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Preptics

The Digital SAT math reference sheet, explained

In both Math modules the test gives you a sheet of formulas, one click away for the whole section. You do not have to memorise what is on it. You do have to know what is not, because the questions assume it.

What the sheet gives you

  • r

    Circle

    A = πr²

    C = 2πr

    Area and circumference, and with the facts at the foot of the sheet, arcs and sectors.

  • ℓw

    Rectangle

    A = ℓw

    Area problems, and the faces of a box.

  • bh

    Triangle

    A = ½bh

    Area. The height is measured at a right angle to the base, which may mean drawing it outside the triangle.

  • bac

    Right triangle

    a² + b² = c²

    Any missing side of a right triangle, and the distance between two points on a graph.

  • x√3xss

    Special right triangles

    30–60–90 → x, x√3, 2x

    45–45–90 → s, s, s√2

    A 30°, 60° or 45° angle in a right triangle: the sides follow without a calculator.

  • Rectangular solid

    V = ℓwh

    Volume of a box. Surface area is not on the sheet: add the six faces.

  • Cylinder

    V = πr²h

    Volume of a tank, a can or a pipe.

  • Sphere

    V = ⁴⁄₃ πr³

    Volume of a ball. Rare, and the formula is here when it comes.

  • Cone

    V = ⅓ πr²h

    A third of the cylinder with the same base and height.

  • Pyramid

    V = ⅓ ℓwh

    A third of the box with the same base and height.

  • The sum of the interior angles of a triangle is 180 degrees.
  • There are 360 degrees of arc in a circle.
  • There are 2π radians of arc in a circle.

The same sheet, in our words and our drawings, is in every Math module of the practice tests, where it opens beside the question and stays open while you work.

What is not on it, and has to be known

A question that needs one of these will not tell you it, and the sheet will not either.

Slope
m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}, and a line as y=mx+by = mx + b. Parallel lines have equal slopes; perpendicular slopes multiply to −1-1.
Distance and midpoint
Distance is the right-triangle formula on the sheet, with the two differences as the legs. A midpoint averages the xx-values and the yy-values.
Quadratics
x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}; the vertex sits at x=−b2ax = -\frac{b}{2a}; b2−4acb^2 - 4ac says two, one or no real solutions. Graphing and tapping the curve finds all of these too.
Circle equation
(x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, centre (h,k)(h, k), radius rr. Complete the square when the equation arrives expanded.
Arcs and sectors
The fraction of the circle times the whole: angle360\frac{\text{angle}}{360} of the circumference or of the area. Built from the facts the sheet does give.
Right-triangle trigonometry
sin⁡=oppositehypotenuse\sin = \frac{\text{opposite}}{\text{hypotenuse}}, cos⁡=adjacenthypotenuse\cos = \frac{\text{adjacent}}{\text{hypotenuse}}, tan⁡=oppositeadjacent\tan = \frac{\text{opposite}}{\text{adjacent}}, and sin⁡x∘=cos⁡(90−x)∘\sin x^\circ = \cos (90 - x)^\circ.
Degrees and radians
π\pi radians is 180∘180^\circ. The sheet gives a full turn in both, which is the same fact.
Polygon angles
The interior angles of a shape with nn sides add to (n−2)×180∘(n - 2) \times 180^\circ.
Similar triangles
Matching sides are in one ratio. Area scales by the square of it, volume by the cube.
Growth and decay
y=a(1+r)ty = a(1 + r)^t and y=a(1−r)ty = a(1 - r)^t: aa is the start, rr the rate as a decimal, tt the number of periods.
Percentages
Percent change is the change over the original. With no starting amount, call it 100.
Mean and probability
A mean is a total over a count, so a mean times its count gives the total back. A probability is the favourable cases over all the cases.

Several of these can be read off a graph instead of worked out: the vertex and the zeros of a quadratic, where two lines cross, the value of a function. That is what the graphing calculator is for.

Common questions

Is there a reference sheet on the Digital SAT?
Yes, in the Math section only. It opens from a button at the top of the screen in Bluebook, in both Math modules. It is not offered in Reading and Writing.
What formulas are on the SAT reference sheet?
Areas of a circle, rectangle and triangle, the circumference of a circle, the Pythagorean theorem, the two special right triangles, and the volumes of a box, cylinder, sphere, cone and pyramid. It also states that a circle has 360 degrees and 2 pi radians of arc and that a triangle's angles add to 180 degrees.
Do I need to memorise the SAT formulas?
Not the ones on the sheet. The ones that are not on it, such as slope, the quadratic formula, the equation of a circle and the trigonometric ratios, are assumed, so those are worth knowing cold.
Is the quadratic formula on the SAT reference sheet?
No. Neither is the vertex formula or the discriminant. On many questions the graphing calculator finds the same answers: graph the quadratic and tap the curve for its zeros and its turning point.

The other tools: the full set. For the questions with no choices: how to enter an answer.

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