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# Y11+gdc+maximize+your+use+of+the++ev+2

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### Y11+gdc+maximize+your+use+of+the++ev+2

1. 1. Maximize your use of the Graphic Display Calculator
2. 2. Solve the equation: 2a 2 6a 8
3. 3. Given f x 2x 2 8x 10 Write down f(x) in the forms: a) b) f x 2 x h f x 2 x 2 k p x q c) Write down the equation of the axis of symmetry of the graph.
4. 4. Consider the curve f x x 3 2 x 2 x Find the transformations of this curve where: g x hx f x 1 2f x 1
5. 5. Solve the simultaneous equations a) b) 2x y 3 0 x y 2 2e x e 3e x y e y 15 10
6. 6. Find the sum of the first 30 terms of the sequence 3, 5, 7, 9, …
7. 7. Find the following sums 15 a) 23 5n n 1 20 b) 320 3.2 n 5 c) 0.2 n 1 n n
8. 8. Find the numbers in the Pascal’s triangle: th 6 row of
9. 9. Evaluate the following: 5 0 5 1 5 2 5 3 5 4 5 5
10. 10. Find the coefficient of x5 in the 7 expansion of (2 x 3)
11. 11. Solve the equations: a) x 3 b) ln(1 3x 2 x) e x 5 3 xe 2x 2
12. 12. Consider the functionf x x 3 5 x 2 7 x 50 Draw the tangent to the curve at x=0 and give its equation. Find the other point of intersection of this tangent with the curve.
13. 13. 8) Find the equation of the tangent and normal at x =3 of the following function: f x 0.5 x 3 0.5 x 2 10x
14. 14. Find the area between the curve y x( x 6) and the x-axis .
15. 15. Represent on the same pair of axes f(x), its inverse function and the line y=x. f x e x 3
16. 16. Consider the function f x 2x 6 x 3 (a) Write down the equations of the asymptotes to the graph of f x (b) Find the set of values of for which f x 0 (c) Find the gradient at -5 (d) Explain why f x 0 for any value of x.
17. 17. Given f x 3 xe 2x 2 and g x ln 1 x a. Write down the domain of g. b. Sketch the graph of f for f(x) >0 c. Write down the coordinates of the maximum point on the graph of f. d. Find lim f x x e. Find the x-coordinate of the points at which the graphs of f and g have the same gradient in the interval 0<x<1.5
18. 18. On the same pair of coordinate axes draw the graphs of the function f(x) and its inverse function if. f x ln x 10 State the domain of f(x) and its inverse.
19. 19. Solve the equations a) b) x 1 1 x 1 x 2 1 x c) e x ln x e 5 2x