept and x-intercept 14 (2pts). Which of the following is the equation of a line that is perpendicular to the line y = − 37 x−25 3 a) y = 7 b) y = − 73 x − 5 c) y = 37 x + 55 d) y = − 73 x + 25 15 (2pts). Which of the following is the equation of a line that is parallel to the line y = − 37 x − 25 3 a) y = 7 b) y = − 73 x − 5 c) y = 37 x + 55 d) y = − 73 x + 25 16 (2pts). The midpoint of C(-5,3) and D(-1,13) is: a) M (3, 8) b) M (−2, −5) c) M (2, 5) d) M (8, 3) 17 (2pts). Find the distance between the points A(-5,5) and B(3,7) √ √ a) 4 b) 80 c) 80 5 d) 2 17 18 (2pts). Two triangles are similar, and the ratio of each pair of corresponding sides is 4:3. Which statement regarding the two triangles is true? a) Their areas have a ratio of 16 : 9 b) Their perimeters have a ratio of 16 : 9 c) Their altitudes have a ratio of 1 : 1 d) Their corresponding angles have a ratio of 4 : 3 19 (2pts). Find x: 20 a) 14 b) 4.5 c) 21 d) 7 20 (2pts). Two triangles are similar if: a) They have same area b) Two sides are equal c) One angle is equal d) Two angles are equal  Part II: Long answers 21 (5pts). If the diameter of a circle is 20 cm, find the shortest distance from a chord of length 16 cm to the centre of the circle. 22 (5pts). A circle has radius 3 cm. A tangent is drawn to the circle from point P which is 9 cm from O, the circle’s centre. How long is the tangent? 1√ 23 (5pts). Simplify: 3− 5 24 (5pts). Consider a regular 12-sided polygon a) What is the sum of its interior angles? b) What is the measure of each interior angle? c) What is the sum of its exterior angles? 25 (5pts). Given the points A(2,-3) and B(-6,7) a) Find the coordinates of the midpoint of the segment AB b) Find the slope of AB c) Find the equation of the perpendicular bisector of AB 26 (5pts). A 4.9 m high flagpole casts a shadow of 4.5 m. At the same time, the shadow of a nearby building falls at the same point (S). The shadow cast by the building measures 13.5 m. Find h , the height of the building, using a proportion statement. Formulas: y = mx + c p d= (x2 − x1 )2 + (y2 − y1 )2   x1 + x2 y1 + y2 M , 2 2 y2 − y1 m= x2 − x1 b = y1 − mx1