1. 1
   Triangle $PQR$ is right-angled at $Q$. $PQ = 9$ cm and $QR = 12$ cm.

   (a)

   Calculate the length of $PR$.

   [1 mark]

   • A$21$ cm
   • B$15$ cm
   • C$225$ cm
   • D$10.8$ cm

   (b)

   Calculate $\tan(\angle QPR)$, giving your answer as a fraction in its simplest form.

   [1 mark]

   • A$\frac{3}{5}$
   • B$\frac{3}{4}$
   • C$\frac{4}{5}$
   • D$\frac{4}{3}$

   (c)

   The exact trigonometric values below are used to check calculator answers for triangles such as $PQR$. What is the exact value of $\cos(60^\circ)$?

   [1 mark]

   • A$1$
   • B$\frac{\sqrt{3}}{2}$
   • C$\frac{1}{2}$
   • D$\frac{\sqrt{2}}{2}$

   Total for question 1: 3 marks

2. 2
   A ladder of length $6.5$ m rests against a vertical wall, making a right angle with the level ground at its foot. The foot of the ladder is $2.5$ m from the base of the wall.

   (a)

   Calculate the height above the ground that the ladder reaches on the wall.

   [2 marks]

   (b)

   Calculate the angle between the ladder and the ground, giving your answer to 1 decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In triangle $ABC$, angle $ABC = 90^\circ$. $AB = 7$ cm and angle $BAC = 35^\circ$.

   (a)

   Show that $BC = 4.90$ cm, correct to 3 significant figures.

   [3 marks]

   (b)

   Hence find the length of $AC$, giving your answer to 3 significant figures.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A cuboid $ABCDEFGH$ has rectangular base $ABCD$, with vertical edges $AE$, $BF$, $CG$ and $DH$. $AB = 12$ cm, $BC = 5$ cm, and the vertical edge $CG = 8$ cm. All edges meet at right angles.

   (a)

   Calculate the length of the diagonal $AC$ of the base $ABCD$, giving your answer to 3 significant figures.

   [4 marks]

   (b)

   Show that the length of the space diagonal $AG$ is $15.3$ cm, correct to 3 significant figures.

   [4 marks]

   (c)

   Calculate the angle between the diagonal $AG$ and the base $ABCD$, giving your answer to 1 decimal place.

   [5 marks]

   Total for question 4: 13 marks

End of questions