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A Level Maths - Exam Questions

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A Level Maths – Exam Questions – Introduction 

Preparing for A Level Maths exams requires practice and a solid understanding of the subject. In this blog post, we will discuss the importance of doing A Level Maths exam questions and share insights from a student’s point of view.

The Value of Doing A Level Maths Exam Questions:

  • Enhances Problem-Solving Skills: Regularly attempting exam questions helps develop critical thinking and problem-solving abilities, which are crucial for success in A Level Maths.
  • Familiarise with Exam Format: Practising exam-style questions helps students become familiar with the structure and format of A Level Maths exams, reducing anxiety and increasing confidence during the actual exam.
  • Identifies Weak Areas: By attempting a variety of questions, students can identify their weaker areas and focus on improving their understanding and skills in those specific topics.
  • Builds Speed and Accuracy: Consistently working on exam questions helps students improve their speed and accuracy, ensuring they can answer questions within the given time constraints.

Effective Strategies for Doing A Level Maths Exam Questions:

  • Start with Basics: Begin by revisiting the fundamental concepts and formulas related to the topic before attempting exam questions. This ensures a strong foundation for solving more complex problems.
  • Understand Marking Schemes: Familiarise yourself with the marking schemes and criteria used in A Level Maths exams. This knowledge can help you structure your answers and maximise your score.
  • Practice Time Management: Simulate exam conditions by setting time limits for solving questions. This practice will help you manage your time efficiently during the actual exam.
  • Review and Learn from Mistakes: After attempting exam questions, carefully review your answers, understand your mistakes, and learn from them. This process will help improve your understanding and prevent repeating similar errors.

Resources for A Level Maths Exam Questions:

  • Past Papers: Utilise past papers from official exam boards to practise a wide range of questions. These papers provide an accurate representation of the type and difficulty level of questions that may appear in A Level Maths exams.
  • Textbooks and Study Guides: Refer to recommended textbooks and study guides that provide comprehensive explanations and practice questions.
  • Online Platforms and Tutoring: Explore online platforms and tutoring services that offer additional resources, practice questions, and personalised guidance tailored to A Level Maths.
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A Level Maths Exam Questions

Q1 


Solution

\begin{aligned} & f(-2)=0 \\ &(-2-4)\left((-2)^2-3(-2)+k\right)-42=0 \\ &-6(10+k)-42=0 \\ &-60-6 k-42=0 \\ &-102=6 k \\ & k=-17 \end{aligned}

Q2


Solution

\begin{aligned} & x^2-10 x+y^2+16 y=80 \\ &(x-5)^2-25+(y+8)^2-64=80 \\ &(x-5)^2+(y+8)^2=169 \\ & \text { i) }(5,-8) \\ & \text { ii) } 13 \end{aligned}

Part b) 

\begin{aligned} &\begin{aligned} x^2 & =5^2+8^2 \\ x & =\sqrt{5^2+8^2} \\ & =\sqrt{89} \end{aligned}\\ &13+\sqrt{89} \end{aligned}

Q3.  


Part a) 

\int_{2.1}^{6.3} \frac{2}{x} d x

Part b) 

$$ \begin{aligned} & {[2 \ln x]_{2.1}^{6.3}} \\ & 2 \ln 6.3-2 \ln 2.1 \\ & 2(\ln 6.3-\ln 2.1) \\ & 2 \ln 3 \end{aligned} $$ $\ln 3^2$ $\ln 9$

Q4. 


Solution

Let $p=2 n+1$ Let $q=2 m+1$ $$ \begin{aligned} p q & =(2 n+1)(2 m+1) \\ & =4 n m+2 n+2 m+1 \\ & =2(2 n m+n+m)+1 \end{aligned} $$

This is a contradiction.

Q5. 


\begin{aligned} & \int v \frac{d u}{d x} d x=u v-\int u \frac{d v}{d x} d x \\ & v=\ln x \quad \frac{d u}{d x}=x^3 \\ & \frac{d v}{d x}=\frac{1}{x} \quad u=\frac{1}{4} x^4 \end{aligned}\begin{gathered} \frac{1}{4} x^4 \ln x-\int \frac{1}{4 x} \cdot x^4 d x \\ \frac{1}{4} x^4 \ln x-\int \frac{1}{4} x^3 d x \\ {\left[\frac{1}{4} x^4 \ln x-\frac{1}{16} x^4+c\right]_1^{e^2}} \\ \left(\frac{1}{4}\left(e^2\right)^4 \ln e^2-\frac{1}{16}\left(e^2\right)^4\right)-\left(\frac{1}{4} \ln 1-\frac{1}{16}\right) \\ \frac{1}{4} e^8(2)-\frac{1}{16} e^8-\left(-\frac{1}{16}\right) \\ \frac{1}{2} e^8-\frac{1}{16} e^8+\frac{1}{16} \\ \frac{7}{16} e^8+\frac{1}{16} \end{gathered}

Q6. 


Solution

\begin{aligned} \sin (A-B) & =\sin A \cos B-\cos A \sin B \\ \cos (A-B) & =\cos A \cos B+\sin A \sin B \\ 2(\sin x \cos 60-\cos x \sin 60) & =\cos x \cos 30+\sin x \sin 30 \\ 2\left(\frac{1}{2} \sin x-\frac{\sqrt{3}}{2} \cos x\right) & =\frac{\sqrt{3}}{2} \cos x+\frac{1}{2} \sin x \\ \sin x-\sqrt{3} \cos x & =\frac{\sqrt{3}}{2} \cos x+\frac{1}{2} \sin x \\ \frac{1}{2} \sin x & =\frac{3 \sqrt{3}}{2} \cos x \\ \sin x & =3 \sqrt{3} \cos x \\ \tan x & =3 \sqrt{3} \end{aligned}

Part b) 

\begin{aligned} \tan (2 \theta+60) & =3 \sqrt{3} \\ 20+60 & =79.1,259.1,439.1 \\ \theta & =9.6^{\circ}, 99.6^{\circ}, \end{aligned}

Doing A Level Maths exam questions is essential for success in the subject. By regularly practising exam-style questions, students can improve their problem-solving skills, become familiar with the exam format, identify weak areas, and build speed and accuracy. Remember to implement effective strategies, utilise available resources, and review mistakes for continuous improvement. Embrace the challenge and let the journey of conquering A Level Maths begin!

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