1. © T Madas Trial and Improvement

2. © T Madas Find the solution of x 2 + 2x = 39 to 1 decimal place, given that x lies between 5 and 6. too high39.322510.728.62255.35 too low38.6910.628.095.3 too high39.9610.829.165.4 too high41.251130.255.5 too high4812366 too low3510255 resultx 2 + 2x2x2xx 2x 2 x x ≈ 5.3

3. © T Madas Find the solution of x 3 – 2x = 280 to 1 decimal place, given that x lies between 6 and 7. too high280.77962513.3294.0796256.65 too high287.36313.4300.7636.7 too low274.29613.2287.4966.6 too low261.62513274.6256.5 too high329143437 too low204122166 resultx 3 – 2x2x2xx 3x 3 x x ≈ 6.6

4. © T Madas too low999.89062968.7656231.125 968.4544 969.0769 970.3225 967.21 973.44 1024 961 x 2 too low999.574431.12 too high1000.206931.13 too high1001.472531.15 too low998.3131.1 too high1004.6431.2 too high105632 too low99331 resultx + x 2 x Find the solution of x 2 + x = 1000 to 2 decimal places, given that x lies between 31 and 32. x ≈ 31.13

5. © T Madas Find to 2 d.p. the square root of 70, i.e 70 without using the square root button. too low69.9732258.365 too high70.05698.37 too low69.88968.36 too low69.72258.35 too low68.898.3 too high70.568.4 too high72.258.5 too high819 too low648 resultsquare ittry 70 ≈ 8.37

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7. Solve these equations by trial and improvement to 1 d.p. x lies between 16 and 172x 2 – 3x = 500 x lies between 3 and 4x 3 – x = 50 x lies between 2 and 3x 2 + 2x = 10 x lies between 4 and 5x 2 + x = 25

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9. Find the solution of x 3 + 3x = 11 to 2 decimal places, given that it lies between 1 and 2. too high11.042411631.785 too high11.1053391.79 too low10.9797521.78 too low10.8552331.77 too low10.7317761.76 too low10.6093751.75 too high11.2321.8 too low10.0131.7 too low7.8751.5 resultx 3 + 3xx x ≈ 1.78

10. © T Madas Find the solution of x 3 + x = 10 to 3 decimal places, given that it lies between 2 and 3. too high10.001633382.0465 too high10.00809192.047 too low9.99517792.046 too low9.982276092.045 too low9.9179496862.04 too high10.046907112.05 too high10.710137672.1 too high13.683575092.3 too high17.206138832.5 resultx 3 + xx x ≈ 2.046

11. © T Madas Find the solution of x 3 – x = 30 to 3 decimal places, given that it lies between 3 and 4. too high30.000961453.2145 too low29.985964343.214 too high30.015963383.215 too high30.1662483.22 too low29.8661613.21 too low29.5683.2 too high32.6373.3 too high39.3753.5 resultx 3 – xx x ≈ 3.214

12. © T Madas Solve these equations by trial and improvement to 2 d.p. The root lies between the values given.

13. © T Madas