Mathematics GCSE Examination Instructions and Key Points

Examination Details

• Date: Wednesday, 7 June 2023
• Time: 1 hour 30 minutes
• Paper: 1MA1/2H (Calculator) Higher Tier
• Total Marks: 80

Required Materials

• Ruler (cm and mm)
• Protractor
• Pair of compasses
• Pen and HB pencil
• Eraser
• Calculator
• Formulae Sheet (enclosed)
• Tracing paper (optional)

Instructions for Candidates

• Use black ink or ball-point pen.
• Fill in your name, centre number, and candidate number at the top of the page.
• Answer all questions in the provided spaces.
• Show all stages of your working.
• Diagrams are not precisely drawn unless stated otherwise.
• Calculators may be used (use π as 3.142 unless otherwise stated).

Marking and Time Management

• Total mark for the paper is 80.
• Marks for each question are shown in brackets.
• Use marks as a guide for time management.

Advice

• Read each question carefully.
• Attempt to answer every question.
• Check your answers if time permits.

Key Questions Summary

1. Basic Calculations and Reciprocals

   • Calculate: 25 / 43 x 87 / 6 - 2 / 1 - 2
   • Find the reciprocal of 0.625.

2. Prime Factorization

   • Write 60 as a product of its prime factors.

3. Ratio and Proportion

   • Verify if Helen's calculation of red counters is correct (1 red : 2 blue).

4. Inequalities and Number Lines

   • Greatest integer n for 2 < n < 5.
   • Show inequality 4 < m ≤ 1 on a number line.
   • Solve 25g - 4 < 6 for g.

5. Geometry and Area Calculations

   • Relate the area difference between a triangle and rectangle to find x.

6. Percentage and Ratios in Context

   • Calculate the weight of glass recycled from 800 kg total waste (57% paper and glass).

7. Rounding and Error Intervals

   • Determine the error interval for d rounded to 12.7.

8. Investment Growth Analysis

   • Compare house value appreciation over 2 years between Tamsin and Rachel.

9. Cumulative Frequency and Median Estimation

   • Draw a cumulative frequency graph and estimate the median age.

10. Probability with Biased Dice

    • Estimate the probability of landing on 6 twice.
    • Discuss reliability improvement with increased trials.

11. Simultaneous Equations

    • Solve 2x + 6y = 5 and 3x - 4y = 12 using algebra.

12. Circle Geometry

    • Calculate the circumference of a circle given rectangle dimensions within it.

13. Trigonometry in Triangles

    • Calculate angle BAC in a triangle.

14. Algebraic Manipulations

    • Express given inequality in ax + bx + c form.

15. Quadratic Sequences

    • Find the nth term expression for a sequence.

16. Histogram Interpretation

    • Complete a histogram based on given data.
    • Calculate the total number of students.

17. Iterative Methods

    • Use iteration to solve x^4 - x^2 - 5 = 0.

18. Ratio Problems

    • Solve a + b : b + c = 17 : 20 with given ratios.

19. Right-Angle Triangle Bounds

    • Calculate lower bound for angle x using bounds of side lengths.

20. Vector and Geometry

    • Express vector MT in terms of a and b.

21. Graph Transformations

• Draw transformations of y = f(x).

22. Probability Expressions

    • Derive expression for probability of drawing different colored pens.

23. Similar Triangles and Area Ratios

    • Show area ratio of similar triangles.

24. Composite Shape Area

    • Calculate area of shaded shape formed by octagons.

Additional Information

• Page Annotations: Several pages marked "DO NOT WRITE IN THIS AREA."
• Paper Total Marks: 80
• Ensure all solutions are clearly written and organized.