Graph sketching

Check out this graph sketcher: http://physics-animations.com/graph.html

Oxbridge Mathematics

Oxford Mathematics

For information on how to apply: http://www.maths.ox.ac.uk/study-here/undergraduate-study/how-apply

For information about the MAT (mathematics admissions test), including past papers and solutions: MAT TEST

Pre university sample problems: https://www.maths.ox.ac.uk/study-here/undergraduate-study/practice-problems

Cambridge Mathematics

http://www.maths.cam.ac.uk/undergrad/admissions/

STEP information

Link to some recommended reading: Recommended reading

Maths Helper has some great resources and tough practice questions

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]

4th Year Exam Tuning

Homework 6: To be done neatly in the front of your books
TOTAL 20 marks

1. The point (1, -5) is on this line $2x+3y+k=0$ What is the value of k?

[2 marks]

2. Consider this line: $y=3-2x$

1. What is the gradient of this line?
2. What is the equation of a line which is PARALELL to the line but has y intercept -5?
3. Write down the equation of a line PARALLELto $y=3-2x$ which passes through (-9,7)

[5 marks]

3. Copy and complete the table. \begin{array}{|c|c|c|} \hline \text{No. of siblings} & \text{Frequency} & \text{... } \\ \hline \text{0} & 8 & \\ \hline \text{1} & 9 & \\ \hline \text{2} & 4 & \\ \hline \text{3} & 2 & \\ \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]

4. Copy and complete the table and use it find an estimate of the mean height. \begin{array}{|c|c|c|} \hline \text{Height in cm} & \text{Frequency} & \text{M.P. $\times$ F} \\ \hline \text{20 $\leq$ h < 25} & 2 \\ \hline \text{25 $\leq$ h < 30} & 13\\ \hline \text{30 $\leq$ h < 35} & 14\\ \hline \text{35 $\leq$ h < 40} & 7\\ \hline \end{array}

[3 marks]

5. Copy and complete the table for $y=7+2x-x^2$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & -8 & & & & & & & \\ \hline \end{array}

1. Plot the points on a set of axes and join to form a smooth curve
2. Use your graph to solve the equation $7+2x-x^2=0$
3. Use your graph to find the solutions to $7+2x-x^2=1$

[6 marks]