Q1. Abid is waiting for a bus. The probability that his bus will be early is 0.2 . The probability that his bus will be on time is 0.7 Work out the probability that his bus will be either early or on time. ........................................................... (Total for question = 2 marks) Q2. A box contains four different kinds of chocolates. Debbie takes at random a chocolate from the box. The table shows the probability of Debbie taking an Orange or a Coffee or a Caramel chocolate. (a) Work out the probability that Debbie takes a Strawberry chocolate. ............................... (2) (b) Work out the probability that Debbie takes an Orange chocolate or a Coffee chocolate. ...............................(2) (Total for question = 4 marks) Q3. Here are 8 dominoes. The 8 dominoes are put in a bag.
Transcript
Q1. Abid is waiting for a bus. The probability that his bus will be early is 0.2 .The probability that his bus will be on time is 0.7 Work out the probability that his bus will beeither early or on time.
(Total for question = 2 marks)Q2. A box contains four different kinds of chocolates.Debbie takes at random a chocolate from the box.The table shows the probability of Debbie taking an Orange or a Coffee or a Caramel chocolate.
(a) Work out the probability that Debbie takes a Strawberry chocolate.
...............................(2)
(b) Work out the probability that Debbie takes an Orange chocolate or a Coffee chocolate.
...............................(2) (Total for question = 4 marks)Q3.
Here are 8 dominoes.
The 8 dominoes are put in a bag.
Riaz takes at random a domino from the bag.
(a) Find the probability that he takes a domino with a total of 8 spots or a domino witha total of 9 spots.
(Total for question is 7 marks)Q4. The diagram shows a triangular prism with a horizontal rectangular base ABCD.AB = 10 cm. BC = 7 cm.M is the midpoint of AD.The vertex T is vertically above M.MT = 6 cm.
Calculate the size of the angle between TB and the base ABCD.
Give your answer correct to 1 decimal place.
.............................................°(Total for question = 4 marks)
Q5. Here are two supermarket price tickets.
The two supermarket price tickets are mathematically similar.The area of the smaller ticket is 7 cm2.Calculate the area of the larger ticket.
(Total for question = 6 marks)Q9. Jomo invested an amount of money at 4% per annum compound interest.At the end of 2 years, the value of his investment was £3380 How much of the £3380 was interest?
Fern puts the counter back into the bag.Then Rajan takes at random one of the ten counters from the bag.He does not put the counter back into the bag.He then takes at random a second counter from the bag.
(b) Calculate the probability that 3 is the number on each of the two counters he takes.
Q24. The incomplete histogram and table give information about the ages of people living ina village.
(i) Use the histogram to complete the table.
(ii) Use the table to complete the histogram.
(Total for question = 4 marks)Q25. The histogram shows information about the times, t hours, for which some cars were leftin a car park.
Calculate an estimate for the number of cars which were left in the car park for between4.5 hours and 8 hours.
...............................
(Total for question = 3 marks)
Q26. There are 31 students in a class.The only languages available for the class to study are French and Spanish.17 students study French. 15 students study Spanish. 6 students study neither French nor
Spanish. Using a Venn diagram, or otherwise, work out how many students study only onelanguage.
Q27. A, B and C are three sets. A ∩ B = ∅ and C ⊂ A
(a) Complete the Venn diagram to show the sets B and C(2)
(b) On the Venn diagram, shade the region that represents A ∩ C ′(1)
(Total for question = 3 marks)Q28. The Venn diagram shows a universal set and 3 sets A, B and C.
2, 4, 7, 3, 6 and 10 represent numbers of elements.
Find (i) n (A ∪ B) .............................. (ii) n (B′) ............................... (iii) n (A ∩ C′) ......................
(iv) n (B′ ∩ C′) ...............................(Total for question = 4 marks)
Q29. A garage tests cars for faults. There are three types of fault - braking, steering and lighting.A car fails the test if it has one or more of these three types of fault.
Last week, 11 cars had braking faults 9 cars had steering faults 7 cars had lighting faultsno car had both steering faults and lighting faults 2 cars had both braking faults and steering faults3 cars had both braking faults and lighting faults. By drawing a Venn Diagram, or otherwise, find thenumber of cars which failed the test last week.
Q30. A group of students take a test.The group consists of 12 boys and 8 girls. The mean mark for the boys is 18The mean mark for the girls is 16.5 Calculate the mean mark for the whole group.
The diagram shows a vertical flagpole in Chennai, India.The point A is at the top of the flagpole.The point B is at the foot of the flagpole.There is a platform at the point D on the flagpole.
B and C are points on horizontal ground.
AD = 16.5 m The angle of elevation of A from C is 69°The angle of elevation of D from C is 59° Calculate the height, AB, of the flagpole.Give your answer correct to 3 significant figures.
In the isosceles triangle ABC,AB = ACangle B = (3x + 32)°angle C = (87 − 2x)°
Work out the value of x. Show clear algebraic working.
x = ...........................................................
(Total for question = 4 marks)
Q38. John throws a biased coin 120 times. It shows heads 90 times.(a) John throws the coin once more. Work out an estimate for the probability that the coin shows tails.
Carly throws the same coin 200 times.(b) Work out an estimate for the number of times the coin shows tails.
...........................................................(2) (Total for question = 4 marks)
Q39. Bill and Jo play some games of table tennis.The probability that Bill wins the first game is 0.7When Bill wins a game, the probability that he wins the next game is 0.8When Jo wins a game, the probability that she wins the next game is 0.5
The first person to win two games wins the match.(a) Complete the probability tree diagram.
(3)(b) Calculate the probability that Bill wins the match.
...........................................................(3) (Total for question = 6 marks)
Q40.
AB is parallel to DE. The lines AE and BD intersect at C. AB = 7.5 cm, AC = 7 cm, CD = 5.2 cm,CE = 5.6 cm.
(3)(Total for question = 7 marks)Q41. Peter and John play two games of badminton against each other.For each game, the probability that Peter wins is 0.15
(a) Complete the probability tree diagram.
(3)(b) Calculate the probability that Peter wins both games.
The table shows information about the number of letters in the first name of each of50 people.
(i) Work out the mean number of letters in the first names of the 50 people.
...........................................................(ii) One more person joins the 50 people.The mean number of letters in the first names of the 51 people is less than the meannumber of letters in the first names of the 50 people.
Write down the greatest number of letters in the first name of the person who joinsthe group.
Q44. The histogram shows information about the times, t minutes, patients spent at a doctors'surgery on one day.No patient spent more than 40 minutes at the surgery.
(a) Calculate the percentage of the patients who spent between 25 and 40 minutes at thesurgery.
