Pre-Calculus
Due: _________
Spiral #2
Full Name___________________________
Block ________
Score______/40
Solve each formula for the indicated variable. (1 point each)
1.
𝑃 = 2𝑙 + 2𝑤 for w
1
1. ____________
2. 2. 𝐴 = 2 (𝐵 + 𝑏)ℎ for B
2. ____________
3. 𝑎𝑥 + 𝑏 = 2(𝑥 − 𝑎) for x
3. ____________
1
4. 𝑠 = 𝑔𝑡 2 for g
2
4. _____________
5. One computer can do a job twice as fast as another. Working together, both computers can do the job in 2
hours. How long would it take each computer, working alone, to do the job? (4 points)
(No Work, No Credit)
5. _____________
6. David gets to work in 20 min when he drives his car. Riding his bike (by the same route) takes him 45 min. His
average driving speed is 4.5 mph greater than his average biking speed. How far does he travel to work? (4 points)
(No Work, No Credit)
6. _____________
7. A rectangular sheet of metal has a length that is three times the width. Equal size squares, measuring 5 in per
side, are to be cut from the corners. The metal can then be folded into an open box by folding up the flaps. If the
volume of the box is to be 1435 𝑖𝑛3 , find the dimensions of the original piece of metal. (4 points)
(No Work, No Credit)
7. _____________
8. If a rectangle is r feet long and s feet wide, express the length of the diagonal in terms of r and s. (4 points)
(No Work, No Credit)
8. _____________
Solve each equation. (3 points each)
9.
2𝑥+5
2
−
3𝑥
𝑥−2
=𝑥
9. _____________
10. √3𝑥 + 7 = 3𝑥 + 5
10. _____________
11. 𝑥 2 = 2𝑥 − 5
11. _____________
12. A projectile is launched upward from the ground. Its height s in feet above the ground after t seconds is given
by the equation 𝑠 = 320𝑡 − 16𝑡 2 . After how many seconds in the air will it hit the ground? (4 point)
(No Work, No Credit)
12. _____________
13. Find the equation of the line that passes through (−3, 2) and (2, −4). (2 point)
13. _____________
(No Work, No Credit)
14. Graph the function. 𝑓(𝑥) =
4 − 𝑥 𝑓𝑜𝑟 𝑥 < 2
1 + 2𝑥 𝑓𝑜𝑟 𝑥 ≥ 2
a) Graph (4 points)
b) Evaluate 𝑓(−1). (1 point)
14a)
14b) ________