This chapter will focus on showing you the most efficient strategies to solve systems of equations so that you can get through these problems as quickly as possible on the PSAT. While you could use “brute-force” and substitution to solve this problem, looking for patterns first results in a process that is much quicker and relies on simpler, less error-prone calculations. If you get stuck, review the information on simplifying and solving equations in the previous chapter. Add 6 to your result and you should see that (C) is the correct answer.Įxplanations for each simplifying step are not always included in this chapter. Step 3: Check that you answered the right questionīe careful! The question isn’t asking for the value of r. Once you’ve written the first equation in terms of r + s, substitute the value of r + s (which is 12) into the second equation and solve for r. How can you effectively use both equations? Is there any way you can make the first equation look like the second one? Does the quantity r + s exist in the first equation in some form? Step 2: Choose the best strategy to answer the question There are two equations that involve r and s. In this case, you’re looking for the value of r. Step 1: Read the question, identifying and organizing important information as you go The following table contains some strategic thinking designed to help you find the most efficient way to solve this problem on Test Day, along with some suggested scratchwork. You could plug the resulting expression back into the other equation and eventually solve for r, but remember, the PSAT tests your ability to solve math problems in the most efficient way. You might be tempted to switch on math autopilot at this point and employ substitution, solving the second equation for s in terms of r: The question is asking for r + 6, so A is a trap corresponding to the value of r alone. Now you can substitute 12 in for ( r + s), simplify, and solve for r. Then factor a 2 out of the left-hand side to get r + 2( r + s) = 24. Rewrite the first equation so that ( r + s) is a component. Getting to the Answer: Although substitution will certainly work here, there is a quicker way. If 3 r + 2 s = 24 and r + s = 12, what is the value of r + 6 ?Ĭategory: Heart of Algebra / Linear Equations The following question shows an example of such a system in the context of a test-like question. To solve systems of equations, you’ll need to rely on a different set of tools that builds on the algebra you’re already familiar with. Solving such a system would enable you to determine the maximum number of text messages and voice calls you could make under this plan, while optimizing total usage.
Psat sample math questions free#
Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.$ 0.05 t + $ 0.40 v = $ 50 t + v = 1, 000
Negative numbers: multiplication and division.Negative numbers: addition and subtraction.Multi-digit multiplication and division.Arithmetic patterns and problem solving.Equivalent fractions and comparing fractions.And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun! Just choose your grade level or topic to get access to 100% free practice questions: That’s because Khan Academy has over 100,000 free practice questions.
0 kommentar(er)
