Below are formulas/properties/theorems/etc you just gotta know. This is NOT a comprehensive list.

There are formulas/identities on the last couple pages of the syllabus that you should have memorized.

\(\sqrt{2} \approx 1.41\)

\(\sqrt{3} \approx 1.73\)

\(\sqrt{2} < \sqrt{3} < 4 < \sqrt{5}\)

\(\pi \approx 3.14\)

\(e \approx 2.718\)

Given a polynomial of the form \(ax^2 + bx + c\), the values of \(x\) such that \(ax^2 + bx + c=0\) can be found using the quadratic equation: $$\frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$
The quantity under the square root, i.e., \(b^2 – 4ac\), is known as the discriminant. Here is a link to a handout I found online that discusses what the discriminant tells us about the roots of the equation \(ax^2 + bx + c\). Note that this handout says that if the discriminant is equal to zero, then there is just one real solution. Your text book calls this a solution a double root.

You have to know the unit circle, (specifically this image).

Here is an image of the six trig functions.

Here is a page about some common graphs, along with what happens when you do some basic transpositions.

The two limit definitions of a derivative: $$f'(a)=\displaystyle \lim_{h \rightarrow 0} \frac{f(a+h) \, – \, f(a)}{h} \qquad \text{and} \qquad f'(a)=\displaystyle \lim_{x \rightarrow a} \frac{f(x) \, – \, f(a)}{x-a}$$

The equation of the line through the point \((a,b)\) with slope \(m\) is $$y-b=m(x-a)$$
If you are looking for the tangent line at the point \((a,f(a))\) then your slope is \(f'(a)\) and the equation of the tangent line is $$y \, – \, f(a) = f'(a) (x-a)$$

The derivative rules, many of which are listed here.

For linear motion, if \(s(t)\) is the position function, then the velocity function is the derivative of the position function, i.e., \(v(t) = s'(t)\).

Gravity: \(g \approx 9.8 \text{ m/s}^2\) or \(g \approx 32 \text{ ft/s}^2\)