a) -64 b) 225 c) 27 d) 48 e) Find the corresponding conjugate of given complex numbers a)3-4i b) 4 5i c) 7 8i d)13 11i

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1 Syllabus Unit 1: Similarity, Congruence, and Proof Unit 3: Circles and Spheres Unit 2: Right Triangle Trigonometry Unit 4: Extending the Number System 1. Simplify the following a) -64 b) 225 c) 27 d) 48 e) Find the corresponding conjugate of given complex numbers a)3-4i b) 4 5i c) 7 8i d)13 11i 3. Simplify the integral powers of i a)i (b)i c)i d)i e)i 4. Simplify the expression a)i+i +i +i (b)-2i +3i c)4i+3i -5i + d)-i+3i -5i +2i 5. Simplify the following expression using complex conjugate of the denominator a) i (b) i c) i d) i i e) 2 3i 4 5i 1 2i 2 3i 1 i 6. Simplify the following polynomials a. (12y y - 4) + (9y 2-13y + 3) b. (3a 2 + 2a - 2) - (a 2-3a + 7) c. (6x 3-4x 2 + x - 9) - (3x 2 + 7x + 3) d. 3(x 2-2x + 3) - 4(4x + 1) - (3x 2-2x) 7. in a right triangle ABC, if C is right angle which of the following relations is true. a.sina=sinb b.cosa=cosb c.sina=cosb d.sina=cosc 8. in a right triangle PQR, if P is right angle which of the following relations is true. a.sinp=sinq b.cosq=cosr c.sinp=cosp d.sinq=cosr 9. in a right triangle LMN, if M is right angle which of the following relations is true. a.sinn=cosl b.cosm=cosn c.sinl=cosm d.sinm=cosm. 10. Find the similarity of two circles a. Center O circumference 2π to Center P with circumference 5π b. Center P area 27 to Center M area 54. c. Center O diameter 15 to Center P diameter 5. d. Center M radius 60 to Center N radius A bridge is constructed across a river to relocate water main to prevent water over flow as shown below; find the height of the bridge from water surface h In a ABC, if and A and B are complementary angles then which one of the following is true a. sina=sinb b.cosa=sinb c.cosa=cosb d. tana=tanb

2 13. The below picture shows how earthquakes are occurred due to disturbance under the ground. Using the below picture find the height of the rock if the layer marked in the graph is 3 in. D 3in C h A in B 14. In the diagram, RST is equilateral, and U is the midpoint of RT. If the length of ST is 20 cm, what is the length of SU? 15. In the figure given to the side, right triangle BCD sits on line AC. What is the value of x? 16. A paratrooper intends to jump from a plane even though she s been warned about the strong winds. If she intends to jump from 1,500 feet above ground, she ll drift 8º. How far from the drop zone, directly under the plane, will she drift? 17.Two cars are travelling on the same road. One car is in front of the other. There is a billboard that both drivers are looking at. With an angle of elevation of 61º, the driver of the first car can see the billboard clearly. The driver of the second car can see the billboard with an angle of elevation of 53º. How far apart of the two cars? 18. The faces of the presidents at Mount Rushmore are 60 feet tall. A visitor sees the top of George Washington s head at an angle of elevation of 48º and his chin at an angle of elevation of 44.76º. Find the height of Mount Rushmore.

3 19. A pizza-making kit contains three circular baking stones with diameters 24 cm, 36 cm, and 48 cm. Find the area of each stone. Round to the nearest tenth. 20. A drum kit contains three drums with diameters of 10 in., 12 in., and 14 in. Find the circumference of each drum Find the volume of a cylinder with base area 121 cm and a height equal to twice the radius. Give your answer in terms of and rounded to the nearest tenth. 2 An art gallery is a 6-story square pyramid with base area acre (1 acre = 4840 yd, 1 story 10 ft). Estimate the volume in cubic yards and cubic feet. 23.Which form of transformation does not preserve the congruencce a.translation b.rotation c.dilation d.reflection 24.Which transformation in the figure that is similar to the original figure but will have smaller area. a.a dilation of reactangle ABCD with a scale factor of.5 b. a dilation of reactangle ABCD with a scale factor of.25 c. a dilation of reactangle ABCD with a scale factor of 1 d. a dilation of reactangle ABCD with a scale factor of Which transformation in the figure that is similar to the original figure but will have bigger area. a.a dilation of pentagon PQRST with a scale factor of.5 b. a dilation of reactangle PQRST with a scale factor of.25 c. a dilation of reactangle PQRST with a scale factor of 1 d. a dilation of reactangle PQRST with a scale factor of In the diagram of circle O shown below Chords CD and AB are parallel to each other. If mcd= What is the measure of AC? a. Measure of AC= 50 0 b. Measure of AC=45 0 c. Measure of AC=140 0 d. Measure of AC=40 0 O 27. In the diagram of circle O shown below Chords PR and SOT are parallel to each other. If mrt= What is the measure of PR? A C D B e. Measure of PR= 50 0 f. Measure of PR=130 0 g. Measure of AC=140 0 h. Measure of AC=40 0 S P O R T 28. What is the sector area of a circle with diameter 12 cm and having central angle 55 0?

4 29.Find missing measurement in the given table CA 2 CA SA= πr AL= 2πr Radius Central angle Sector area Arc length sqcm 150 ft m 30. An electrician bent a section of copper wire into a partial circle as shown. The dimensions are given in feet. What is the length of the section of wire to the nearest hundredth of a foot? If JLK=37.50, find mjk. 32. Each student measured the circumference and diameter of a different circle. The results are shown below. Student Results Student Circumference Diameter (Centimeter) (Centimeter) E F G H J Based on the data, which statement can be used to prove that all circles are similar? a.the circumference circle is greater than diameter c. The ratio of circumference to diameter is sometimes proportional c. the circumference multiplied by the diameter is always equals to the constant π. d. The circumference divided by the diameter always approximate the constant π. 33.In circle O, which is a right angle? a. angle P b. angle Q c. angle R d. angle S

5 34. Points A, B, C, and D are consecutive points on a cirlce W as shown below which angle must be equal to BAC? 35.A quadritlateral is ABCD inscribed in a cirlce as shown below. which statement must be true? a.ac is diamter b. angle A is right angle c. angle A and C are supplementary d.abce is rectangle 36.