Write down the size of angle BAF.

Hence or otherwise find the area of the triangular end of the chocolate bar.

Find the total surface area of the chocolate bar.

It is known that 1 cm³ of this chocolate weighs 1.5 g. Calculate the weight of the chocolate bar.

A different chocolate bar made with the same mixture also has the shape of a triangular prism. The ends are triangles with sides of length 4 cm, 6 cm and 7 cm.

Show that the size of the angle between the sides of 6 cm and 4 cm is 86.4° correct to 3 significant figures.

The weight of this chocolate bar is 500 g. Find its length.

60°     (A1)

[1 mark]

Unit penalty (UP) applies in this part

\({\text{Area}} = \frac{{6 \times 6 \times \sin 60^\circ }}{2}\)     (M1)(A1)

(UP)     = 15.6 cm²   \((9 \sqrt{3})\)     (A1)(ft)(G2)

Note: Award (M1) for substitution into correct formula, (A1) for correct values. Accept alternative correct methods.

[3 marks]

Unit penalty (UP) applies in this part

\({\text{Surface Area}} =15.58 \times 2 + 23 \times 6 \times 3\)     (M1)(M1)

Note: Award (M1) for two terms with 2 and 3 respectively, (M1) for \(23 \times 6\) (138).

(UP)     Surface Area = 445 cm²     (A1)(ft)(G2)

[3 marks]

Unit penalty (UP) applies in this part

\({\text{weight}} = 1.5 \times 15.59 \times 23\)     (M1)(M1)

Note: Award (M1) for finding the volume, (M1) for multiplying their volume by 1.5.

(UP)     weight = 538 g     (A1)(ft)(G3)

[3 marks]

\(\cos \alpha  = \frac{{{4^2} + {6^2} - {7^2}}}{{2 \times 4 \times 6}}\)     (M1)(A1)

Note: Award (M1) for using cosine rule with values from the problem, (A1) for correct substitution.

\(\alpha = 86.41…\)     (A1)

\(\alpha = 86.4^{\circ}\)     (AG)

Note: 86.41… must be seen for final (A1) to be awarded.

[3 marks]

Unit penalty (UP) applies in this part

\(l \times \frac{{4 \times 6 \times \sin 86.4^\circ }}{2} \times 1.5 = 500\)     (M1)(A1)(M1)

Notes: Award (M1) for finding an expression for the volume, (A1) for correct substitution, (M1) for multiplying the volume by 1.5 and equating to 500, or for equating the volume to \(\frac{500}{1.5}\).

If formula for volume is not correct but consistent with that in (c) award at most (M1)(A0)(ft)(M1)(A0).

(UP)     l = 27.8 cm     (A1)(G3)

[4 marks]

It was pleasing to show candidate working throughout this question. Follow through marks could be awarded when incorrect answers were given. Many candidates incorrectly calculated the weight of the chocolate bar by multiplying the surface area by 1.5g. Also a large number of students incorrectly used the formula for the volume of a pyramid rather than for a prism. Most candidates were successful in their use of the cosine rule but did not give the answer before it was rounded to 86.4, resulting in the loss of the final A mark. The last part acted as a clear discriminator, very few students were able to find the correct length of the new chocolate bar. Most students used units correctly.

It was pleasing to show candidate working throughout this question. Follow through marks could be awarded when incorrect answers were given. Many candidates incorrectly calculated the weight of the chocolate bar by multiplying the surface area by 1.5g. Also a large number of students incorrectly used the formula for the volume of a pyramid rather than for a prism.Most candidates were successful in their use of the cosine rule but did not give the answer before it was rounded to 86.4, resulting in the loss of the final A mark. The last part acted as a clear discriminator, very few students were able to find the correct length of the new chocolate bar. Most students used units correctly.

It was pleasing to show candidate working throughout this question. Follow through marks could be awarded when incorrect answers were given. Many candidates incorrectly calculated the weight of the chocolate bar by multiplying the surface area by 1.5g. Also a large number of students incorrectly used the formula for the volume of a pyramid rather than for a prism. Most candidates were successful in their use of the cosine rule but did not give the answer before it was rounded to 86.4, resulting in the loss of the final A mark. The last part acted as a clear discriminator, very few students were able to find the correct length of the new chocolate bar. Most students used units correctly.

It was pleasing to show candidate working throughout this question. Follow through marks could be awarded when incorrect answers were given. Many candidates incorrectly calculated the weight of the chocolate bar by multiplying the surface area by 1.5g. Also a large number of students incorrectly used the formula for the volume of a pyramid rather than for a prism. Most candidates were successful in their use of the cosine rule but did not give the answer before it was rounded to 86.4, resulting in the loss of the final A mark. The last part acted as a clear discriminator, very few students were able to find the correct length of the new chocolate bar. Most students used units correctly.

It was pleasing to show candidate working throughout this question. Follow through marks could be awarded when incorrect answers were given. Many candidates incorrectly calculated the weight of the chocolate bar by multiplying the surface area by 1.5g. Also a large number of students incorrectly used the formula for the volume of a pyramid rather than for a prism. Most candidates were successful in their use of the cosine rule but did not give the answer before it was rounded to 86.4, resulting in the loss of the final A mark. The last part acted as a clear discriminator, very few students were able to find the correct length of the new chocolate bar. Most students used units correctly.

It was pleasing to show candidate working throughout this question. Follow through marks could be awarded when incorrect answers were given. Many candidates incorrectly calculated the weight of the chocolate bar by multiplying the surface area by 1.5g. Also a large number of students incorrectly used the formula for the volume of a pyramid rather than for a prism. Most candidates were successful in their use of the cosine rule but did not give the answer before it was rounded to 86.4, resulting in the loss of the final A mark. The last part acted as a clear discriminator, very few students were able to find the correct length of the new chocolate bar. Most students used units correctly.