SUPPLEMENTAL FINAL REVIEW PROBLEMS ALGEBRA 1 Spring 2014

Transcription

1 Name: SUPPLEMENTAL FINAL REVIEW PROBLEMS ALGEBRA 1 Spring ) The formula for the circumference of a circle is, where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference? It is a fraction. It is a repeating or terminating decimal. It is a rational number. It is an irrational number. 51) Which of the following is always irrational? the sum of two fractions the product of a fraction and a repeating decimal the sum of a terminating decimal and the square root of a perfect square the product of a repeating decimal and the square root of a non-perfect square 52) Why is the product of a rational number and an irrational number irrational? because the product is always a non-terminating, non-repeating decimal because the product is always a fraction because the product is always a negative number because the product is always a repeating or a terminating decimal 53) Which number is irrational? 54) Find the x-intercepts for the following quadratic function.

2 55) Find the vertex of by converting the equation to vertex form. Check your answer by converting the equation to factor form. 56) Write two equations for the graph shown below? 57) Complete the square. What is the y intercept, the vertex, and the solution to the equation shown.

3 58) Suppose you hit a fly ball with an initial upward velocity of 20 feet per second. Which of the following equations would be a realistic model for the height of the ball after t seconds? A. B. C. D. 59) A fireworks display is launched from a platform 10 feet above ground with an initial upward velocity of 70 feet per second. The height of the fireworks above ground after t seconds is given by the equation h = 16t t + 10, where h is the height of the fireworks in feet and t is the time in seconds after they are launched. What is the maximum height of the fireworks display, to the nearest foot? Solve by completing the square 60) How many real solutions does a quadratic equation have if its discriminant is negative? A. 0 B. 1 C. 2 D. infinite 61) What other name(s) are the solutions of a quadratic equation known by? A. roots B. x-intercepts C. zeros D. all of the above

4 62) Solve for x using the quadratic formula. 63) Solve the inequality 6x + 2 < 10 and graph its solution on the number line. 64) Troy was trying to catch up with the rest of his group, who had left earlier on a kayaking trip. Troy paddled 8 hours downstream, covering 72 miles before realizing that he had passed his group s campground. He had to paddle back upstream for 18 miles to get back to his group s campground. If the trip back upstream took Troy 6 hours, how fast was the river flowing (in mph)? 65) Jenna was selling muffins and bagels in the lobby to support the math club. Bagels sold for $0.75 and muffins sold for $1.50. She sold three times as many bagels as muffins and made $ this morning. Write a system of equations to correctly model this situation.

5 66) How many solutions does the system of equations have? 2x + 3y = 6 67) Which of the following systems of linear inequalities is the best algebraic representation of the graph shown below? A. B. C.

6 D. 68) Jason showed the following work while subtracting these two polynomials. Determine if he made an error. If so write the correct answer. A. Jason did not combine the x terms together correctly. The correct answer is B. Jason did not distribute the subtarction sign to the x. The correct answer is C. Jason's work is correct. D. Jason did not distribute the subtraction sign to the x or the 2. The correct answer is Solve the polynomial multiplication problems below: 69) (4p 1) 2 70) (7x 6)(5x+6) 71) (7k 3)(k 2 2k+7) 72) -4x 3 y(- 2y 2 + xy - x + 9) =

7 73) A landowner wishes to construct a fence around a small section of her property. The fence is rectangular and is meters wide and meters long. What is the exact perimeter of the fence? (Recall that the perimeter is the sum of each individual side of a shape.) 74) Simplify the radicals below. a) b). 75) The parent function f(x) = 1/x Has become a new function g(x) = f(x) +2 Label f(x) and g(x) on the graph below.