Free Practice SAT

What a study plan looks like

An example plan to December 5, 38 days
Example

After your first full test on this site, I build you a plan that runs day by day to your SAT. Students kept asking what that actually looks like before they paid for it, which is fair, so here is one.

This is the plan for an example student who has the SAT on December 5 and starts today. The calendar uses the same rules as the real plans. The topics are real mistakes and basics from my question bank, and three days are opened up below so you can see exactly what is inside them.

Your own plan would look different, because it is built from the questions you missed and the wrong answers you picked.

This plan has

Mistake days, basics, full tests, Desmos days, and a pacing day and a light day at the end.

Building the example calendar…

Days marked "Open below" are shown in full further down this page. In a real plan every day opens, and you can work ahead: finishing a day opens the next one.

The kinds of days

Mistake days

One mistake from your own tests: the wrong answer you picked, a short lesson, practice from easy to hard, and a check at the end.

Basics

The earlier-grade skills under the questions you missed. They come first, because everything else is built on them.

Full tests and reviews

A full timed test, then a review the next day. After every test your plan rebuilds around the new mistakes.

Bluebook days

In plans of 30 days or more, an official College Board practice test in Bluebook, then a day to review it.

Desmos days

Questions with video walkthroughs that show how the graphing calculator answers them faster.

Catch-up, pacing and light days

A weekly day to finish anything you missed, a pacing day near the end, and a light day before the test.

Three days, opened up

These are the actual lessons and practice from the plan. Try the questions.

Day 1 · Basic

Slope formula: rise over run

A basic is a skill from earlier grades that sits underneath questions this student missed. Fixing it first makes the later days easier.
Work each problem out properly on paper, showing as many steps as you can.

1The idea

The idea

The slope of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \dfrac{y_2 - y_1}{x_2 - x_1}$, rise over run.

Slope measures how much $y$ changes for every $1$-unit increase in $x$.

Watch out for putting the $x$-values on top. It is always $y$ on top and $x$ on the bottom.

Worked example

What is the slope of the line through $(1, 3)$ and $(4, 9)$?

$m = \dfrac{9 - 3}{4 - 1} = \dfrac{6}{3} = 2$

2Practice that climbs

Try each one on paper before you open the answer.

Practice 1Easy
What is the slope of the line through $(0, 2)$ and $(4, 10)$?
$m = \dfrac{10 - 2}{4 - 0} = \dfrac{8}{4} = 2$
Practice 2Medium
What is the slope of the line through $(-2, 5)$ and $(4, -1)$?
$m = \dfrac{-1 - 5}{4 - (-2)} = \dfrac{-6}{6} = -1$
Practice 3Hard
The slope of the line through $(k, 3)$ and $(2k, 7)$ is $4$. What is the value of $k$?
$\dfrac{7 - 3}{2k - k} = \dfrac{4}{k} = 4$, so $k = 1$.
Day 7 · Mistake

Fixing one mistake from your test

Every mistake day starts from a wrong answer the student actually chose. The wrong answer tells me what went wrong in their thinking, and that is what the day fixes.
Work each problem out properly on paper, showing as many steps as you can.

1The mistake

Subtracts the coordinates instead of averaging them when finding a midpoint

In the real plan, this step shows the question from your own test and the answer you picked, so you can see the mistake in your own work.

2The lesson

The idea

The midpoint of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is $M = \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)$.

Three things students miss. Add the coordinates, do not subtract them; subtracting is the setup for slope and distance. Divide both sums by $2$, not just one. And if you are given the midpoint and one endpoint, the other endpoint is $B = (2M_x - A_x,\ 2M_y - A_y)$: double the midpoint and subtract the known endpoint.

Worked example

Find the midpoint of $(2, 1)$ and $(8, 7)$.

Add the $x$-coordinates: $2 + 8 = 10$. Divide by $2$: $5$.
Add the $y$-coordinates: $1 + 7 = 8$. Divide by $2$: $4$.

The midpoint is $(5, 4)$.

3Practice that climbs

Easy to hard. You see the answer and the working right after each one.

Practice 1Easy
What is the midpoint of the segment with endpoints $(0, 0)$ and $(10, 6)$?
Practice 2Medium
What is the midpoint of the segment with endpoints $(1, 4)$ and $(6, 9)$?
Practice 3Hard
Point $M(4, 6)$ is the midpoint of segment $AB$. If point $A$ is at $(1, 2)$, what are the coordinates of point $B$?

4The exit check

Each mistake day ends with a short check on fresh questions. Pass it and the mistake is marked fixed. Miss it and it comes back on a later day. That is how the plan keeps working on what is still costing you points instead of what you already know.

Day 12 · Desmos

Let the graphing calculator do the work

Desmos is built into the digital SAT for every math question. Most students only use it as a calculator. These days teach the questions it can answer in seconds.

1Try it, then watch

Each Desmos day has questions with a short video walkthrough. Try the question first, then watch how Desmos gets there. This one solves a system of equations by graphing both lines and clicking where they cross.

Your plan starts with one free test

Take a full practice test. When you finish, I ask for your test date and show your own plan, with the first days named, before you decide anything.

Take the free test

The plan is one payment of $29 to your test date, no subscription, with a seven-day money-back guarantee. The practice tests themselves are always free.