AQA Level 2 Further Maths Specimen Paper 1 2020 Walkthrough

[redfinance]

Also, I have a question for Q19. The function given there is quite simple and can be factorised using completing the square. But do you think there will ever be a scenario with a non-quadratic function that can't be factorised? If so, does this approach work : Find the derivative of f(x). For a function to be increasing, f'(x) > 0. Therefore, we need to show that the minimum value of f'(x) > 0. Then find the f''(x) and set it equal to 0. This will give the stationary points. We can verify which points are minimum points by finding f'''(x) and substituting them into it to see if its + or -. Then for the minimum points, if their values when substituted into f'(x) are >0, the function will be increasing for all values of x. the reverse idea for decreasing function could be applied with f'(x) < 0 and using maximum points instead.

[redfinance]

question 11 can be done much more simply. because the center of a circle is always positioned at the middle of the chord, the shift of the circles center in the horizontal direction will simply be the average of the above points values, aka (1 + 5)/2 = 6/2 = 3. So, (x-3)^2 + (y-2)^2 = r^2. To figure out r, sub in using point (0, 2) and get r = 9. 😀

[benstevenson]

For the prove question 9, can you not use the angle in a semicircle through the diameter is 90⁰ as both CDA and CBA are equal as are both 180-5x and 10x is equal to 18⁰? Basically is there any other alternative proofs ?