1st Semester Algebra Partial Review

Unit Analysis

100

If a toddler weighs 14 pounds and 8 ounces, how many kilograms does he weigh, to the nearest tenth of a kilogram?

6.6 kilograms

200

If a giant sequoia tree can grow about 24 cm each month, how many feet tall will you expect it to be in 60 years?  Round to the nearest foot.

567 feet tall

300

I made some punch for Christmas.  It took 6 cups of cranberry juice, 3 cups of pineapple juice, and 3 liters of ginger ale.  How many cups of punch did I make?  Round to the nearest tenth.

12.7 cups

400

If a message in a bottle traveled 22 inches in 7 seconds in the ocean, how many miles could it travel in a year? Round to the nearest mile.

1564 miles

500

If a faucet drips 83 ml every 3 hours and the city charges $0.02 per gallon of water used, how many dollars does the leaky faucet cost a family in a year?

$1.28

Isolate a variable

100

Solve this equation for t:

28 = t(r + 4)

t = 28/(r + 4)

200

Solve this equation for a:

(2b - a) / c = (-1/2)(d)

a =  (1/2)cd + 2b

or  a = (cd + 4b)/2

300

Solve this equation for x:

3x - 4z = 7 - xy

x = (7 + 4z) / (3 + y)

400

In uniform circular motion, the speed v of a point on the edge of a spinning disk is v=(6.28/t)*r.  In this formula, r is the radius of the disk and t is the time it takes the point to travel once around the circle.   Solve this formula for r.

r = tv/6.28

500

In uniform circular motion, the speed v of a point on the edge of a spinning disk is v=(6.28/t)*r.  In this formula, r is the radius of the disk and t is the time it takes the point to travel once around the circle.  Suppose a merry-go-round is spinning once every 3 seconds.  If a point on the outside edge has a speed of 12.56 feet per second, what is the radius of the merry-go-round, to the nearest foot?

6 feet

Function Notation

100

For f(x) = -4x + 7,    find f(-3) +1

20

200

If f(x) = 6x + 7,    find f(m)

6m + 7

300

If g(x) = x² - 4,    find g(-4t)

16t² - 4

400

If f(t) = 2t³,    find     f(-3) - f(1)

-56

500

If f(x) = 2x³,    find   3[f(x)] + 2

6x³ + 2

Proportional Reasoning

100

Are these two ratios equivalent ratios?

10/18  and 25/45

Yes.  One way to know this is that the cross products of equivalent ratios are always equal.

(10)(45) = 450

(18)(25) = 450

200

Solve this proportion:

(a - 18)/12  =  15/3

a = 78

300

Solve the proportion:

(4v + 7)/15 = (6v + 2)/10

v = 0.8 

or v = 4/5

400

Janice paints a room that has 400 square feet of wall space in 2.5 hours.  At this rate, how long will it take her to paint a room that has 720 square feet of wall space?

4.5 hours

500

A new gym is being built at Greenfield Middle School.  The length of the gym is shown on the builder's blueprints as 12 inches long.  If every 3/4 inches in the blueprint represents 5 feet in the actual building, find the actual length of the new gym.

80 feet long

Number Sense

100

-11.1 + 8.5 = ?

-2.6

200

If an iPod was 30% off, and it rang up for $75, what was the original price?

$107.14

300

If you would take the square roots of these numbers, which of their square roots would be irrational numbers?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

The square roots of non-perfect squares are irrational.  Thus, the square roots of these numbers are irrational:  2, 3, 5, 6, 7, 8, 10

400

What are the square roots of 

a)  100/256

b)  0.0004

a)  10/15  or 2/3

b)  0.02

500

Write each of these decimals as a fraction.

a)  0.089

b) 5.7272727272727272.....

c) 0.66666666.... / 0.6

a)  89/1000

b) 5_72/99  or 5_8/11

c) 10/9  or 1_1/9