5th Year Homework 3

Homework 3: To be done neatly in the front of your books
TOTAL 17 marks

1. Copy and complete the table for $y=-\frac{1}{3}x^2+3x+1$, \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline y & & & 3\frac{2}{3} & & & & & \\ \hline \end{array}

1. Plot the points on a set of axes (use 1 square for 1 unit on x and y axes) and join them to form a smooth curve, your curve should look like this:

   

2. Use your graph to solve the equation $-\frac{1}{3}x^2+3x+1=0$
3. Use your graph to find the solutions to $-\frac{1}{3}x^2+3x+1=3$

[6 marks]

2. The volume of a balloon is directly proportional to the cube of its radius. A balloon of radius 5cm has volume $525cm^3$:

1. Find a formula for v in terms of r
2. Find the volume of the balloon when the radius is 15cm
3. What is the radius of a balloon with volume $2560cm^3$?

[4 marks]

3. The force between 2 masses varies indirectly as the square of the distance between them. Copy and complete the table \begin{array}{|c|c|c|c|} \hline d & 2 & 5 & \\ \hline F & 8 & & 17 \\ \hline \end{array}

[4 marks]

4. A line passes through the point (-1,5) and has gradient 3. Write down the equation of the line in the form y=mx+c

[3 marks]