Level Up Your Edexcel Maths Prep with Challenging Past Paper Problems!

Answer the following

1. (a) Find the highest common factor (HCF) of 84 and 108.

    (b) Two numbers have an HCF of 12 and a least common multiple (LCM) of 240. If one of the numbers is 48, find the other number.(6 marks)

2. Solve the simultaneous equations 2x+3y=12x−2y=−4

3. The diagram shows a triangle ABC where AB=9cm, BC=12cm, and AC=15cm. Prove that △ABC is a right triangle.(5 marks)

4. A triangle has sides of lengths 8 cm, 6 cm, and 10 cm. Calculate the largest angle in the triangle using the cosine rule.(5 marks)

5. The nth term of a sequence is given by: Tn​=3n2−5n+2 

(a) Find the 5th term of the sequence. 

(b) Prove that all terms of the sequence are positive when n>2.(5 marks)

6. The table shows the time (in minutes) that 40 students spent on homework:

Time (minutes)   Frequency 

0≤t<10              6

10≤t<20            12

20≤t<30            14

30≤t<40              5

40≤t<50              3

(a) Calculate the mean time spent on homework.
(b) Draw a histogram to represent the data. (7 marks)

7. A triangle with vertices A(1,2)B(3,2) and C(1,5)C(1, 5)is reflected in the line x = 2. Write down the coordinates of the image of the triangle.(5 marks)

8. A bag contains 3 red balls, 4 green balls, and 5 blue balls. A ball is selected at random.
(a) What is the probability of selecting a green ball?
(b) If two balls are selected without replacement, calculate the probability that both are blue.(6 marks)

9. Given $f(x) = 2x^2 - 3x + 5$:
(a) Calculate $f(3)$.
(b) Solve $f(x) = 0$. (6 marks)

10. A cone has a base radius of 7 cm and a height of 24 cm. Calculate:

(a) The slant height of the cone.
(b) The total surface area of the cone. (7 marks)

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