Placement Test for Algebra 1B and Algebra 2 www.mathinabox.com

Susan O. Johnsey sjohnsey@bellsouth.net

Please show a little work on each problem. Send your answers/work by email, please. I will reply within one day. Please let me know with a polite note if I do not.

Complete test within 1 hour. Tell me the amount of time that you worked on the test.

* means multiply.

1. Simplify: (3/5)*(5)^{2} Note: the 3/5 is the fraction 3-fifths.

2. Simplify: 80 divided by 5*(5+3)

3. Simplify: -18 – (1 -10)^{2}

4. Simplify: { (-10+4) divided by (4+2) } divided by 2

5. Simplify 2x + [ 2 – 4] +3(-4 +5x)

6. Simplify -4x^{2} – 2x^{2} + 5x – 9x^{2}

7. Translate to a variable expression: the product of 5 and the sum of twice a number and 3.

8. Is 1/2 a solution of x/2 + 1/4 = 0 ?

9. Is –2 a solution of 4x + 7 = -1 ?

10. Solve for x: ( show some of your steps) 6 – 5x = x+ 3 –2x

11. Solve for x: ( show some of your steps) 8 – 5(x+4) = 2

12. . Translate into a variable equation and then solve. Give your equation and your answer.

Fifty-four is 5 times the difference between a number and 6.

13. 612 is 85% of what number?

14. 30% of a class is boys. There are 120 boys. How many girls are there?

15. How far in miles can a man drive at 40 mph to return on the same route

at 30 mph if he travels for 7 hours? You must state your equation and your solution.

16. SUBTRACT: (4X^{2} – 6X + 7) – ( 7X^{2} +5X – 3)

17. MULTIPLY then simplify: (X – 4 )( 4X^{2} – 4X + 8)

18. MULTIPLY then simplify: (X – 5p)(X +5p)

19. DIVIDE: (24X^{2} + 40XY ) DIVIDED BY 8X.

20. Factor completely: v^{2} – 12v +20

21. Factor completely: m^{2}(x+3) – y^{2}(x+3).

22. Factor completely: 9d^{2} – 24d + 16

23. Factor completely: x^{2} y^{2} – 49.

24. Factor completely: x^{3} – 27 .

25. Solve by factoring: x^{2} + 16x +63 = 0

26. State the numerator only of the quadratic formula. You may use symbols or words. Just try to be clear in what you mean. I am looking for understanding, not a perfect definition or explanation.

27. For the quadratic, 9d^{2} – 24d + 16 =0 , state the values of a, b, and c. These are used in the quadratic formula. Then state the solution to the equation.

28. Graph the line y = 3x -4. You do not need to send me the graph, but you must do it on paper for yourself. Then send me at least 4 points that are found on this line.

29. State the slope of the line that you drew above. Also state its y-intercept and x-intercept. Be sure to tell me which of these 3 items are which!!

30. Simplify: squareroot(25x^{2}y^{6})

31. Simplify: squareroot(250x^{7})

32. Solve this system of equations by the addition method:

5x +2y = 11

5x – 2y = 24. Show some of your work. Answers alone not accepted.

33. Set up the equations to solve this problem to receive credit for it.

A plane flying with the jet stream from L.A, to Chicago , a distance of 2250 miles, took 5 hours. Flying against the stream , the plane could only fly 1750 miles in the same time. Find the rate of the plane in calm air and the rate of the wind.

Susan O. Johnsey mathinabox.com sjohnsey@bellsouth.net