fieldingsclasses.weebly.com€¦ · Web viewWord problems relating to quadratics. Arithmetic and...
Transcript of fieldingsclasses.weebly.com€¦ · Web viewWord problems relating to quadratics. Arithmetic and...
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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.
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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.
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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.
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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.
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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
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Geometric Sequence and Series
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Differentaition
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