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S6MA3ENA WINTER B TEST 5th December 2016

What have we covered?

1. Quadraticsa. Sketch a quadraticb. Find and plot points and lines. x-intercepts, y-intercept, vertex, line of symmetry.c. Using manual method or calculator.d. Word problems relating to quadratics.

2. Arithmetic and Geometric Sequences and Seriesa. Ability to see and show if a sequence is Arithmetic or Geometric.b. Ability to find a certain term or the sum of a number of terms.c. Sum of infinite series.d. Word problems relating to AS and GS.e. Use of a manual method and calculator.

3. Differentiation

a. Ability to differentiate a polynomial. b. Realize that when you differentiate it tells you the “instantaneous rate of change.”c. Realize that when you differentiate it tells you the slop/gradient.d. Can find the slope of a polynomial at a given point and find its equation.e. Can recognize a Local Maximum, Local Minimum and a Point of Infection.f. Can locate Minimum, Maximum and point of inflection.g. Can see when a polynomial is increasing or decreasing and describe it’s range.h. Use of a manual method and calculator.

Quadratics1. When seven times a number n is subtracted from the square of the same number, the result is 30.

a. Show that n2−7n−30=0 .

b. Hence find the values of n.

Answer.................................

2.

3. ,

4. The graph of is shown on the axis below.

a. Draw the graph of on the same axes.b. Use your graph to find :

I. The value of when

II. The value of x that gives the minimum value of

5. The diagram shows the graph of . The graph crosses the x-axis at the point A, and has a vertex at B. Write down the co-ordinates of each of these points A and B.

6. The perimeter of this rectangular field is 100m. One side is m as shown.

a. Express the width in terms of

b. Write an expression, in terms of only, for the area of the field.

c. If the length is 30m, find the area.

d. What is the maximum possible area?

7. Sketch the graph of the parabola . (can use lots of equations to practice)Your sketch must show the co-ordinates for any points of intersection with the coordinate axes and the coordinates of the vertex. Give your answers in surd form when necessary.

8. A rectangle has a width of w cm and a length of (w+6) cm. Draw a labelled diagram of the rectangle.a. Find an expression for its area in terms of w, in cm2.

Answer.................................

b. If the area is 55cm2, show that w2+6w−55=0 .

c. Hence find the width of the rectangle.

Answer.................................

Arithmetic Sequence and Series

Geometric Sequence and Series

Differentaition