GCSE Bitesize examinations
General Certificate of Secondary Education
MATHEMATICS
Higher Tier
Paper 1 Non-calculator
Marking scheme
Unless otherwise stated, correct answers only should be accepted.
1
Answer all questions in the spaces provided
1. (a) 432 = 33 × 2 4
522 = 2 × 3² × 29 (1 mark)
(b) HCF = 18 (1 mark)
2. AC = 8 cm (2 marks)
3. (a) (i) 4n – 1 (1 mark)
1
(ii) (1 mark)
n2
(iii) n 2 + 3 or any equivalent (1 mark)
(b) 406 (2 marks)
1 mark for showing 3, 16, 81, 406
4, (a) (2 marks)
(b) (2 marks)
2
5. (a) 0.375 (1 mark)
(b) x = 0.24242424… (1)
100x = 24.24242424…(2)
(2) - (1) 99x = 24
24
x= (2 marks)
99
8
x= (1 mark)
33
(You must show working for first two marks)
6. (a) 3a 2 b(a + 4b + 3a 3 b 2 ) (1 mark)
−3
(b) x =2, x= (2 marks)
2
1 mark for showing (2x+ 3)(x− 2)
−3
(c) x= (2 marks)
2
1 mark for showing 3x + 2 + 3x - 3 = 4x - 4 or equivalent removal of
quotient.
7. (a) Add a bar to the histogram showing the frequency density for the interval
350-499.
1 mark for showing 0.333 or 1/3 (2 marks)
(b) 1 mark for showing frequency = width x frequency density (3 marks)
Price £000s 0-99 100-249 250-299 300-349 350-499
Frequency 10 60 40 45 50
3
8. Using a ruler and pair of compasses only, and making sure you leave all
construction lines visible:
(a) Construct a triangle of side lengths 4cm, 5cm and 6cm (2 marks)
or 2 marks for side lengths to within ± 2mm
(b) Construct a square of side length 5cm (3 marks)
or 2 marks for side lengths to within ± 2mm
9.
(2 marks)
(1 mark for or )
4
−9
10. (a) x≤ or equivalent (1 mark)
2
(b) –3, –2, –1, 0, 1, 2, 3 (1 mark)
(c) –2, –1, 0, 1, 2, 3, 4, 5, 6, 7 (2 marks)
11. (a) Either:
23 7
−
5 3
69 35
= − (1 mark)
15 15
34
= (1 mark)
15
4
= 2 (1 mark)
15
Or:
3 1
2+( − ) (1 mark)
5 3
9 5
= 2+( − ) (1 mark)
15 15
4
= 2 (1 mark)
15
9 3
(b) ÷ (1 mark)
4 5
9 5
= × (1 mark)
4 3
15
=
4
3
= 3 (1 mark)
4
5
12. (a) (i)
1 mark if 2 or less incorrect. (2 marks)
1
(ii) 8 or equivalent (2 marks)
5
(b) or equivalent (3 marks)
12
13. (a) Angle ACB 37.5° (1 mark)
(b) Angle BDA 37.5° (2 marks)
(c) Angle ABD 112.5° (2 marks)
1 mark for indicating triangle ABD and 180°
14.
(a) Are you in favour of the new road? (2 marks)
1 mark only for each suggestion biased towards either side.
(b) (3 marks)
(i) Range of different places, ie different villages and town
(ii) Different jobs
(iii) Different types of housing or position in each place chosen.
Reasonable equivalents acceptable
(c) 3210 (1 mark)
6
1
15. (a) (1 mark)
7
(b) 212 (1 mark)
(c) 49 (2 marks)
16. (a) 2 x(x +1) + 2(x +1)(x + 2) + 2x(x + 2) or any equivalent (3 marks)
1 mark for showing x(x + 1) or (x + 1)(x + 2) or x(x + 2)
(b) Length of shortest side = 2 units (3 marks)
OR
1 mark for showing x 2 + 2 x − 8 = 0 or equivalent
1 mark for showing ( x +4)( x −2) = 0
7
17. (a) EF = - b (1 mark)
(b) DB = –( b + c) or - b - c (1 mark)
(c) FD = a + b (1 mark)
(d) AO = ½ ( a + b + c ) (2 marks)
or a + c
or b
1 mark each, maximum 2
18. x = −1 ± 5
1 mark for a = 1 b=2 c=-4
(4 marks)
1 mark for showing:
− 2 x ± (4 + 16)
2
or 1 mark for showing 5
8
19. 3 marks for one error, 2 marks for 2 errors, 1 mark for 3 errors and 0 marks for
more errors. (4 marks)
Function Graph
y = ( x − 1) 2 B
y = x + 5x + 6
2
A
y = 2x +1
2
D
y = x2 − x − 6 C
y = 2( x − 2) 2
E
20. (a) 2.310 x 103 (2 marks)
(1 mark for 2310 seen)
(b) 5 x 10-2 (3 marks)
1
(1 mark for or 0.05)
20
(c) 250 000 (2 marks)
(1 mark for showing 2.5 x 105)
9
21. (a) 60° (2 marks)
1 mark for showing 4π = x ο / 360 × 24π
(b) 2.5 cm (2 marks)
⎛−3 −4⎞
22. Solutions: (0,1) ⎜ , ⎟ (3 marks)
⎝ 5 5 ⎠
1 mark for showing x 2 + y 2 = 1 , y = 3 x + 1
−3
1 mark for showing either 10 x 2 + 6 x = 0 or x =
5
10
