Essential Algebra Practice for Students of TASC-math - Solve Algebra Questions for the TASC Math Subtest

Sep 14, 2026

Essential Algebra Practice for Students of TASC-math focuses on the algebra topics emphasized in the TASC math subtest, noting that roughly a quarter of the questions involve algebra. It explains algebra as the use of symbols for generalized arithmetic and then organizes key skills needed for success. The material includes practice sections and worked examples, including solving linear equations and inequalities in one variable, with strategies such as balancing both sides and using order of operations, plus “check your algebra” testing tips.

LanguageEnglish

CategoryExam

FormatPDF

Pages20

Reading Time50 min

AccessFree to download

Algebra Overview

Algebra as Generalized Arithmetic

Essential Algebra Questions

Solve Linear Equations and Inequalities in One Variable

Read Graphs of Equations and Inequalities in Two Variables

Write Equations and Inequalities in One Variable

Write Equations and Inequalities in Two Variables

Write and Solve a System of Equations

Interpret Expressions and Identify Equivalent Expressions

Solve Quadratic Functions Graphically

Solve Quadratic Functions and Equations Algebraically

Essential Algebra Practice for Students ofTASC-math This packet was created by NYSED Teacher Leader, Todd Orelli in collaboration with the CUNY Adult Literacy & HSE professional development team as part of a mini-grant project funded by the New York State Education Department, Office of Adult Career and Continuing Education Services. Essential Algebra Practice for Students ofTASC-math Approximately 26% of the questions on the TASC math subtest focus on algebra. That is at least 1 in 4 questions. It’s clear that you need to be strong in this area of math to pass this test. But, what is algebra, and what do you need to know about algebra to pass the TASC math subtest? Algebra: the use of symbols in place of numbers to perform generalized arithmetic. “Generalized arithmetic”???– Let’s look at a simple example. If we have 3 turkeys and we add 5 more turkeys, we have 8 turkeys. That’s obvious. It’s also true that if we have 3 fours and we add 5 more fours, we have 8 fours. 4 4 4 12 + | 4 4 | 4 4
4 | | --- | --- | = 4 4 4 4 4 4 4 4 + 20 = 32 It turns out, that no matter what we have, whether it be turkeys, rocks, apples, or fours, for example, if we add 3 of some quantity to 5 of the same quantity we have 8 of that quantity. That’s pretty wordy though. We can use a symbol, let’s say x, to represent some quantity. That allows to write: 3x + 5x = 8x This equation says that no matter what x stands for, 3(of a quantity) + 5(of the same quantity) = 8(of that quantity) . Writing 3x + 5x = 8x is just so much simpler. See, generalized arithmetic, or algebra, isn’t so bad after all. Of course, there’s more to it than that. Some of the most common types of algebra questions you will find on the TASC math subtest will require that you know how to: 1. Solve linear equations and inequalities in one variable; 2. Read graphs of equations and inequalities in two variables; 3. Write equations and inequalities in one variable; 4. Write equations in two variables; 5. Write a system of equations; 6. Interpret expressions; 7. Identify equivalent expressions; 8. Solve quadratic functions graphically; 9. Solve quadratic functions and equations algebraically. Essential Algebra Questions Below you will find practice algebra questions like those you will see on the TASC. There are many more types of questions you will see on the exam, but these represent some of the most common topics on the test. I. Solve Linear Equations and Inequalities in One Variable Example 1 | The equation 0.25x– 60 = 40 can be used to calculate the profit of a lemonade stand given the number of lemonades sold, x.
What is the value of x? | | | --- | --- | Solution to Example 1 According to the problem, the equation 0.25x– 60 = 40 can be used to calculate the profit of a lemonade stand. However, since the equation is equal to 40, we already know the profit we are looking for, $40. But, what input value for x will give us an output of 40? How many lemonades would that be? Let’s try a guess of 100 lemonades. First, replace x with 100 in the equation: 0.25(100)– 60 = 40 Next, evaluate using the order of operations: 25 – 60 = 40 -35 = 40 -35 = 40? Of course not. Selling 100 lemonades does not give us the output of 40 we wanted. We could continue this guess-and-check process and probably find the correct answer eventually. Or, we could use another strategy. Let’s agree on some terms first: coefficient variable constant 0.25x– 60 = 40 Remember, an equation is like a balance. Both sides will remain balanced, or equal, as long as we do the same thing to both sides. We can get x by itself by getting rid of the coefficient and the constant. Here it’s easiest to deal with the constant,– 60, first. To do so, we can add 60 to both sides. We’ll show that both vertically and horizontally. Vertical Method Horizontal Method 0.25x– 60 = 40 0.25x– 60 + 60 = 40 + 60 + 60 +60 0.25x + 0 = 100 0.25x + 0 = 100 0.25x

FAQs

Why is algebra important on the TASC math subtest?

About 26% of the TASC math questions focus on algebra, meaning at least 1 in 4 questions requires algebra knowledge.

What does the packet say algebra means?

Algebra is defined as using symbols in place of numbers to perform generalized arithmetic, such as replacing specific quantities with a symbol like x.

How does the packet recommend solving a linear equation like 0.25x–60=40?

It suggests getting the variable by balancing both sides—typically handling constants first (adding 60), then undoing the coefficient using division—followed by checking the solution by substitution.

Sep 14, 2026

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