📝 Grade 9 · Exam Paper 1

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Section A – Number & Surds (14 marks)

1. Write 3.6 × 10⁴ as an ordinary number.[1]

2. Write 0.00052 in standard form.[1]

3. Simplify √75.[2]

4. Rationalise the denominator of 6/√3. Give your answer in the form a√3.[2]

a =

5. Expand and simplify (3 + √5)(3 − √5).[2]

6. A measurement is 8.4 cm correct to 1 decimal place. Write the error interval.[2]

Lower: ≤ x < Upper

7. £1200 is invested at 5% compound interest per year. Find the value after 2 years.[2]

£

8. After a 20% increase, a price is £144. What was the original price?[2]

£
  • Q1: 36000
  • Q2: 5.2×10⁻⁴
  • Q3: 5√3
  • Q4: a=2 (6/√3 = 6√3/3 = 2√3)
  • Q5: 4 (difference of two squares: 9−5=4)
  • Q6: 8.35 ≤ x < 8.45
  • Q7: £1323.00
  • Q8: £120
Section B – Algebra (18 marks)

9. Expand and simplify (x + 4)(x − 3).[2]

x² + x +

10. Factorise x² + 7x + 12.[2]

(x + )(x + )

11. Solve x² − 5x + 6 = 0.[2]

x = or x =

12. Solve the simultaneous equations: 2x + y = 7 and x − y = 2.[3]

x = , y =

13. Solve 3x − 5 > 10. Write your answer as an inequality.[2]

x >

14. The nth term of a sequence is 4n − 1. Find the 20th term.[1]

15. f(x) = 3x + 2. Find f(5).[1]

16. Find f⁻¹(x) when f(x) = 2x − 6. Give f⁻¹(4).[2]

17. Find the gradient of the line joining (1, 3) and (5, 11).[1]

18. Write the equation of the line with gradient 3 passing through (0, −2).[2]

y = x +
  • Q9: x²+x−12 → coeff x=1, const=−12
  • Q10: (x+3)(x+4)
  • Q11: x=2 or x=3
  • Q12: x=3, y=1
  • Q13: x>5
  • Q14: 79
  • Q15: 17
  • Q16: f⁻¹(x)=(x+6)/2 → f⁻¹(4)=5
  • Q17: gradient=2
  • Q18: y=3x−2
Section C – Geometry (12 marks)

19. A right-angled triangle has legs 6 cm and 8 cm. Find the hypotenuse.[2]

cm

20. In a right-angled triangle, the opposite side is 5 cm and hypotenuse is 10 cm. Find the angle (to 1 dp).[2]

°

21. O is the centre of a circle. Angle AOB = 110°. Find the angle in the same segment ACB.[2]

°

22. ABCD is a cyclic quadrilateral. Angle A = 73°. Find angle C.[2]

°

23. A tangent from external point P touches a circle at T. OT = 5 cm, OP = 13 cm. Find PT.[2]

cm

24. Vector a = (3, 4). Find |a|.[2]

  • Q19: 10 cm
  • Q20: sin⁻¹(0.5)=30.0°
  • Q21: 55° (angle at circumference = half angle at centre)
  • Q22: 107° (opposite angles sum to 180°)
  • Q23: PT = √(13²−5²) = √144 = 12 cm
  • Q24: |a| = √(9+16) = 5
Section D – Statistics & Probability (6 marks)

25. A frequency table has class 20–30 with frequency 12. The class width is 10. Find the frequency density.[1]

26. From a bag of 5 red and 3 blue balls, two are drawn without replacement. Find P(both red) as a fraction.[2]

27. P(A)=0.4, P(B)=0.3, A and B are independent. Find P(A and B).[1]

28. The lower quartile of a data set is 32 and the upper quartile is 56. Find the IQR.[1]

29. P(A)=0.6. Find P(A').[1]

  • Q25: 1.2
  • Q26: 5/8 × 4/7 = 20/56 = 5/14
  • Q27: 0.12
  • Q28: 24
  • Q29: 0.4