First Semester Comprehensive Exam 2018..docx

Comprehensive Exam First Semester 2018. Name:_________________________Score:______

1. Find the difference (3n2-4n +1) –(8n2 -4n + 17).

2. Find the product (6y +1)2.

3. Solve the equation a2 + 26a =0.

4. Factor the trinomial p2 + 9p + 14.

5. Vertical motion A cricket jumps off the ground with an initial vertical velocity of 4 feet per second. a. Write an equation that gives the height (in feet) of the cricket as a function of time (in seconds) since it jumps.

b. After how many seconds does the cricket land on the ground ?

6. Complete the steps to solve the equation x2 – 8x - 9 = 0 by completing the square. x2 – 8x = ___. x2 – 8x + ____ = 25. ( x - __)2 = 25. x - ___ = _____. x = _______.

7. Graph the function y= x2 – 6x + 8. Find the axis of symmetry and the vertex of the graph of the function. Then tell whether the function has a maximum or a minimum value. Find this value.

8. Use the quadratic formula to solve the equation x 2 – 8x + 15 = 0.

9. Tell whether the equation has two solution, one solution or no solution 2h2 - 4h + 3 = 0.

10. Let a and b represent the lengths of the legs of a right triangle, and let c represent the length of the hypotenuse. Find the unknown length. Right your answer in its simplest radical form. b = 7 and c= 11.

11. Find the distance between the 2 points (9, 6) and (4,1).

12. Find the midpoint of the line segment with the given endpoints (20,5) and (30, - 5).

13. Refer to the diagram below to answer the following: a. Name an obtuse angle:

_______________

b. Name an acute angle:

_______________

c. Name two supplementary angles:

_______________ and ________________

d. If m3 = 63°, find the measures of :4: _______________ and 5: _______________

14. E is between D and F. Find DF.

15. Solve the equation and write a reason for each step. 1 (−𝑥 − 8) = 45 4