32. Q6(c): Remove brackets and simplify: (4x + 1)²
[2 marks]
Answer:
Working:
33. Q7(a): Factorise fully: 8y - 16
[1 mark]
Answer:
34. Q7(b): Factorise fully: xy² - 2xy
[1 mark]
Answer:
35. Q7(c): Factorise fully: 8y - 16 + xy² - 2xy
[2 marks]
Answer:
Working:
36. Q8(a): Solve for x: 6x + 1 = -2
[2 marks]
Answer:
Working:
37. Q8(b): Solve for x: 5 - 2(x + 3) = 4 - x
[2 marks]
Answer:
Working:
38. Q8(c): Solve for x: 4 - x/3 = 7/2
[2 marks]
Answer:
Working:
39. Q8(d): Solve for x: (9x + 2)/(9x - 2) = 2
[2 marks]
Answer:
Working:
40. Q9: John takes 40 minutes to walk to school and then to run home. When he runs both ways, it takes him 24 minutes. He has one constant speed whenever he walks, and another constant speed whenever he runs. How long would it take him to walk both ways?
[3 marks]
Answer:
Working:
41. Q10(a): You are told that x² - y² = (x + y)(x - y). Use this result (and NOT long multiplication) to find the value of 45² - 15²
[1 mark]
Answer:
42. Q10(b): You are told that x² - y² = (x + y)(x - y). Use this result (and NOT long multiplication) to find the value of 736² - 264²
[1 mark]
Answer:
43. Q10(c): You are told that x² - y² = (x + y)(x - y). Use this result (and NOT long multiplication) to find the value of 1007 × 993
[1 mark]
Answer:
44. Q11: Asif is shopping for a new outfit for a special occasion. He needs a shirt, a pair of trousers and a pair of shoes. If he doesn't buy the shirt, he can get the other items for £115. If he doesn't buy the trousers, he can get the other items for £100. If he doesn't buy the shoes, he can get the other items for £75. How much will he have to pay for all of them?
[3 marks]
Answer:
Working:
45. Q12: In a bag, there are 180 marbles, of which n are red and the others green. A marble is to be drawn randomly from the bag. If 10 more red marbles were added to the bag, the probability of drawing a red would be doubled. Write down and solve an equation in n to work out how many red marbles were originally in the bag.
[4 marks]
Answer:
Working:
46. Q13: A solid cuboid has dimensions 3 cm by 5 cm by 6 cm. A spider at point S (bottom corner of the 6 cm edge on the front face) needs to crawl on the outside of the cuboid to reach a fly at point F (top corner diagonally opposite, at the back of the top face). What is the shortest distance the spider can travel to reach the fly? (Refer to original PDF for figure.)
[3 marks]
Answer:
Working:
47. Q14: A rectangle ABCD has a diagonal line from a point on the top edge (1 cm from corner A along the top) to corner C. The length along the bottom from D is split as 1 cm and 4 cm, making DC = 5 cm. The shaded region consists of a vertical strip on the left of width 1 cm (full height) and the triangle below the diagonal in the remaining portion. Express the shaded area as a fraction of the whole rectangle ABCD. (Refer to original PDF for figure.)
[4 marks]
Answer:
Working:
48. Q15: A rectangular piece of card ABCD has AB = 12 cm and AD = 16 cm, where A is the bottom-left corner, B is top-left, C is top-right, and D is bottom-right. If the card is folded so that C is on top of A, how long is the crease? (Refer to original PDF for figure.)