4th Year Homework 5

Homework 4: To be done neatly in the front of your books for next wed 7th May
TOTAL 31 marks

1. Solve this equation \[\frac{3x}{4}-\frac{5(3-2x)}{3}=-x\]

[4 marks]

2. Draw a prime factor tree for 132 and use this to work out the NUMBER of factors of 132 (you do not need to list them)

[2 marks]

3. The point (-2, -5) is on this line $3x=k-5y$ What is the value of k?

[2 marks]

4. Find HCF(65,39) by any method an use this to find the LCM(65,39)

[2 marks]

5. Find HCF($4xy^2$,$12x^2 yz$) by any method an use this to find the LCM($4xy^2$,$12x^2 yz$)

[2 marks]

6. Consider this line: $8y+4x=15$

1. Make y the subject of: $8y+4x=15$
2. What is the gradient of this line? Give your answer as a fraction
3. What is the equation of a line which is PARALELL to the line but has y intercept -3?
4. Using your answer to a. find the gradient of a line which is PERPENDICULAR to $8y+4x=15$
5. Using d. write down the equation of a line PERPENDICULAR to $8y+4x=15$ which passes through (0,7)

Remember for perpendicular gradient: flip the fraction and change sign.

[5 marks]

7. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{No. of petals} & \text{Frequency} & \text{... } \\ \hline \text{3} & 4 & \\ \hline \text{4} & 15 & \\ \hline \text{5} & 22 & \\ \hline \text{6} & 14 & \\ \hline \end{array} Use it to:
a. Find the mean
b. Find the median (note it is not a grouped table of data!)

[4 marks]

8. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{Height in cm} & \text{Freq-Girls} & \text{M.P. $\times$ F} & \text{Freq-Boys} & \text{M.P. $\times$ F} \\ \hline \text{110 $\leq$ h < 115} & 5 & & 11 \\ \hline \text{115 $\leq$ h < 120} & 21 & & 29\\ \hline \text{120 $\leq$ h < 125} & 29 & & 14\\ \hline \text{125 $\leq$ h < 130} & 15 & & 16\\ \hline \end{array} Use it to:
a. Find separate estimates of the mean for the boys and girls
b. Make a comment comparing boys height to girls using this data.

[5 marks]

9. HARD: Boat A sails 5 miles on a bearing of $099^\circ$ from Dover. Boat B sails 7 miles on a bearing of $200^\circ$ from Dover. Draw a clear diagram and use it to find the distance between Boat A and Boat B. HINT: you might want to look up the Cosine Rule.

[4 marks]