Algebra 1 worksheets
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Multiplying and dividing in scientific notation
Grade 8
Multiply and divide in scientific notation, and renormalise the answer
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Algebra 1 worksheets, easiest first
Each sheet assumes the one above it is comfortable. Start where your child is, not at the top.- Multiplying and dividing in scientific notation
Print (5 × 10³) × (4 × 10²) - Rate of change from a table
Print x: 2, 5, 8, 11 y: 9, 21, 33, 45 - Which rate is greater?
Print A y = 7x B 45 km in 9 hours - Taking out a common factor
Print 12x + 18 - Difference of two squares
Print 9x² − 64 - Factoring x² + bx + c
Print x² + 7x + 12 - Solving x² + bx + c = 0
Print x² + 2x − 15 = 0 - Solving quadratics by square roots
Print x² = 49 - How many real solutions?
Print x² + 2x + 5 = 0 - Adding and subtracting polynomials
Print (3x² + 5x) − (x² − 4x) - Function notation
Print f(x) = 3x − 5 - Arithmetic and geometric sequences
Print 3, 7, 11, … 20th term - x- and y-intercepts of a line
Print 3x + 4y = 24 → x-int - Absolute value equations
Print |x − 3| = 7 - Writing linear equations
Print (1, 3) and (3, 7) - Exponential functions
Print f(x) = 3 · 2ˣ - Comparing rates in words
Print 60 mi in 5 h vs 84 mi in 7 h - Comparing rates from a table
Print x: 2, 4 y: 10, 20 - Factor a difference of squares
Print x² − 64 - Difference of squares with coefficients
Print 9x² − 64 - Common factor of two terms
Print 12x + 18 - Common factor of three terms
Print 6x² + 9x + 12 - Factoring x² − bx + c
Print x² − 9x + 20 - Factoring x² + bx − c
Print x² + 3x − 28 - Evaluating functions
Print f(x) = 3x − 5, find f(−4) - Composing functions
Print f(g(2)) - The discriminant
Print x² + 2x + 5 = 0 - Discriminant with a leading coefficient
Print 3x² + 4x + 2 = 0 - Finding the rate of change
Print x: 2, 5, 8 y: 9, 21, 33 - Initial value from a table
Print x: 2, 5, 8 y: 9, 21, 33 - Multiplying in scientific notation
Print (5 × 10³) × (4 × 10²) - Dividing in scientific notation
Print (8 × 10⁵) ÷ (2 × 10²) - Arithmetic sequence nth term
Print 5, 12, 19, … 20th term - Common difference of a sequence
Print 5, 12, 19, 26 → d - Geometric sequence nth term
Print 3, 6, 12, … 8th term - Common ratio of a sequence
Print 3, 6, 12, 24 → r - Finding the x-intercept
Print 3x + 4y = 24 → x-int - Finding the y-intercept
Print 3x + 4y = 24 → y-int - Solving absolute value equations
Print |x − 3| = 7 - Absolute value equations with coefficients
Print |3x − 18| = 3 - Line equation from two points
Print (1, 3) and (3, 7) - Point-slope equation of a line
Print m = 2 through (1, 3) - Evaluating exponential functions
Print f(x) = 3 · 2ˣ, x = 4 - Solving exponential equations
Print 3 · 2ˣ = 48 → x - Solving x² = p by square roots
Print x² = 49 - Solving (x − h)² = k by square roots
Print (x − 2)² = 9
A simple way through algebra 1
Factoring comes in a fixed order and the order is the point. Take out a common factor first, because everything after it is smaller once you have. Then look for a difference of two squares, because it needs no search at all. Only then hunt for two numbers that multiply and add. A student who tries them in that order rarely gets stuck; one who reaches for the search every time will meet 4x² − 16 and grind at it.
Why this order works
Solving is the payoff, and it rests on one sentence rather than on the factoring: a product is zero only when one of the things being multiplied is zero. That is the step the marks are for, and it is where the sign turns over — (x − 3)(x + 5) = 0 gives x = 3 and x = −5, not −3 and 5. Handing a student the brackets already factored is what isolates it.