New York City SHSAT 2017

SOLVING EQUATIONS Solving a Linear Equation To solve an equation, do whatever is necessary to both sides to isolate the variab ...

x + y = 3, multiply both sides of the second equation by −3 to get −3x − 3y = −9. Now add the two equations; the 3y and the −3y ...

FUNCTIONS Function Notation and Evaluation Standard function notation is written f(x) and read “f of 4.” To evaluate the funct ...

COORDINATE GEOMETRY Finding the Distance Between Two Points To find the distance between points, use the Pythagorean theorem or ...

Using Two Points to Find the Slope The slope of the line that contains the points (2, 3) and (0, −1) is Using an Equation to ...

LINES AND ANGLES Intersecting Lines When two lines intersect, adjacent angles are supplementary, and vertical angles are equal. ...

TRIANGLES—GENERAL Interior and Exterior Angles of a Triangle The three angles of any triangle add up to 180 degrees. In the fi ...

In the figure above, a + b + c = 360. Similar Triangles Similar triangles have the same shape: Corresponding angles are equal, ...

The height is the perpendicular distance between the side that’s chosen as the base and the opposite vertex. In the triangle abo ...

RIGHT TRIANGLES Pythagorean Theorem For all right triangles: (leg 1 )^2 + (leg 2 )^2 = (hypotenuse)^2 If one leg is 2 and the ...

The 5-12-13 Triangle If a right triangle’s leg-to-leg ratio is 5:12, or if the leg-to-hypotenuse ratio is 5:13 or 12:13, then i ...

If one leg has a length of 3, then the other leg also has a length of 3, and the hypotenuse is equal to a leg times or ...

OTHER POLYGONS Characteristics of a Rectangle A rectangle is a four-sided figure with four right angles. Opposite sides are equ ...

In the figure above, s is the length of the side opposite the 3, so s = 3. Area of Parallelogram = base × height In parallelogra ...

If PQRS is a square, all sides are the same length as QR. The perimeter of a square is equal to four times the length of one sid ...

CIRCLES Circumference of a Circle Circumference = 2 πr In the circle above, the radius has a length of 3, so the circumference ...

In the figure above, the radius has a length of 5, and the measure of the central angle is 72 degrees. The arc length is of the ...

In the figure above, the radius has a length of 6, and the measure of the sector’s central angle is 30 degrees. The sector has o ...

SOLIDS Surface Area of a Rectangular Solid The surface of a rectangular solid consists of three pairs of identical faces. To fi ...

A cube is a rectangular solid with length, width, and height all equal. If s is the length of an edge of a cube, the volume form ...