Maths Higher Tier Mark Scheme 2015

1. Stem and leaf diagram

(a)

15 | 6 9
16 | 4 5 7 7 8 9
17 | 2 3 6 6 8 9
18 | 0 2 3 8
19 | 0 2

Example of a key: 15 | 6 = 156 cm (3 marks)

(b) 15% (2 marks)


2. Algebra

(a) 36 (1 mark)

(b) x = 2.5 (2 marks)


3. Questionnaire

How many times per week do you use the BMX track in town?

0 - 1

2 - 3

4 - 5

more than 5 (2 marks)


4. Plants

Kirsty's Plants costs £59.75 and Hedge World costs £63. Tom should buy from Kirsty's Plants. (5 marks)


5. Cheese cuboids

x = 12 (3 marks)


6. Scatter graph

(a) Negative correlation OR as the age increases the price decreases (1 mark)

(b) Draw line of best fit to find £6600 approx (2 marks)


7. Transformations

(a) Triangle with vertices at (-3, 3), (-3, 4) and (-1, 4) (2 marks)

(b) Reflection in the line y = x (2 marks)


8. Algebra

(a) 2g - 3h (2 marks)

(b) y(y-2) (1 mark)

(c) p^5 (2 marks)


9. Pencils and pens

3 boxes of pencils
8 packets of pens (3 marks)


10. Conservatory

Yes Mary has £7 more than she needs (5 marks)


11. Dice game

(a) \frac{1}{5} (2 marks)

(b) £10 (3 marks)


12. Parallel lines

Angle BEF = 60 degrees (alternate angles are equal)

Angle REF = x (alternate angles are equal)

x = 40 degrees (angles at a point on a straight line sum to 180 degrees) (4 marks)


13. Rectangles and triangles

48 cm (5 marks)


14. Speed

54 mph (3 marks)


15. Coordinate geometry

(a) (3, 6.5) (2 marks)

(b) No it doesn't as it doesn't lie on the line y=\frac{1}{2}x+5 (3 marks)


16. Cumulative frequency

(a) 4, 20, 56, 80, 94, 100 (1 mark)

(b) Plot graph correctly using endpoints (2 marks)

(c) 48 minutes approx (1 mark)

(d) 18 approx (2 marks)


17. Pentagon and square

18 degrees (4 marks)


18. Graphing inequalities

You should end up with a small triangle as R (4 marks)


19. Sweets

(a) Show quadratic equation (3 marks)

(b) 10 (3 marks)


20. Changing the subject

a=\frac{4p-5}{3+p} (4 marks)


21. Algebraic proof

Correct proof (3 marks)


22. Indices and surds

(a) \frac{1}{8} (1 mark)

(b) k=\frac{3}{2} (1 mark)

(c) 3 (2 marks)


23. Grain

\frac{14}{3} (5 marks)


24. Graph transformations

(a) (i) (0, 5) (1 mark)

(ii) (3, 10) (1 mark)

(iii) (1, 5) (1 mark)

(b) Translation 4 units in the negative y direction (1 mark)