Mathematics Paper 2 November 2010

Answer this when you sit the paper.

Answer this when you sit the paper.

1. A$x = 1$ or $x = 3$, the two numbers whose product is 3 and sum is 4
2. B$x = 2$ only, because the curve turns on the axis at that point
3. C$x = 0$ or $x = 4$, obtained by taking $x$ out as a common factor
4. D$x = -1$ or $x = -3$, the two numbers whose sum is $-4$

1. A$\frac{3}{2x}$, obtained by adding numerators and adding denominators
2. B$\frac{3x - 1}{(x - 1)(x + 1)}$, since $(x + 1) + 2(x - 1) = 3x - 1$
3. C$\frac{2x + 3}{(x - 1)(x + 1)}$, since $(x + 1) + 2(x + 1) = 2x + 3$
4. D$\frac{3}{(x - 1)(x + 1)}$, adding the numerators over the common denominator

Answer this when you sit the paper.

1. A$1 \le y < 3$
2. B$-3 < y \le 1$
3. C$-3 \le y < 1$
4. D$y < -3$ or $y \ge 1$

1. A$-3$, $-2$, $-1$, $0$, $1$, taking both end values as included
2. B$-2$, $-1$, $0$, taking neither of the two end values as included
3. C$-3$, $-2$, $-1$, $0$, taking the left end value as included instead
4. D$-2$, $-1$, $0$, $1$, since $-3$ is excluded but $1$ is included

Answer this when you sit the paper.

Answer this when you sit the paper.

1. A$g = 2t^2(ut - s)$
2. B$g = \frac{ut - s}{2t^2}$
3. C$g = \frac{s - ut}{2t^2}$
4. D$g = \frac{2(ut - s)}{t^2}$

Tap to enlarge

1. ATriangle AED
2. BTriangle ADE
3. CTriangle BCD
4. DTriangle CDE

Tap to enlarge

Answer this when you sit the paper.

1. A$P = kTV$, multiplying both quantities by the constant
2. B$P = \frac{kV}{T}$, putting the directly varying quantity below
3. C$P = k + \frac{T}{V}$, adding the constant to the ratio of the two
4. D$P = \frac{kT}{V}$, with T on top and V underneath

Answer this when you sit the paper.

Answer this when you sit the paper.

1. A$\frac{1}{10}\begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix}$
2. B$\frac{1}{14}\begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix}$
3. C$\frac{1}{10}\begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix}$
4. D$\frac{1}{10}\begin{pmatrix} 4 & -2 \\ -1 & 3 \end{pmatrix}$

Answer this when you sit the paper.

Tap to enlarge

Answer this when you sit the paper.

Tap to enlarge

1. A$76^\circ$, the supplement of $104^\circ$ along the straight line AEF
2. B$36^\circ$, equal to the angle marked between BA and CA
3. C$104^\circ$, the sum of the two angles marked at A
4. D$68^\circ$, equal to the angle marked between CA and AE

Tap to enlarge

Answer this when you sit the paper.

Answer this when you sit the paper.

Answer this when you sit the paper.

Answer this when you sit the paper.

1. AA circle of radius 3 cm centred on the midpoint of AB, drawn inside the plot
2. BThe perpendicular bisector of AB, since its points sit 3 cm from each end of AB
3. COne straight line parallel to AB drawn 3 cm inside the plot, because points beyond the boundary lie off the farmer's land
4. DA pair of straight lines parallel to AB, one on each side of AB and each 3 cm from it

1. AThe bisector of the angle at B, drawn with compasses from the corner B
2. BA line drawn parallel to AB and exactly midway between the two lines that lie 3 cm from AB
3. CThe perpendicular bisector of AB, constructed with equal arcs from A and from B
4. DAn arc centred on the midpoint of AB whose radius is half the length of AB

Answer this when you sit the paper.

1. A$\frac{4}{3}\pi r^3$, since the height is $4r$
2. B$2\pi r^3$, since the height is $6r$
3. C$\frac{2}{3}\pi r^3$, since the height is $2r$
4. D$\frac{1}{3}\pi r^3$, since the height is $r$

Answer this when you sit the paper.

Answer this when you sit the paper.

1. A$2x(x - 7)$ cm$^2$, twice the base multiplied by the height
2. B$x + (x - 7)$ cm$^2$, the base added to the height
3. C$\frac{1}{2}x(x - 7)$ cm$^2$, half the base multiplied by the height
4. D$x(x - 7)$ cm$^2$, the base multiplied by the height

Answer this when you sit the paper.

Answer this when you sit the paper.

Answer this when you sit the paper.

1. A$x = 1,32$ or $x = -5,32$
2. B$x = 7,00$ or $x = -1,00$
3. C$x = 6,14$ or $x = -1,14$
4. D$x = 1,14$ or $x = -6,14$

Answer this when you sit the paper.

Answer this when you sit the paper.

Answer this when you sit the paper.

Answer this when you sit the paper.

Tap to enlarge

Answer this when you sit the paper.

Tap to enlarge

Answer this when you sit the paper.

Answer this when you sit the paper.

Answer this when you sit the paper.

Answer this when you sit the paper.

Answer this when you sit the paper.

1. A$146^\circ$
2. B$194^\circ$
3. C$242^\circ$
4. D$048^\circ$

1. A$x > 6$ and $y > x$
2. B$x \ge 6$ and $y \ge x$
3. C$x > 6$ and $x > y$
4. D$y > 6$ and $x > y$

1. A$400x + 300y \le 6\,000$, since the land used cannot exceed the plot
2. B$300x + 400y \le 6\,000$, with each house taking 300 m$^2$
3. C$400x + 300y \ge 6\,000$, since the plot must be filled completely
4. D$700(x + y) \le 6\,000$, since a house and a flat together take 700 m$^2$

Answer this when you sit the paper.

Answer this when you sit the paper.

1. A$x = 8$ and $y = 8$, giving 16 dwelling units in total
2. B$x = 7$ and $y = 10$, or $x = 8$ and $y = 9$, giving 17 dwelling units
3. C$x = 7$ and $y = 8$, giving 15 dwelling units in total
4. D$x = 6$ and $y = 12$, giving 18 dwelling units in total

1. AA reflection in the line $y = -x$, which sends each point across that line
2. BA translation with vector $\begin{pmatrix} -5 \\ -4 \end{pmatrix}$
3. CA translation with vector $\begin{pmatrix} -4 \\ -5 \end{pmatrix}$
4. DA rotation of $180^\circ$ about the origin, which turns the triangle over

1. AP$_2$(-3; -1), Q$_2$(-4; -1), R$_2$(-4; -3)
2. BP$_2$(-3; 1), Q$_2$(-4; 1), R$_2$(-4; 3)
3. CP$_2$(1; 3), Q$_2$(1; 4), R$_2$(3; 4)
4. DP$_2$(1; -3), Q$_2$(1; -4), R$_2$(3; -4)

Answer this when you sit the paper.

Answer this when you sit the paper.

Answer this when you sit the paper.