Tackling the Toughest Questions in the June 2022 Maths Papers for Edexcel, AQA, and OCR

The last question in the AQA June 2022 higher paper involves a detailed analysis of trigonometric values. It is strongly recommended to include a table in your study notes to clearly present this information.

Let's look at the question together!

As this is a 4 marker, try to complete this question in 4 minutes.

If you have memorised the table, you should not find this task too challenging.

In this illustration, we have correlated trigonometric angles with their respective trigonometric values.

We are required to multiply each trigonometric value, so ensure you are familiar with fraction and surd multiplication for this step!

The final step consists of either squaring your answer or multiplying it by itself.

You will be awarded a mark for correctly identifying the trigonometric values, multiplying them, simplifying the result, and presenting your final answer!

Following this, we will examine a more advanced Edexcel question concerning circles, sectors, and area.

As this is a 5 marker, try to complete this question in 5 minutes.

This question is quite intricate, so it's crucial to break it down into manageable parts.

We are provided with the radius of each circle, along with two small shaded segments. Our task is to determine the combined area of these two shaded regions (segments). It's important to note that this assessment does not allow the use of a calculator, so ensure you practice simplifying your calculations.

To simplify the problem visually, I have sketched an equilateral triangle.

Essentially, the area of each segment can be calculated as the sector's area minus the equilateral triangle's area.

The formula for the area of a sector is: angle/360 x (π x r^2)

Keep in mind that in an equilateral triangle, all sides and angles are equal. The sum of all angles in a triangle is 180 degrees, so each angle in the triangle will be 60 degrees (180/3).

By substituting the angle (60 degrees) and the radius (4 cm) into the sector area formula, I obtained the sector's area in terms of π. Next, I computed the area of the equilateral triangle using the formula: 1/2abSinC, where a and b are 4 cm and angle C is 60 degrees.

Referring to the trigonometric table, I simplified the answer for the triangle's area. The final step is to subtract the triangle's area from the sector's area to find the segment's area. Remember that there are two segments, so multiply the segment's area by 2 to get the total shaded area.

We will now examine a challenging problem in the higher OCR Maths exam, focusing on sectors and arc length.

As this is a 5 marker, try to complete this question in 5 minutes.

Given two sectors each with a 60-degree angle are provided in this question.

For the radius of OA:OC, a ratio of 2:3 is given. If OA has a radius of r cm, then OC must have a radius of 1.5r or 3/2r. It is important to review ratios for this scenario.

Now focusing on arc length, the formula is as follows:

angle/360 x 2πr

With an angle of 60 degrees and a radius of r cm for OA and 1.5r for OC.

By applying this, I have calculated the arc length for AB and CD in terms of π and r.

As the question seeks the total length of arc AB and CD, it is necessary to sum both values. Present your answer using π and r, and the question will be successfully solved!

In conclusion, mastering trigonometric values, sectors, and arc lengths is crucial for excelling in higher level maths exams such as AQA, Edexcel, and OCR. By incorporating detailed study notes and practicing complex problems, you can enhance your problem-solving skills and boost your confidence.

For the AQA trigonometry question, remember to use your trigonometric value table to streamline your calculations and aim to complete the 4 marker in 4 minutes. Similarly, for the Edexcel question on circles and sectors, breaking down the problem into manageable parts and applying the correct formulas will help you efficiently tackle the 5 marker. Finally, for the OCR problem involving sectors and arc lengths, understanding ratios and arc length calculations will be key to arriving at the correct answer.

Consistent practice and a thorough understanding of these concepts will not only prepare you for the upcoming exams but also build a strong foundation for future mathematical challenges. Good luck, and keep practicing!