ATHS FC Math Department Al Ain Revision worksheet

Transcription

1 ATHS FC Math Department Al Ain Revision worksheet Section Name ID Date Lesson Marks 3.3, 13.1 to 13.6, 5.1, 5.2, 5.3 Lesson 3.3 (Solving Systems of Inequalities by Graphing) Question: 1 Solve each system of inequalities by graphing. 1. y < 3 x + 2y < Find the coordinates of the vertices of the triangle formed by each system of inequalities. x -2 y x 2 x + y 2 Intervention Plan Page 1 of 16 Gr 10 core

2 Chapter 13: Trigonometric Functions (13.1 to 13.6) Question: 1 Find the values of the six trigonometric functions for angle θ. Question: 2 Use trigonometric functions to find the values of x and y. Round to the nearest tenth if necessary. 1.. Intervention Plan Page 2 of 16 Gr 10 core

3 2. Question: 3 Draw an angle measuring -50 in standard position. Intervention Plan Page 3 of 16 Gr 10 core

4 Draw an angle measuring 305 in standard position. Question: 4 Rewrite each degree measure in radians and each radian measure in degrees Question: 5 Find the length of the arc. Round to the nearest tenth. Intervention Plan Page 4 of 16 Gr 10 core

5 Question: 6 Find the exact value of each trigonometric function cos(3π/4) Question: 7 The terminal side of θ in standard position contains each point. Find the exact values of the six trigonometric functions of θ. 1. (-20, 21) 2. (0, -5) Intervention Plan Page 5 of 16 Gr 10 core

6 Question: 8 Three cities are arranged on the map in a shape of triangle as below 80 9m 7m 34 What is the area enclosed by the cities? Question: 9 Determine whether each triangle should be solved by beginning with the Law of Sines or Law of Cosines. Then solve the triangle. 1. Intervention Plan Page 6 of 16 Gr 10 core

7 2. 3. C = 35, a = 5, b = 8 4. B = 125, a = 8, b = 14 Question: 10 Determine the period of each function. 1. Intervention Plan Page 7 of 16 Gr 10 core

8 2. 3. Question: 11 The terminal side of angle θ in standard position intersects the unit circle at each point P. Find cos θ and sin θ Intervention Plan Page 8 of 16 Gr 10 core

9 Chapter 5: Quadratic Functions and Relations Question: 1 (5.1,5.2,5.3) Complete parts a-c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. 1. f(x) = x 2 8x f(x) = -x 2 4x + 12 Intervention Plan Page 9 of 16 Gr 10 core

10 Question: 2 Determine whether each function has a maximum or minimum value, and find that value. Then state the domain and range of the function. 1. f(x) = 2x 2 + 4x 6 2. Question: 3 GRAVITATION From above a swimming pool, Susan throws a ball. The height h(t) of the ball t seconds after Susan throws it is given by h(t) = -16t t + 4. For t 0, find the maximum height reached by the ball and the time that this height is reached. Intervention Plan Page 10 of 16 Gr 10 core

11 Question: 4 Use the related graph of each equation to determine its solutions x = x 2 + x + 3 = 0 3. x 2 3x + 2 = 0 Intervention Plan Page 11 of 16 Gr 10 core

12 Question: 5 Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located x 2 6x + 5 = 0 2. x x + 24 = 0 Intervention Plan Page 12 of 16 Gr 10 core

13 Question: 6 Write a quadratic equation in standard form with the given root(s) , , Question: 7 Factor each polynomial. 1. r 3 + 3r 2 54r 2. 8a 2 + 2a 6 3. c r x x + 1 Intervention Plan Page 13 of 16 Gr 10 core

14 6. 3x 2 12x + 12 Question: 8 Solve each equation by factoring. 1. x 2 4x 12 = x 2 = 4x 3. x 2 = 2x x 2 35x + 60 = x 2 = 25 Question: 9 NUMBER THEORY Find two consecutive even positive integers whose product is 624. Intervention Plan Page 14 of 16 Gr 10 core

15 Question: 10 NUMBER THEORY: Use a quadratic equation to find to real numbers that satisfy each situation, or show that no such numbers exist. 1. Their sum is 15, and their product is Their sum is 7, and their product is 15. Question: 11 GEOMETRY: Find x and the dimensions of the rectangle X + 4 Area = 104 m 2 X - 1 Intervention Plan Page 15 of 16 Gr 10 core

16 Intervention Plan Page 16 of 16 Gr 10 core