Choose an efficient strategy (algebraic, numeric, graphical) under time constraints. | Multi-step Reasoning | ACT Mathematics

核心知识

The fastest method depends on how the information is presented. If the pattern is already visible in numbers, a quick numeric comparison can beat building a full algebra model from scratch.

深入理解

Fastest path: use the representation that already shows the relationship.

If a table or paired values reveal the rate, use them. If a graph already shows the intercept or intersection, read it directly. If the choices are numeric, back-solving may be faster than building the whole equation.

Table or values: compare differences or ratios first.
Graph: read the visible key value instead of recreating it.
Numeric choices: test the choices when that is shorter.

Before you start, ask which route gets to the answer in the fewest steps.

分步讲解

Notice whether the problem is easiest from numbers, equations, or a graph.
Use the representation that reveals the key relationship with the fewest steps.
Only build a full equation when the shorter route does not settle the question.
Do one quick reasonableness check before moving on.

常见误解

Defaulting to lengthy algebra even when a numeric pattern is already visible.
Ignoring that a graph or table may already contain the answer or the key rate.
Choosing a shortcut without checking that it matches the question being asked.

题目

示例解析

A taxi company charges a linear fare. A 4-mile trip costs $$ 11$ , and a 10-mile trip costs $$ 20$ . At the same rate, how much would a 7-mile trip cost?

选择一个答案查看解析