ACT Math Formulas “Cheat Sheet”
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ACT Math Formulas – Statistics
Mean: sum of the numbers ÷ amount of items in set
Median: middle number in set when items are in order
Mode: number that is most frequent in the set
Range: high number minus low number
Example data set: 1, 2, 3, 1, 4, 5, 2, 1, 7 [There are 9 items in the set.]
Mean = (1 + 2 + 3 + 1 + 4 + 5 + 2 + 1 + 7) ÷ 9 = 3.714
Median = 2 [middle number: 1, 1, 1, 2, 2, 3, 4, 5, 7]
Mode = 1 [the number 1 is in the set three times]
Range= 7 – 1 = 6 [high minus low]
ACT Formula – Probability
Probability: Event ÷ Sample Space [event is the number of items available for the desired outcome; sample space is the total number of items available]
ACT Math Formulas – Coordinate Geometry
Midpoints: Midpoint x = (x1 + x2) ÷ 2 Midpoint y = (y1 + y2) ÷ 2
x and y intercepts: For the x-intercept, substitute 0 for y and solve. For the y-intercept, substitute 0 for x and solve.
Slope formula: m = (y2 – y1)/ (x2 – x1)
Slope-intercept formula: y = mx + b ( where m = slope; b = y intercept; and x and y are points on the graph)
Horizontal line: y = h [h is any constant value]
Vertical line: x = v [v is any constant value]
Point-slope formula: (y – y1) = m(x – x1)
Parallel lines: Parallel lines have the same slope.
Perpendicular lines: The slopes of perpendicular lines are negative reciprocals. If slope is 2, slope of perpendicular line = – 1/2
Distance formula:
Linear equation: y = mx + b [The slope-intercept formula is sometimes called the linear equation.]
ACT Math Formulas – Plane Geometry
Area of circle: π × R2 (radius squared)
Circumference of a circle: π × diameter
Diameter: radius × 2
Area of square or rectangle: length × width
Perimeter of squares and rectangles: (length × 2) + (width × 2)
Area of triangle: (base × height) ÷ 2
Cone volume: (π × radius2 × height) ÷ 3
Cylinder volume: πr2h (where r = radius and h = height)
Box volume: length × width × height
Sphere volume: 4/3 × π × R3
Hypotenuse length: a2 + b2 = c2
Arcs: Arc length is a partial distance along the outside of a circle. Calculate the circumference for the part of circle for the degrees stated.
Chords: A chord is a line that connects two points on the circumference of the circle. Use the degrees stated for the given angle to calculate chord length.
ACT Formulas – Other Concepts
Combinations: C = n! ÷ [r! × (n – r)!] n = number of objects taken at a rate of r items per time
Permutations: P = n! ÷ (n – r)! n = number of objects taken at a rate of r items per time
Logarithmic functions: y = logax is equivalent to x = ay
ACT Formulas- Trigonometry
Radians: θ = s ÷ r [where θ = radians; s = arc length; and r = radius]
360° = π × 2 × radians
180° = π × radians
90° = π ÷ 2 × radians
45° = π ÷ 4 × radians
30° = π ÷ 6 × radians
Tangent, sine, and cosine:
sine = opposite/adjacent
cosine = hypotenuse/adjacent
tangent = opposite/hypotenuse
cos2 A + sin2 A = 1
cos2 A = 1 − sin2 A
sin2 A = 1 − cos2 A
tan A = sin A ÷ cos A
More ACT Math
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