1 Calculate the product of 0.1987 and 0.3. Round off the answer correct to two significant figures. flag bookmark A 0.05 B 0.059 C 0.06 D 0.060 $0.1987 \times 0.3 = 0.05961$. The first significant figure is 5; to two significant figures we keep 5 and 9, and the next digit 6 rounds the 9 up: 0.060 (the final 0 is needed to show two significant figures).
2 Given that $100706_8 = p(8^5) + 7(8^q) + 6(8^r)$. Which of the following are the correct values of $p$, $q$ and $r$? flag bookmark A $p = 1,\ q = 2,\ r = 0$ B $p = 5,\ q = 3,\ r = 1$ C $p = 1,\ q = 3,\ r = 1$ D $p = 5,\ q = 2,\ r = 0$ T4 Chapter 2.1b Determining the Number Value of a Number in Various Bases $100706_8 = 1(8^5) + 0(8^4) + 0(8^3) + 7(8^2) + 0(8^1) + 6(8^0)$. So $p = 1$, $q = 2$ and $r = 0$.
3 $$\frac{0.0000086 - 2.4 \times 10^{-7}}{0.03} =$$ flag bookmark A $2.864 \times 10^{-4}$ B $2.787 \times 10^{-4}$ C $2.859 \times 10^{-3}$ D $2.866 \times 10^{-3}$ $0.0000086 - 0.00000024 = 0.00000836$. Then $0.00000836 \div 0.03 = 0.000278\,67 \approx 2.787 \times 10^{-4}$.
4 Given that $R(-12, 0)$ and $S$ is located on the $y$-axis, 16 units below the $x$-axis. State the midpoint of the straight line $RS$. flag bookmark A $(-6, 8)$ B $(-6, -8)$ C $(6, -8)$ D $(6, 8)$ $S$ is on the $y$-axis 16 units below the $x$-axis, so $S(0, -16)$. Midpoint $= \left(\frac{-12 + 0}{2}, \frac{0 + (-16)}{2}\right) = (-6, -8)$.
5 Diagram 1 shows two circles with centres $O$ and $V$ respectively. $PQRS$ is a common tangent to both circles. Calculate the value of $x + y$. flag bookmark A 139° B 149° C 152° D 154° The radius $VR$ is perpendicular to the tangent, so $\angle VRT = 90° - 62° = 28°$. $VR = VT$, so $\angle VTR = 28°$. $VU = VT$, so $\angle VTU = \angle VUT = 13°$. Hence $x = 13° + 28° = 41°$. In triangle $UVT$, $\angle UVT = 180° - 26° = 154°$; in triangle $RVT$, $\angle RVT = 180° - 56° = 124°$, so $\angle OVR = 360° - 154° - 124° = 82°$. In quadrilateral $OQRV$, $\angle OQR = \angle QRV = 90°$, so $y = 360° - 90° - 90° - 82° = 98°$. $x + y = 41° + 98° = 139°$.
6 Diagram 2 shows four congruent polygons, $J$, $K$, $L$ and $M$, under a rotation about the centre $O$. Which of the following is the correct rotation pair? flag bookmark A Object $J$, 90° anticlockwise, image $K$ B Object $M$, 90° anticlockwise, image $J$ C Object $L$, 270° clockwise, image $M$ D Object $K$, 270° clockwise, image $J$ $J$ is upper right, $K$ lower right, $L$ lower left and $M$ upper left of $O$. Turning $K$ through 90° anticlockwise brings it up to $J$, and 90° anticlockwise is the same as 270° clockwise, so "$K$, 270° clockwise, $J$" is correct. (90° anticlockwise takes $J$ to $M$, not $K$; $M$ to $L$, not $J$; and $L$ to $K$, not $M$.)
7 Given that the areas of the object and the image under an enlargement are 63 cm$^2$ and 7 cm$^2$ respectively. Calculate the scale factor of the enlargement. flag bookmark A $\frac{1}{9}$ B $\frac{1}{3}$ C 3 D 9 T5 Chapter 5.2d Relation Between Area of Image and Area of Object Under Enlargement Area of image = $k^2 \times$ area of object: $7 = k^2 \times 63$, so $k^2 = \frac{1}{9}$ and $k = \frac{1}{3}$ (the image is smaller).
8 Diagram 3 shows two triangles $PQR$ and $JKT$. Which of the following is correct if triangles $PQR$ and $JKT$ are congruent? flag bookmark A $\angle PQR = \angle JTK$ B $\angle PQR = \angle TJK$ C $\angle PRQ = \angle JTK$ D $\angle PRQ = \angle TJK$ T5 Chapter 5.1a Congruency and the Properties of Triangle Congruency The double tick marks show $PQ = KT$ and the single tick marks show $QR = JK$. So $Q \leftrightarrow K$, $P \leftrightarrow T$ and $R \leftrightarrow J$. Corresponding angles are equal: $\angle PRQ = \angle TJK$.
9 A quadratic function $f(x) = ax^2 + bx + c$, where $a < 0$, passes through $(4, 0)$ and $(-6, 0)$. State the equation of the quadratic function $f(x)$. flag bookmark A $f(x) = -x^2 - 2x - 24$ B $f(x) = -x^2 + 2x + 24$ C $f(x) = -x^2 - 2x + 24$ D $f(x) = -x^2 + 2x - 24$ T4 Chapter 1.1g Roots of a Quadratic Equation The roots are 4 and $-6$, and $a < 0$: $f(x) = -(x - 4)(x + 6) = -(x^2 + 2x - 24) = -x^2 - 2x + 24$.
10 Given that $$3^2 p^6 q^x \times \left(\frac{p^{-5} q^4}{p^3}\right) = \frac{9}{p^y q^3}$$ Calculate the value of $x$ and of $y$. flag bookmark A $x = -7,\ y = 4$ B $x = -7,\ y = 2$ C $x = 1,\ y = -4$ D $x = 7,\ y = -2$ Left side $= 9p^{6 - 5 - 3} q^{x + 4} = 9p^{-2} q^{x + 4}$. Right side $= 9p^{-y} q^{-3}$. Comparing powers: $-2 = -y$, so $y = 2$; $x + 4 = -3$, so $x = -7$.