Chapter 9 — English Preparation + Mixed Maths Review

This day is split: ~1.5 hours English, ~1.5 hours Maths review.

PART A: English — Reading Comprehension and Writing Tips

Reading Comprehension Strategy

The English section of the ISMA entrance test typically includes reading comprehension and a writing task. Here is an approach:

Reading Comprehension — SCAN method:
1. Skim the questions FIRST (before reading the passage)
2. Carefully read the passage, underlining key points
3. Answer questions, referring back to specific lines
4. Never leave a blank — always attempt an answer

Question types you may encounter:

• Main idea / purpose of the text
• Vocabulary in context ("What does the word ___ mean in line X?")
• Inference ("What can you conclude from paragraph 3?")
• Author's tone / attitude
• True / False / Not Given
• Short answer / summary writing

Writing Tips

If asked to write an essay, letter, or response:

Structure: Introduction → 2-3 Body Paragraphs → Conclusion

• Use linking words: however, furthermore, in addition, on the other hand, consequently, therefore, in conclusion
• Vary sentence length: mix short punchy sentences with longer complex ones
• Use specific examples to support your points
• Check your work for spelling, punctuation, subject-verb agreement

Common writing tasks:

• Persuasive essay ("Should students wear uniforms?")
• Descriptive writing
• Letter (formal/informal)
• Summary of a passage
• Response to a text

Key Grammar to Review

• Subject-verb agreement (especially with "each", "every", "neither...nor")
• Tenses: present perfect vs past simple
• Conditionals: If + present → will (1st); If + past → would (2nd)
• Passive voice
• Relative clauses (who, which, that, whose)
• Articles (a/an/the)

PART B: Maths Review — Weak Areas

Go through all practice problems from Chapters 1-7. Identify topics where mistakes were made.

Priority Review Checklist

Check off each topic. If you made errors, redo those problems.

• [ ] Index laws (negative and rational indices)
• [ ] Factorisation (especially splitting the middle term)
• [ ] Quadratic formula and completing the square
• [ ] Simultaneous equations (including non-linear)
• [ ] Gradient, equation of a line
• [ ] Trigonometry (SOHCAHTOA + sine/cosine rules)
• [ ] Area of triangle using sine
• [ ] Circle theorems
• [ ] Similar figures (area/volume ratios)
• [ ] Probability (tree diagrams, Venn diagrams)
• [ ] Cumulative frequency and median
• [ ] Arithmetic sequences
• [ ] Standard form
• [ ] Rearranging formulae

Quick Drill: 10 Mixed Problems

1. Simplify $\displaystyle (27x^{6})^{\frac{2}{3}}$

2. Factorise $6x^{2} - x - 12$

3. Solve 5x² − 3x − 1 = 0 (give exact answers)

4. Line passes through (2, 5) and is perpendicular to y = 3x + 1. Find its equation.

5. Triangle: sides 7, 10, angle between them = 65°. Find the area.

6. $P(A) = 0.4, P(B) = 0.3, independent. Find P(A ∪ B).$

7. Arithmetic sequence: u₃ = 11, u₈ = 31. Find u₁₅.

8. Make x the subject: $\displaystyle y = \frac{2x+1}{x-3}$

9. A = k/r². When r = 5, A = 8. Find A when r = 2.

10. Simplify: $\displaystyle \frac{x^{2}-4}{x^{2}+4x+4}$

ANSWERS TO QUICK DRILL

1. $\displaystyle (27)^{\frac{2}{3}} \times (x^{6})^{\frac{2}{3}} = 9x^{4}$

2. a×c = −72. Sum = −1. Numbers: −9 and 8.
$6x^{2}-9x+8x-12 = 3x(2x-3)+4(2x-3) = (3x+4)(2x-3)$

3. $\displaystyle x = \frac{3 \pm \sqrt{9+20}}{10} = \frac{3 \pm \sqrt{29}}{10}$

4. Perpendicular gradient = −1/3. y−5 = −(1/3)(x−2) → y = −(1/3)x + 17/3

5. Area = (1/2)(7)(10)sin65° = 35 × 0.906 = 31.7 cm²

6. $P(A∪B) = 0.4+0.3-0.4(0.3) = 0.58$

7. $\displaystyle d = \frac{31-11}{5} = 4. a = 11-2(4) = 3. u_{15} = 3+14(4) = 59$

8. $y(x-3) = 2x+1 \rightarrow xy-3y = 2x+1 \rightarrow xy-2x = 3y+1 \rightarrow x(y-2) = 3y+1$
$\displaystyle x = \frac{3y+1}{y-2}$

9. $\displaystyle k = 8\times 25 = 200. A = \frac{200}{4} = 50$

10. $\displaystyle \frac{(x+2)(x-2)}{(x+2)^{2}} = \frac{x-2}{x+2}$