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]

3rd Year Homework 4

Homework 4: To be done neatly in the front of your books for first lesson back after bank holiday
TOTAL 34 marks

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

[4 marks]

2. A cuboid has a bottom face with sides 5 and 8 cm with a height of 12cm. Find the length of the longest line between 2 vertices. Also find the angle between this line and the lower face.

[5 marks]

3. A car bought for £9000 depreciates at rate r% per year. If it is worth £5300 after 3 years what is r?

[4 marks]

4. By showing your working and not using a calculator, find the value of $ \left( \frac {27}{64} \right)^{-\frac{2}{3}}$

[2 marks]

5. Find the area of a sector of a circle with radius 10cm and angle 272 degrees to 2 significant figures

[3 marks]

6. Find the gradient of this line: $4y+7x=3$ and use this value to find the equation of a line perpendicular to this line which passes through (0,-1)

[4 marks]

7. Solve the simultaneous equations: \[4x+y=-1\\-6x-3y=4.5\]

[3 marks]

8. HARD: A ship sails 7 km on a bearing of 011 degrees and then 17 km on a bearing of 177 degrees. Draw a diagram and work out how far it must travel to return to the starting position. (HINT: one way to do this would be take a look at the Cosine Rule)

[5 marks]

9. Find coordinates of the image of the point (-3,2) after:

1. A reflection in the line y=-x
2. A rotation 90 degrees clockwise about (0,-1)
3. A translation $\left(\begin{array} \left \\ 4 \\ -2 \end{array}\right)$
4. An enlargement scale factor 2, centre (0,1)

[4 marks]

Check out the maths in these

Nope

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4th Year Homework 4

Homework 4: To be done neatly in the front of your books for first lesson back
TOTAL 33 marks

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

[4 marks]

2. Copy and complete this table for a pie chart \begin{array}{|c|c|c|} \hline \text{Fav. colour} & \text{Frequency} & \text{Angle (1 d.p.)} \\ \hline \text{red} & 8 & \\ \hline \text{green} & 33 & \\ \hline \text{blue} & 19 & \\ \hline \text{pink} & 7 & \\ \hline \text{other} & 2 & \\ \hline \end{array}

[3 marks]

3. Draw a prime factor tree for 84 and list all the factors of 84

[2 marks]

4. The point (3, -5) is on this line $4x-2y=k$ What is the value of k?

[2 marks]

5. Express 156 as a product of it's prime factors and use this to work out how many factors 156 has without actually listing them all.

HINT: E.g. $392=2^3 \times 7^2$; add one to each index; $3+1=4$ and $2+1=3$; then multiply; So $392$ has $3\times 4 = 12$ factors

[2 marks]

6. Find the gradient of this line: $8y+4x=15$ and use this value to find the gradient of a line which is perpendicular (at right angles) to this line. Remember for perpendicular gradient: flip the fraction and change sign.

[4 marks]

7. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{Age} & \text{Frequency} & \text{Age $\times$ Frequency} \\ \hline \text{14} & 4 & \\ \hline \text{15} & 11 & \\ \hline \text{16} & 31 & \\ \hline \text{17} & 27 & \\ \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{Freq-Girls} & \text{M.P. $\times$ F} & \text{Freq-Boys} & \text{M.P. $\times$ F} \\ \hline \text{10 $\leq$ w < 15} & 4 & & 10 \\ \hline \text{15 $\leq$ w < 20} & 25 & & 15\\ \hline \text{20 $\leq$ w < 25} & 31 & & 21\\ \hline \text{25 $\leq$ w < 30} & 10 & & 26\\ \hline \end{array} Use it to:
a. Find an estimate of the mean for boys and girls
b. Draw a a fully labelled frequency polygon to include the data for the boys and girls on the same diagram

[8 marks]

9. HARD: Find the value of p by splitting the triangle

[4 marks]

3rd Year Homework 3

Homework 3: To be done neatly in the front of your books for first lesson back after Easter
TOTAL 30 marks

1. Solve this equation \[\frac{2x+1}{3}-\frac{2(4-3x)}{7}=x\]

[4 marks]

2. Find
a. The length of AV
b. the angle between AV and the base ABCD

[5 marks]

3. Rob puts £200 in a bank account with interest rate r for 8 years? When he checks his balance it is £446.31. What was the interest rate (r)?

[4 marks]

4. By showing your working and not using a calculator, find the value of $ \left( \frac {9}{4} \right)^{-\frac{3}{2}}$

[2 marks]

5. Find the perimeter of a sector of a circle with radius 4cm and angle 52 degrees to 2 significant figures

[3 marks]

6. Find the gradient of this line: $5y+3x=2$ and use this value to find the equation of a line perpendicular to this line which passes through (0,5)

[4 marks]

7. Solve the simultaneous equations: \[3x+2y=-8\\-5x+4y=17\]

[3 marks]

8. HARD: A ship sails 9 km on a bearing of 092 degrees and then 10 km on a bearing of 115 degrees. Draw a diagram and work out how far it must travel to return to the starting position. (HINT: one way to do this would be take a look at the Cosine Rule)

[5 marks]