Mathematics Paper 2 June 2014

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1. A$3,168 \times 10^{-5}$, from dividing the index by 4 instead of the number
2. B$0,792 \times 10^{-4}$, the right value but with a mantissa smaller than 1
3. C$7,92 \times 10^{-5}$, a quarter of the number with a mantissa between 1 and 10
4. D$7,92 \times 10^{-3}$, from moving the decimal point the wrong way when adjusting

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1. A$31^\circ$, taking $A\hat{P}Q$ as alternate to $P\hat{A}Q$ across the parallels
2. B$118^\circ$, from the three angles of triangle APQ adding to $180^\circ$
3. C$62^\circ$, taking $A\hat{P}Q$ to be the whole of the bisected angle $P\hat{Q}B$
4. D$149^\circ$, taking $A\hat{P}Q$ as $180^\circ$ less the single angle of $31^\circ$

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1. A$(6mn - 5)(mn + 3)$, which expands to $6m^2n^2 + 13mn - 15$
2. B$(6mn + 5)(mn - 3)$, which expands to $6m^2n^2 - 13mn - 15$
3. C$(3mn - 5)(2mn + 3)$, which expands to $6m^2n^2 - mn - 15$
4. D$(3mn + 5)(2mn - 3)$, which expands to $6m^2n^2 + mn - 15$

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1. A10, the goats-only families plus the goats-and-sheep-only families
2. B24, every family in the set G, whether or not it also keeps cattle
3. C3, only those families whose goats are the only animals they keep
4. D14, the number of families that have both cattle and goats together

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1. A$27,2^\circ$, from the sine rule using $QR = 41,2$ m and $PQ = 20$ m
2. B$43,3^\circ$, which is the third angle $P\hat{Q}R$ rather than the angle at R
3. C$70,5^\circ$, from taking the acute angle whose cosine is $+\frac{1}{3}$
4. D$35,3^\circ$, from halving what is left when $R\hat{P}Q$ is taken from $180^\circ$

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1. A$317^\circ$, the back bearing of the $136,7^\circ$ bearing of P from Q
2. B$137^\circ$, which is the bearing of P from Q rather than of Q from P
3. C$043^\circ$, from measuring the angle at Q from north instead of from south
4. D$223^\circ$, the back bearing of $043^\circ$ rather than the one of $137^\circ$

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1. A$27^\circ$, taking $A\hat{C}D$ to be the angle $B\hat{D}C$ in the same segment
2. B$78^\circ$, taking $A\hat{C}D$ as equal to the angle $A\hat{P}D$ at the crossing
3. C$39^\circ$, taking the tangent to meet the chord AD at a right angle at A
4. D$51^\circ$, the angle AD subtends in the segment alternate to the tangent

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1. ATriangle BPC, which has $51^\circ$ at B, $78^\circ$ at P and $51^\circ$ at C
2. BTriangle DCP, which has $27^\circ$ at D, $51^\circ$ at C and DP equal to AP
3. CTriangle ADP, which has AP in common but $51^\circ$ rather than $27^\circ$ at A
4. DTriangle DBC, which stands on the same chord but has no vertex at the point P

1. AThe circle whose centre is the mid-point of WY and whose radius is half of WY
2. BThe bisector of the angle of the quadrilateral at the vertex W, drawn inwards
3. CThe straight line drawn through W and Y and extended beyond both of them
4. DThe perpendicular bisector of the line joining the two points W and Y

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1. AA cyclic quadrilateral, because its four vertices lie on one circle centre O
2. BA rhombus, because the four sides are all constructed to the same length
3. CA kite, because the two pairs of adjacent sides are constructed equal
4. DA parallelogram, because both pairs of opposite sides come out parallel to each other

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1. A100, rounding the 106,67 rods' worth of copper down to the nearest hundred
2. B107, rounding the 106,67 rods' worth of copper up to a whole number
3. C113, dividing the ball's volume by the rod's length instead of its volume
4. D106, since 106,67 rods' worth of copper only casts 106 complete rods

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1. A$k = 3$, taking the product of the two roots $-1$ and 3 to be $+3$ here
2. B$k = 15$, adding 3 to 12 rather than subtracting when comparing terms
3. C$k = -3$, taking the constant term of $x^2 - 2x - 3 = 0$ as $k$ itself
4. D$k = 9$, since $k - 12$ must equal the $-3$ in $x^2 - 2x - 3 = 0$

1. A$P = h + kN^2$, a fixed part plus a part varying as the square of $N$
2. B$P = h + kN$, a fixed part $h$ plus a part varying directly as $N$
3. C$P = hkN$, the whole salary varying directly as the number of cars sold
4. D$P = h + \frac{k}{N}$, a fixed part plus a part varying inversely as $N$

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1. A8, the 80 pupils less the 72 who are 70 kg or lighter on the table
2. B12, the difference between the cumulative frequencies at 70 kg and 65 kg
3. C6, the 80 pupils less the 74 who are 72 kg or lighter on the curve
4. D74, the cumulative frequency read off the curve at a mass of 72 kg

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1. A$h = \frac{1}{5}$, which is the value of $k$ rather than the value of $h$
2. B$h = \frac{2}{5}$, which is the fraction of XP making up RP and not XR
3. C$h = \frac{3}{5}$, from $h = 3k$ used together with $5 - 18k = 7k$
4. D$h = \frac{5}{3}$, from inverting the correct ratio of XR to XP here

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1. A$\begin{pmatrix} -\frac{1}{2} & 0 \\ 0 & -\frac{1}{2} \end{pmatrix}$, scale factor $-\frac{1}{2}$ on both axes
2. B$\begin{pmatrix} -2 & 0 \\ 0 & -2 \end{pmatrix}$, an enlargement of scale factor $-2$ instead
3. C$\begin{pmatrix} -\frac{1}{2} & 0 \\ 0 & \frac{1}{2} \end{pmatrix}$, a stretch reversing only the $x$ direction
4. D$\begin{pmatrix} \frac{1}{2} & 0 \\ 0 & \frac{1}{2} \end{pmatrix}$, an enlargement of scale factor $+\frac{1}{2}$

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1. AA rotation of $180^\circ$ about the centre $(0;-2)$, a half turn
2. BA rotation of $90^\circ$ clockwise about the centre $(0;-2)$
3. CA rotation of $90^\circ$ anticlockwise about the centre $(0;-2)$
4. DA rotation of $90^\circ$ clockwise about the origin $(0;0)$