Pre-AP Algebra 1 Unit 3 Test Review Problems - Denton ISD

Pre-AP Algebra 1

Unit 3 Test Review Problems

1. 32 - 2 = 3 -72 + 42 = 233

2. 22 - 82 = 50 32 + 2 = 543

3. The sum of the ages of Nicole and Kristin is 32. In two years Nicole will be three times as old as Kristin. How old are they now?

4. Jenny leaves Dallas and goes south traveling 60 mph. 1.5 hours later, Jack leaves Dallas traveling South at 75 mph. How long will it take Jack to catch up to Jenny?

5. Two cars are 795 miles apart and traveling towards each other. The slower car is traveling 60 mph and the faster car is traveling 75 mph, but the slower car left 2 hours before the faster car. How long will both cars have been traveling at the point when their paths cross?

6. The length of a rectangular room is 5 feet more than its width. The perimeter of the room is 66 feet. What are the room's dimensions?

7. The perimeter of a rectangular picture frame is 62 inches. The difference of the length of the frame and twice its width is 1. What are the dimensions of the frame?

8. The sum of the digits in a two-digit number is 12. The tens digit is two more than the ones digit. What is the number?

9. A jar contains dimes and nickels. There are 20 coins in the jar and the total value of the coins is $1.40. How many nickels and how many dimes are in the jar?

10. Howard and Chris are two brothers who are going to visit their family in Texas Town (fictional place). Howard lives in Galveston and is traveling north towards Texas Town while Chris lives in Tulsa, OK and must travel south to get there. Howard is a speedster and drives 1.5 times faster than Chris and he also left 1 hour earlier than Chris. If Tulsa, OK and Galveston are about 540 miles apart, how fast was each brother driving if Chris made it in 3 hours?

11. The perimeter of an equilateral triangle is twice the perimeter of a square. If each side length of the triangle is increased by 10cm, then the new perimeter is 6 more than four times the perimeter of the square. What is the side length of each shape?

Answers:

Equations

1. = 2, = 2 3 - = 3 -7 + 4 = 233

2. = 2, = 2 2 - 8 = 50 3 + = 543

3. + = 32 + 2 = 3( + 2)

4. 60 + 90 = 75 =

5. (s = speed of slow car, f = speed of fast car) 60 + 75 = 795 = + 2

6. = + 5 2 + 2 = 66

7. 2 + 2 = 62 - 2 = 1

8. (t = tens digit, n = ones digit) + = 12 = + 2

9. + = 20 . 10 + .05 = 1.40

10. (h = speed Howard drives, c = speed Chris drives) = 1.5 4 + 3 = 540

11. (t = side length of triangle, s = side length of square) 3 = 2(4) 3( + 10) = 4(4) + 6

Solution(s)

(7, 12) (7, -12) (-7, 12) (-7, -12)

(13, 6) (13, -6) (-13, 6) (-13, -6)

Nicole is 25 and Kristin is 7.

It will take Jack 6 hours to catch up to Jenny after traveling 450 miles. The slow car traveled 7 hours and the fast car traveled 5 hours.

The width of the room is 14 feet and the length is 19 feet. The width of the frame is 10 inches and the length is 21 inches. The number is 75.

There are 8 dimes and 12 nickels.

Chris drove 60 mph and Howard drove 90 mph.

The side length of the triangle is 8cm and the side length of the square is 3cm.

OR (t = perimeter of triangle, s = perimeter of square, but you need to divide each answer by the number of sides to get the side length) = 2 + 3(10) = 4 + 6

Review of Explicit and Recursive functions

You will see a table like this on the test. Your job is to fill in the blank boxes.

Sequence (first 6 terms)

Explicit

Recursive

1 4, 20, 100, 500, 2500, 12500, ...

2

() = 12 - 5

3

{1

= =

-6 -1

+

7

4 0, 5, 12, 21, 32, 45, ...

5

1 = 1 {1 = 2 = 2 -1 + -2

Answers:

Sequence (first 6 terms)

1 4, 20, 100, 500, 2500, 12500, ...

Explicit () = -

2 7, 19, 31, 43, 55, 67, ...

() = 12 - 5

3 -6, 1, 8, 15, 22, 29, ...

() = -

Recursive

{

= =

-

{

= =

- -

+

{1

= =

-6 -1

+

7

4 0, 5, 12, 21, 32, 45, ... () = + -

5 -1, 2, 3, 8, 19, 46, ...

1 = -1 { 1 = 2

= 2 -1 + -2

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