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Math Sheet Studio

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Unit test: 20 questions, easy to hard, 2 points each, roomy spacing. Keeps your selected skills.

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Complex numbers

Operations with complex numbersHSN.CN.A.2Powers of iHSN.CN.A.2Quadratic equations with complex solutionsHSN.CN.C.7

Polynomial functions

Dividing polynomials (long and synthetic division)HSA.APR.D.6The remainder and factor theoremsHSA.APR.B.2Finding zeros of polynomialsHSA.APR.B.3Factoring sums and differences of cubesHSA.SSE.A.2The binomial theoremHSA.APR.C.5Graphs of polynomial functionsHSF.IF.C.7c

Rational expressions & functions

Simplifying rational expressionsHSA.APR.D.6Multiplying and dividing rational expressionsHSA.APR.D.7Adding and subtracting rational expressionsHSA.APR.D.7Solving rational equationsHSA.REI.A.2Asymptotes and holes of rational functionsHSF.IF.C.7d

Exponential & logarithmic functions

Exponential and logarithmic formHSF.BF.B.5Evaluating logarithmsHSF.LE.A.4Properties of logarithms (expanding and condensing)HSF.LE.A.4Solving exponential equationsHSF.LE.A.4Solving logarithmic equationsHSF.LE.A.4Compound and continuous interestHSA.SSE.B.3c

Functions

Composition of functionsHSF.BF.A.1cInverse functionsHSF.BF.B.4aTransformations of functionsHSF.BF.B.3Evaluating piecewise functionsHSF.IF.C.7b

Sequences & series

Arithmetic seriesHSA.SSE.B.4Geometric series (finite and infinite)HSA.SSE.B.4

Matrices

Adding, subtracting and scaling matricesHSN.VM.C.8Multiplying matricesHSN.VM.C.8Determinants of 2 × 2 and 3 × 3 matricesHSN.VM.C.12Inverse of a 2 × 2 matrixHSA.REI.C.9

Systems of equations

Systems of three linear equationsHSA.REI.C.6

Conic sections

Parabolas: vertex, focus and directrixHSG.GPE.A.2Ellipses and hyperbolasHSG.GPE.A.3

Trigonometric functions

Converting between radians and degreesHSF.TF.A.1Exact values on the unit circleHSF.TF.A.3Amplitude, period and midline of trig graphsHSF.TF.B.5

Counting

Permutations and combinationsHSS.CP.B.9

Each skill gets its own section. Up to 8 skills per sheet.

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Step-by-step answer keyPro: each answer shows its working in the PDF.QR code for the answersPrints a code that opens the answer key on a phone, so work can be checked at home.

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1. The binomial theorem

Questions

Difficulty

Planned: 12 / 60 questions

12 questionsSign in to download PDFsSettingsShow answers

Name ______________________Date ____________Score ____ / 12

The binomial theorem practice

The binomial theorem · 1–12

Expand, or find the coefficient asked for.

Hard

1.Find the coefficient of x² in (3x + 1)⁷.

Hard

2.Find the coefficient of x⁵ in (3x − 3)⁶.

Hard

3.Find the coefficient of x⁴ in (3x + 1)⁵.

Hard

4.Find the coefficient of x⁷ in (2x + 2)⁸.

Hard

5.Find the coefficient of x³ in (x − 3)⁸.

Hard

6.Find the coefficient of x³ in (2x − 1)⁹.

Hard

7.Find the coefficient of x⁶ in (2x + 3)⁸.

Hard

8.Find the coefficient of x¹ in (3x − 2)⁵.

Hard

9.Find the coefficient of x⁴ in (2x − 3)⁸.

Hard

10.Find the coefficient of x² in (x + 1)⁶.

Hard

11.Find the coefficient of x² in (2x − 3)⁵.

Hard

12.Find the coefficient of x² in (x − 1)⁵.

Answer key — The binomial theorem practice

The binomial theorem

1.189

2.−4,374

3.405

4.2,048

5.−13,608

6.672

7.16,128

8.240

9.90,720

10.15

11.−1,080

12.−10

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