3rd Year Exam Tuning

Homework 5: To be done neatly in the front of your books
TOTAL 28 marks

1. z is the difference between the product of x and y and half their sum. Write down a formula for z and make y the subject. Use your answer to find the value of y when x=3 and z=-2

[4 marks]

2. Solve \[\frac x 4 -7 = \frac x 7\]

[3 marks]

3. A room measures 3.2m x 5.6m. A square tile with edge 20cm cost £1.47. What will it cost to tile the room?

[3 marks]

4. Find the equation of the line that passes through (3,-2) and (-7,4). Rearrange your answer to the form $ax + by = c$ where a,b and c are integers.

[4 marks]

5. The bearing of X from Z is $088^\circ$. What is the bearing of Z from X?

[1 marks]

6. Make $x$ the subject of \[y=\frac {x+2}{3-2x}\]

[4 marks]

7. Expand $(3x-4y)^2$

[2 marks]

8. Factorise $6x^2+7x-20$

[3 marks]

9. Find coordinates of the image of the point (-1,4) after:

1. A reflection in the line y=-x
2. A rotation $90^\circ$ 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]

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]

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]

3rd Year Homework 2

Homework 2: To be done neatly in the front of your books for Monday 31st March
TOTAL 28 marks

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

[4 marks]

2. A wheelchair ramp of length 10m provides an alternative route to steps which climb 86cm. What angle does the wheelchair ramp make with the ground?

[3 marks]

3. Rob puts £500 in a bank account with interest rate r for 5 years? When he check his balance it is £864.63. What was the interest rate (r)?

[4 marks]

4. By showing your working and not using a calculator, find the value of $ \left( \frac {27}{125} \right)^{-\frac{2}{3}}$

[2 marks]

5. Find the area of a sector of a circle with radius 24cm and angle 35 degrees to 2 significant figures

[3 marks]

6. Find the gradient of this line: $7x-2y=7$ 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: \[4x+3y=1\\-2x+5y=8\]

[3 marks]

8. HARD: A ship sails 6 km on a bearing of 141 degrees and then 5km on a bearing of 15 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]

3rd Year Homework 1

Homework 1: To be done neatly in the front of your books for Monday 24th March
TOTAL 28 marks

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

[4 marks]

2. A 3m ladder is leaning up a wall at an angle to the ground of $60^o$. How far up the wall can it reach?

[3 marks]

3. Pete decided to buy a new car. After 4 years depreciation at 20% from new, Pete decides to sell the car. It does not sell and so Pete reduces the price by 15%. The car still does not sell and he reduces it by a further 7% to £3,200. It sells after 3 days. What did the car cost new?

[5 marks]

4. Expand $(3x-2)(4x+3)$

[2 marks]

5. Factorise $6x^2-11x-35$

[3 marks]

6. Find the gradient of this line: $3x-2y=7$ and use this value to find the equation of a line parallel to this line which passes through (0,4)

[4 marks]

7. In a triangle ABC, AB=10cm, BC=6cm and angle C is a right angle. Find angle A.

[3 marks]

8. A ship sails 9.2km from a lighthouse on a bearing of $135^o$ and arrives due east of a pier which happens to be due south of the lighthouse. Draw a diagram and calculate how far east of the pier the boat is.

[4 marks]