1. 0.128

M1 t = k/d2

k is any letter except t, d or αA1 k = 12.8or M1 0.2 × 82 = 12.8

[3]

2. 1.25M1 p = k/(q + 2)2 M1 p = (k/(q + 2))2

or p(q + 2)2 = k A1 k2 = 125 or

A1 k = 125 k =

If no marks awardedSC1 5 : k/25 in this form

p : k/100 (colon optional)or SC1 for either5 = k/(3 + 2)2 or 5 = k/52

Allow 5/4[3]

3. 108M1 y = k(x + 2)3 A1 k = 4or M1 y1 / y2 = x1

3 / x23 A1 y1 / 32 = 27/8

[3*]

4. (a) wf = 300000 oe 2M1 wf = k A1 k = 300000

(b) 500 1√[3]

5. 7.5

M1 F = A1 k = 480 B2 30 × 42 = F × 82

[3*]

© Doublestruck & CIE - Licensed to UCSI International School 1

125

2dk

6. (a) o.e M1

k = 4.8 × 52 A1

(b) 30 B1

(c) 10x2 = 120 o.e. M1

3.46 (3.464101…..) A1

(d) x2 × x = 120 o.e. M1

4.93 (4.932424…..) A1

(e) Divided by 4 o.e. B2SC1 for (2x)2y = 120 o.e. seenor a correct calculation using avalue of x. e.g. x = 4, y = 7.5

x = 8, y = 1.875

(f) Increases by 25% o.e. B2SC1 for 1.5625 seen

(g) Division by y M1

Square root M1[13]

7. (i) 1 : 5 000 000 or n = 5 000 000 B2SC1 for 5 000 000 seen in final answeror n = figs 5 o.e. in final answer

(ii) Time = 2hrs 8 mins or 128 (mins) B1

= 2.13(33..) (hours) o.e. s.o.i. B1Implies previous B1

Accept

1580 ÷ their time M1s.o.i. is by correct answer

738 – 742 cso A1www 4 (12.3 seen earns B1M1)

[6]

8. 20 × 100000 ÷ 80 o.e. M1

25 000 or 2.5 × 104 www2 A125 000 seen in final ans. After M0, SC1for figs 25 or 0.00004 final answer

[2]

© Doublestruck & CIE - Licensed to UCSI International School 2

22 =or1

∞xk

yx

y

60128

9. (i) 2400 B2SC1 for figures 24

(ii) 520 000 B2SC1 for figures 52

[4]

10. (a) 8 1

(b) 2*

B1 for , or

(c) 8 1[4]

11. (a) –14 1

(b) 2x3 – 6x2 + 12x – 9 2M1 attempting to double f(x) and –1

(c) 2M1 valid method

[5]

12. (a) x c.a.o. 1

(b) 9x – 4 2*M1 3(3x – 1) – 1

[3]

© Doublestruck & CIE - Licensed to UCSI International School 3

3–5 x

35x

35 x

35 y

21x

13. (a) (x – 3)(x – 1) [= 0] M1

or (x – 22) = 1 or better

1 and 3 A1

(b) Correct first step of rearrangement M1e.g. y + 1 = 2x or x + 1 = 2y or better

o.e. A1not for x = ( )

(c) x2 – 6x + 4 = 0 MA1Can be implied by later work (method marks)

with p = 6 and r = 2 M1√ft if in the form ax2 + bx + c (= 0) with a ≠ 0[ (x – 3)2 – 5 = 0 M1 then x = (±)√5 + 3 M1 is theequivalent for completing the square.]

and q = (–6)2 – 4.1.4 o.e. or 20 M1√Indep.

5.24 c.a.o. www0.76 c.a.o. www A1SC1 for both answers ‘correct’ but not to 2 dp 1(5.236067977, 0.763932022). Can betruncated or correctly rounded

(d) 29 B2SC1 for [ f(–2) =] 15 seen or 2x2 – 8x + 5 o.eseen

(e) (2x – 1)2 – 4(2x – 1) + 3 M1

4x2 – 12x + 8 or correctly factorisedfinal answer A2After A0, SC1 for 4x2 – 12x + 8 seen

[14]

© Doublestruck & CIE - Licensed to UCSI International School 4

2]3.1.4)4[(4 2

21x

rqp

14. (a) (i) –2, B1

(ii) 26, B1

(iii) o.e. B1

(b) M1If switch x and y first thenM1 for x = 2y – 1 or

(f–1(x) =) o.e. www2 A1If use a diagram/chart thenM1 for any evidence of +1 then result ÷ 2

(c) z = x2 + 1z – 1 = x2 M1Correct rearrangement at any stage for x orx2.

(x =) www2 M1Correct sq root at any stage

Ignore +, – or ± in front of

(d) (2x – 1)2 + 1 M1

= 4x2 – 4x + 2 or 2(2x2 – 2x + 1) www 2 A1Final answer but condone one minorfactorising slip if first answer seen

(e) 9 B1

(f) 2(2x – 1) + x2 + 1 (= 0) or better(x2 + 4x – 1 = 0) B1

(x =) ft M1

or better seen

M1

If in form for – 4 and 2 × 1or betterFt their 1, 4 and –1 from quadraticequation seen

(x =) – 4.24, 0.24 c.a.o. www 4(final answers) A1, A1After A0A0, SC1 for – 4.2 or – 4.235 or– 4.236…and 0.2 or 0.235 or 0.236…..The SC1’s www imply the M marks

© Doublestruck & CIE - Licensed to UCSI International School 5

81

)(2

1x

y

21x

1z

1×2)1–)(1(4–4±4– 2

)1)(1(442

rqorp

(g) (i) Straight line with positive gradient and L1

(ii) negative y-interceptU-shape Parabola C1

vertex on positive y-axis V1Dependent

[18]

© Doublestruck & CIE - Licensed to UCSI International School 6

15. (a) 2 B1

(b) M1

M1Dep on 1st M1

o.e. final ans A1www3

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112

3

x

12123

xx

1–22+2

xx

(c)

or xy = 3 + x M1

Alt

x(y – 1) = 3 M1depDep on 1st M1 y(x –1) = 3

o.e. final answer A1

www3 o.e

If answer is x = allow M2

(d) 256 B2B1 for 23 = 8 or 28 seen

(e) M1M for r.h.s. followed by attempt atrecognising 2x = …………………

–3 A1After M0, SC1 for 1/8 o.e seenwww2

[11]

© Doublestruck & CIE - Licensed to UCSI International School 8

13 x

y

13 y

x

xy 31

yx 31

1–3

x

1–3

x

1–3

x

17

2432

x