Math 121, Practice Questions on Chapter 1 and Complex Numbers
Except for questions 7,8,9,13(b), 20(b) and 27, you should be able to do these problems without
a calculator.
1. (a) Simplify (3 −2i)(4 + i) and write the complex number in standard form.
(b) Simplify i223.
2. Write the complex number 3−2i
4+5iin standard form.
3. (a) Solve the equation 2x+ 5
3x−1= 1.
(b) Solve 3|x−d|=cwhere c > 0.
4. A worker can build a fence in 8 hours. With the help of an assistant, the fence can be built
in 5 hours. How long would it take the assistant to build the fence alone?
5. A radiator contains 6 liters of 20% antifreeze solution. How much should be drained and
replaced with pure antifreeze to produce a 50% antifreeze solution.
6. (a) Solve the equation A=1
2h(b1+b2) for b2.
(b) Solve the equation 1
R=1
R1
+1
R2
for R2.
(c) Solve the equation 1
R=1
R1
+1
R2
for R.
7. An investment of $2500 is made at an annual simple interest rate of 5.5%. How much
additional money must be invested at an annual simple interest rate of 8% so that the total
interest earned is 7% of the total investment?
8. How much pure gold should be melted with 15 grams of 14-karat gold to produce 18-karat
gold? (Note: pure gold measures 24 karats, an alloy that is kkarats is k
24 ·100% gold. For
example 12-karat gold is 50% gold.)
9. A messenger ran at 10 miles per hour from his residence to the King’s palace, he walked
back at 4 miles per hour. The total trip took him 8 3
4hours. How far is it from the messenger’s
residence to the King’s palace?
10. Solve the equation 2x2+ 3x= 4 using the algebraic method of your choice.
11. Solve the quadratic equation (x−5)2−9 = 0 by factoring.
12. Solve the quadratic equation 1
2x2+3
4x+ 1 = 0 by using the quadratic formula.
13. (a) A gardener wishes to use 600 feet of fencing to enclose a rectangular region and
subdivide the region into two smaller rectangles. The total enclosed area is 15,000 square feet.
Find the dimensions of the enclosed area.
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