Algebra II Honors Summer Packet
Algebra II Honors Summer Packet
Algebra II Honors Summer Packet
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Name:<strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong><strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong> <strong>Summer</strong> <strong>Packet</strong>Directions: Complete the following, showing all work and pledging it. A calculator may beused only where indicated, and all approximate answers should be correct to three decimalplaces. All of these questions are review from Geometry <strong>Honors</strong>; use any notes from theprevious year to help you. If you need help with any of these problems, please come to <strong>Summer</strong>Math Help in August.1. Two complementary angles have measures in the ratio 1:4. Find the measure of each angle.2. The measure of the supplement of an angle is 50 less than 4 times the measure of thecomplement of the angle. Find the measure of the angle.3. Given: m∠1= ( 2x+ 5y)°m∠2= ( 10x− 5y)°m ∠1 and m ∠2are in the ratio 1:3.Find x and y.
<strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong> 24. Find the angle formed by the hands of the clock at 6:45.5. Using the diagram below, find m∠ ABD .6. Two parallel lines are crossed by a transversal. Which of the following angles arenecessarily congruent?Adjacent anglesAlternate interior anglesAlternate exterior anglesComplementary anglesCorresponding anglesSame side interior anglesSupplementary anglesVertical angles7. Given that POLY is a parallelogram, find the values of x and y.
<strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong> 38. Define the following:equilateral triangle –isosceles triangle –scalene triangle –acute triangle –right triangle –obtuse triangle -9. A triangle has legs of length 12, 16, and 20. Classify the triangle as acute, right, or obtuse.Justify your answer.10. A triangle has legs of length 10, 11, and 13. Classify the triangle as acute, right, or obtuse.Justify your answer.11. Explain why it is not possible for a triangle to have legs of length 10, 12, and 25.
<strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong> 412. Expand and simplify ( ) 21− 4 3 .13. State the Quadratic Formula.14. Use the quadratic formula to solve the following equations:x 2 + 23 = 10x 2x2 − 5 x −1= 015. Find the equation of↔AB in point-slope form.16. C is the midpoint of ____AB . Find the coordinates of C.17. Find an equation of the perpendicular bisector of ____AB .
<strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong> 518. State the distance formula.19. Derive the distance formula using the Pythagorean Theorem.20. Find the distance between the points (2, 4) and (8, 6).21. If a building casts a 50-ft long shadow at the same time that a 6-ft high post casts a 1.5-ftshadow, how tall is the building? Draw a diagram.22. The length of an arc of a circle of radius 16 is 32π.Find the measurement of the central angle.Find the area of the sector of the circle with the same central angle.
<strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong> 727. What does it mean for a polygon to be regular?28. Find the measure of each interior angle of a regular octagon.29. Find the area of a regular hexagon whose perimeter is 6.30. Find the area of a rectangle with a base of 24 and a diagonal of 25.31. A frustrum of a cone has an altitude of 12 and the radii of its upper and lower bases are 4 and8.Find the surface area of the frustrum.Find the volume of the frustrum.
<strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong> 832. A cube in inscribed in a sphere with diameter of 2 3 .Find the surface area and volume of the cube.Find the surface area and volume of the sphere.33. The ratio of the radii of two spheres is 3:4.What is the ratio of their surface areas?What is the ratio of their volumes?34. Define the sine, cosine, and tangent of θ in terms of the legs of a right triangle.35. Find the sine, cosine, and tangent of θ, given the triangle below.76θ
<strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong> 9calculator 36. The shadow of a 6-ft tall man is 3 ft. Find the angle of elevation of the sun.calculator 37. A hot-air balloon flying 600 feet above the ground views two observers below, on oppositesides of the balloon. The angle of depression between the balloon and the first observer is45º. The angle of depression between the balloon and the second observer is 75º. What isthe distance between the two observers on the ground?calculator 38. In the figure below, the radius of the largest circle is 8 cm and the centers of the 4 smallercircles each lie on the same diameter of the largest circle. Find the area of the shaded region.
<strong>Algebra</strong> <strong>II</strong> <strong>Honors</strong> 10calculator 39. A cylinder whose height is three times its radius is inscribed in a sphere whose radius is 10inches. Draw a diagram and determine the radius and height of the cylinder. Show the workthat leads to your conclusion.
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