mat

Papers (32)
2025
mat_2025.pdf 23
2024
mat_2024.pdf 2
2023
mat_2023.pdf 5
2022
mat_2022.pdf 6
2021
mat_2021.pdf 6
2020
mat_2020.pdf 7
2019
mat_2019.pdf 6
2018
mat_2018.pdf 6
2017
mat_2017.pdf 7
2016
mat_2016.pdf 6
2015
mat_2015.pdf 6
2014
mat_2014.pdf 6
2013
mat_2013.pdf 6
2012
mat_2012.pdf 7
2011
mat_2011.pdf 7
2010
mat_2010.pdf 7
2009
mat_2009.pdf 6
2008
mat_2008.pdf 6
2007
mat_2007.pdf 6
2005
mat_2005.pdf 3
2004
mat_2004.pdf 3
2003
mat_2003.pdf 4
2002
mat_2002.pdf 3
2001
mat_2001.pdf 5
2000
mat_2000.pdf 2
1998
mat_1998.pdf 4
1997
mat_1997.pdf 5
1996
mat_1996.pdf 4
Unknown
specimen_1 7 specimen_2 7 specimen_a 7 specimen_b 7
1996 mat_1996.pdf

4 maths questions

Q2 Solving quadratics and applications Counting solutions or configurations satisfying a quadratic system View
2. (a) Factorise the expression $x ^ { 2 } + x - 6$.
(b) For which values of the real constant $a$ does the equation
$$x ^ { 2 } + x - a = 0$$
have at least one real solution? Write down these solutions in terms of $a$.
(c) Show that, for any value of the real constant $b$, the equation
$$x ^ { 3 } - ( b + 1 ) x + b = 0$$
has $x = 1$ as a solution. Find all values of $b$ for which this equation has exactly two distinct solutions.
Q3 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
3. (a) Write down the equation of the straight line through the point $( 1,2 )$ with slope - 1 .
(b) Let $l$ be a line with equation
$$y = ( 2 - a ) + a x$$
where $a$ is a constant. Show that, for any $a$, the line passes through the point $( 1,2 )$. Find the equation of the line perpendicular to this line which also passes through the point $( 1,2 )$.
(c) Find the equations of the lines which pass through the point $( 1,2 )$ and have perpendicular distance 1 from the origin.
Q4 Areas by integration View
4. (a) Find the values of
(i) $\int _ { - 1 } ^ { 1 } \left( x ^ { 2 } - x \right) \mathrm { d } x$,
(ii) $\int _ { - 1 } ^ { 1 } \left( x ^ { 3 } + x ^ { 2 } - 2 x \right) \mathrm { d } x$.
(b) Sketch the graph of $y = x ^ { 2 } - x$ and indicate which difference in areas is represented by your answer to (a)(i).
(c) Find the total area (measured positively) that lies between the graphs of $y = x ^ { 2 } - x$ and $y = x ^ { 3 } + x ^ { 2 } - 2 x$ between $x = - 1$ and $x = 1$.
(d) The answers to (a)(i) and (a)(ii) are related in a particular way. Explain how the relationship can be seen without working out any integrals.
Q5 Combinations & Selection Selection with Group/Category Constraints View
5. A total of 12 noughts and 4 crosses are arranged in 4 rows of 4 . One such arrangement is illustrated below.
00$\times$0
0$\times$0$\times$
0000
$\times$000

(a) How many arrangements are there altogether?
(b) How many arrangements are there in which there is a cross in every row?
(c) How many arrangements are there in which there is a cross in every row and in every column?