2026 GCSE Maths Higher Practice Paper 3 – Worked Solutions

2026 GCSE Maths Higher Paper 3 – Worked Solutions

MathsWealth · Higher Tier · Calculator · 80 marks

Note: Original MathsWealth worked solutions for the accompanying practice paper. Not an official Pearson mark scheme.

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MATHSWEALTH · GCSE MATHS

2026 HIGHER · PAPER 3

80 MARKS · 1 HOUR 30 MINUTES · CALCULATOR

1[2 marks]

3.6 × 0.75 = 2.7; 2.7 + 2.4 = 5.1.

Answer: 5.1

2[3 marks]

(a) 7.2 × 10⁻⁴
(b) 14

3[2 marks]

2x=18

x = 9

4[4 marks]

84 = 0.70P

P=84÷0.70=120

£120

5[6 marks]

u_n=7+(n−1)5=5n+2

(a) 5n+2

u₄₀=202

(b) 202

6[4 marks]

(3x+2)(x−1)=40

3x²−x−42=0=(3x−14)(x+3)

x = $\frac{14}{3}$

7[4 marks]

P=$\frac{7}{20}$×$\frac{6}{19}$=$\frac{21}{190}$

$\frac{21}{190}$

8[3 marks]

x²=13²−5²=144

x=12 cm

9[2 marks]

y=3x−4+5

y=3x+1

10[3 marks]

Scale factor=$\frac{15}{9}$=$\frac{5}{3}$

Volume factor=$\frac{125}{27}$

162×$\frac{125}{27}$=750

750 cm³

11[7 marks]

Σf=45,   Σfx=80

Mean=$\frac{80}{45}$=1.777...

1.78 books (3 s.f.)

12[4 marks]

4m=−1 ⇒ m=−$\frac{1}{4}$

−$\frac{1}{4}$

13[3 marks]

3x=12 ⇒ x=4

4−y=1 ⇒ y=3

x=4, y=3

14[6 marks]

Acceleration=$\frac{\mathrm{12-8}}{\mathrm{4-2}}$=2

(a) 2 m/s²

Distance=$\frac{1}{2}$(0+8)(2)+$\frac{1}{2}$(8+12)(2)+$\frac{1}{2}$(12+0)(2)

=8+20+12=40

(b) 40 m

15[2 marks]

$\frac{5}{\mathrm{\surd 3}}$×$\frac{\mathrm{\surd 3}}{\mathrm{\surd 3}}$=$\frac{\mathrm{5\surd 3}}{3}$

$\frac{\mathrm{5\surd 3}}{3}$

16[2 marks]

(x−2)(x−3)≥0

x≤2 or x≥3

17[4 marks]

r²=6²+8²=100

(a) r=10

(x−2)²+(y+1)²=100

(b) (x−2)²+(y+1)²=100

18[5 marks]

1, 5, 13, 29

u₅=2(29)+3=61

u₅=61

19[5 marks]

AB²=72, BC²=72

AB=BC, so it is isosceles.

Area=$\frac{1}{2}$×12×6=36

36 square units

20[3 marks]

2x²+7x−15−(x²−4x+4)

x²+11x−19

21[2 marks]

$\frac{1}{2}$+$\frac{1}{2}$+1=2

2

22[4 marks]

√(x+9) = 9 − √x

x+9 = (9−√x)²

x+9 = 81 − 18√x + x

72 = 18√x

4 = √x

x = 16

x=16

Check: √16 + √25 = 4 + 5 = 9 ✓