4th Year Homework 3

Homework 3: To be done neatly in the front of your books for Wed 2nd April
TOTAL 37 marks

1. Solve this equation \[\frac{2x+1}{5}-\frac{3(1-2x)}{3}=x\]

[4 marks]

2. Copy and complete this table for a pie chart \begin{array}{|c|c|c|} \hline \text{Fav. TV Channel} & \text{Frequency} & \text{Angle (1 d.p.)} \\ \hline \text{BBC} & 5 & \\ \hline \text{ITV} & 12 & \\ \hline \text{CH4} & 23 & \\ \hline \text{SKY} & 11 & \\ \hline \text{Other} & 2 & \\ \hline \text{CH5} & 5 & \\ \hline \end{array}

[3 marks]

3. Solve these simultaneous equations algebraically:\[3x+2y=-13\\-x+4y=23\]

[4 marks]

4. True or false the point (3, -2) is on the line $3x-4y=16$? Justify your answer

[2 marks]

5. Draw a Venn diagram and shade the region which represents AnBnC'

[2 marks]

6. Find the gradient of this line: $5y+2x=20$ and use this value to find the gradient of a line which is perpendicular (at right angles) to this line

[4 marks]

7. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{Score on dice} & \text{Frequency} & \text{Score $\times$ Frequency} \\ \hline \text{1} & 4 & \\ \hline \text{2} & 13 & \\ \hline \text{3} & 31 & \\ \hline \text{4} & 29 & \\ \hline \text{5} & 17 & \\ \hline \text{6} & 6 & \\ \hline \end{array} Use it to:
a. Find the mean
b. Find the median

[4 marks]

8. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{Weight (w) in Kg} & \text{Frequency} & \text{M.P. $\times$ Frequency} \\ \hline \text{10 $\leq$ w < 15} & 4 & \\ \hline \text{15 $\leq$ w < 20} & 22 & \\ \hline \text{20 $\leq$ w < 25} & 38 & \\ \hline \text{25 $\leq$ w < 30} & 16 & \\ \hline \end{array} Use it to:
a. Find an estimate of the mean
b. Find an estimate of the median
c. Draw a a fully labelled frequency polygon

[8 marks]

9. HARD: Find the length of AC by splitting the triangle

[4 marks]

10. Work out $1.2\times 10^3 + 3.41\times 10^4$ showing your working

[2 marks]