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)
(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 :
(a) Calculate .
(b) Solve . (6 marks)
(a) Calculate .
(b) Solve . (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)
🖋Online Maths Tutor, Dubai(b) The total surface area of the cone. (7 marks)