TABE Level D Math: Pre-algebra and Algebra

The word “algebra” can sound pretty scary. It has been said that algebra is the “gateway” to mathematics. In algebra you learn the language of math—the symbols and many vocabulary words. Algebra also shows how math can describe patterns. These could be patterns in science and nature or patterns of production and manufacturing. Using math to describe patterns is called mathematical modeling.

You will only need to know fundamental concepts of algebra for the TABE D.

There are five types of problems in this section.

Recognize Patterns
These problems require you to recognize number or picture patterns and either continue them or fill in the missing number or picture.

Example A. Find the next number in the pattern 5, 8, 11, 14,….
In this pattern, each number is 3 more than the one before it, so add 3 to 14, and the next number is 17.

Example B. Find the missing number in the pattern 75, 70, ________, 60, 55, 50,….
In this pattern, the numbers decrease by 5, so the missing number must be 65.
An example of a picture pattern is shown below.

Example C. Find the next row of the tile pattern.

Because the number of dots goes up by 1 each time, the next row should have 5 dots.

Write an Algebra Expression
An algebra expression is numbers, letters, and symbols that represent a situation.

Example D. The Math Department at Central High School ordered lined paper and graph paper. They ordered 50 more reams of graph paper than lined paper. If x represents the number of reams of lined paper, which of the following expressions gives the number of reams of graph paper?

To find 50 more than a number, you add 50 to the number. The correct answer is b, x + 50.

Fill in a Blank with a Number or a Symbol

Example E. What symbol goes in the box to make the following number sentence true?

You need to add the two decimals: , which is more than 4.1. The symbol for “more than” is >, so the correct answer is b.

Example F. What symbol goes in the box to make the number sentence true?

You can do this problem by trying each answer choice. Only ÷ makes the number sentence true because and 3<4.

Interpret an Input-Output Table
This is similar to finding a pattern. You are given several pairs of numbers. Each pair consists of an input and an output. You have to find the math rule (formula) that you follow to change to input numbers to output numbers. The same rule must be used for all pairs.

Example G.

If you multiply the input number by 2 and add 1, you’ll get the output number:

This example is difficult because the rule has two parts: multiply by 2 and add 1.
If a problem asks you to find the output for an input of 10, you multiply 10 by 2 and add 1 to get 21.
Although there is no set method for doing these, there are some things you can try. If the input numbers follow a sequence, such as 1, 2, 3, etc. or 2, 4, 6, etc. see if you can find a sequence for the output numbers. This doesn’t work in the example above because the input numbers 1, 3, 6, and 8, don’t follow a sequence. It does, however, work for the example below:

Example H. Use the input/output table below to find the output for an input of 11.

The number 11 follows the input pattern 1, 3, 5, 7, 9. The output numbers also follow the pattern of counting by 5s. The next output number (that goes with 11) is 30.

Solve Equations
You are given a number sentence with a letter in it. You have to determine what number to replace the letter with to make the number sentence true. For example, what number can you put in place of x to make a true sentence? (3x means 3 times x).

In the TABE D, you should guess numbers to replace and check to see if they work. If you replace x with the number 1, the sentence would say , or , which is false because . If you replace x with the number 2, the equation would say , or , which is true. Therefore, 2 is the solution to the equation.

Pre-Algebra and Algebra Practice

1. What symbol goes in the space to make the number sentence true? A. + B. − C. × D. ÷ A. bicycle rental shop charges $20 for the rental and $15 for each hour the bike is used. The table below shows the total charges based on the amount of time a bike is rented.

Study the table. Then do problems 2 through 4.


2. What would the total charges be if the bike is rented for 5 hours? A. $75 B. $85 C. $95 D. $105

3. C = total cost of a rental
h = the number of hours a bike is rented

Which equation shows the relationship of C to h? A. B. C. D.

4. It cost Cheryl $110 to rent a bike. How long did she rent it? A. 6 hour B. 7 hours C. 8 hours D. 9 hours

5. Steven cut of the grass in his yard before being interrupted by a salesman. Which expression shows the fraction of the lawn that still had to be cut? A. B. C. D.

6. Three friends share a rumor. The number of people who know the rumor doubles every hour. If this pattern continues, how many people will know the rumor after 4 hours? A. 36 B. 48 C. 54 D. 60

7. If , what is the value of y when x = 3? A. 2 B. 8 C. 15 D. 21

8. The table below shows input numbers that have been changed by a certain rule to get output numbers. What is the output number if the input number is 10?

A. 21 B. 20 C. 16 D. 13

9. Which of these expressions gives the perimeter of the rectangle?
A. B. C. D.

10. What symbol goes in the blank space to make the number sentence true?

A. = B. > C. < D. ≥

Answers: Pre-Algebra and Algebra Practice 

1. c.

2. c

3. d

4. a

5. b

6. b

7. d

8. a

9. b

10. c