Question
Diagrams 1 to 4 show a sequence of shapes made up of lines and dots at the intersections of lines.
(a) (i) Complete the table showing the number of dots in each diagram.
| Diagram | 1 | 2 | 3 | 4 | 5 | 6 |
| Dots | 3 | 8 | 13 |
Answer/Explanation
Ans:
| Diagram | 1 | 2 | 3 | 4 | 5 | 6 |
| Dots | 3 | 8 | 13 | 18 | 23 | 28 |
(ii) Write down the rule for continuing the sequence of dots.
Answer/Explanation
Ans: Add 5 oe
(iii) Write down an expression, in terms of n, for the number of dots in Diagram n.
Answer/Explanation
Ans: 5n – 2 oe
(iv) Find the number of dots in Diagram 15.
Answer/Explanation
Ans: 73
(b) The dots are joined by sloping lines and horizontal lines.
(i) Diagram 1 has 2 sloping lines and Diagram 2 has 6 sloping lines.
Find the number of sloping lines in Diagrams 3 and 4.
Answer/Explanation
Ans: 10 14
(ii) Write down an expression, in terms of n, for the number of sloping lines in Diagram n.
Answer/Explanation
Ans: 4n – 2 oe
Question
(a) One day a survey is taken of the ages of 120 children at a fairground.
The results are shown in the frequency table.
(i) On the grid, draw a bar chart for this data.
Complete the scale on the frequency axis.
Answer/Explanation
Ans: Correct diagram with scale
(ii) What is the modal age group?
Answer/Explanation
Ans: 10 to 12 cao
(iii) One of the 120 children is chosen at random.
Write down the probability that the child is aged 4 to 6.
Answer/Explanation
Ans: \(\frac{19}{120}\) or 0.158[3….] or 15.8[3……]%
(b) Lalia says the probability of taking a yellow bead from a bag containing yellow beads and black beads is \(\frac{7}{5}.\)
Explain why \(\frac{7}{5}\) cannot be a correct probability
Answer/Explanation
Ans: Probability must be between 0 and 1 oe
(c) Another bag contains 9 green marbles and 11 red marbles.
A marble is taken at random.
Write down the probability that the marble is
(i) green,
Answer/Explanation
Ans: \(\frac{9}{20}\) or 0.45 or 45%
(ii) blue.
Answer/Explanation
Ans: 0 oe
Question
120 people are asked how they travel to work.
The pie chart shows the results.
(a) (i) Show that 45 people travel by car.
Answer/Explanation
Ans: [Car angle =] 135 (± 2°)
135 ÷ 360 × 120 ( = 45 )
(ii) A person is chosen at random from the 120 people.
Find the probability that this person travels to work by bus or by car
Answer/Explanation
Ans: 2/3 or value from 0.658 to 0.675
(b) One year later, the same 120 people were again asked how they travel to work.
Here is the information.
(i) Use this information to complete the following equation, in terms of x.
………………………………………………………………………………… = 120
Answer/Explanation
Ans: x + 31 + x + 17 + 2x [= 120] or better
(ii) Solve the equation to fi nd the number of people who walk to work.
Answer/Explanation
Ans: 18 cao
Question
(a) 120 children take part in an athletics competition.
(i) Complete the table to show the number of children in each group.
| Girls | Boys | Total | |
| Age 15 | 65 | ||
| Age 16 | 44 | ||
| Total | 70 | 120 |
Answer/Explanation
Ans:
| Girls | Boys | Total | |
| Age 15 | 26 | 39 | 65 |
| Age 16 | 44 | 11 | 55 |
| Total | 70 | 50 | 120 |
(ii) One child is selected at random.
Find the probability that it is a girl aged 16.
Give your answer as a fraction in its lowest terms.
Answer/Explanation
Ans: \(\frac{11}{30}oe\)
(iii) Write down the ratio number of girls aged 15: number of boys aged 15.
Give your answer in its simplest form.
Answer/Explanation
Ans: 2 : 3 cao
(b) Here are the distances, in metres, recorded in the boys’ shot putt.
9.23 6.21 9.86 8.64 7.15 7.72 9.01 7.34 6.53 6.89
(i) Find the median.
Answer/Explanation
Ans: 7.53 m
(ii) Find the range.
Answer/Explanation
Ans: 3.65 m
(iii) Another boy was a late entry to the competition.
After his attempt, the range increased by 20cm.
Work out the two possible distances of his attempt.
Answer/Explanation
Ans: 10.06 m or 6.01 m
Question
(a) 120 children take part in an athletics competition.
(i) Complete the table to show the number of children in each group.
| Girls | Boys | Total | |
| Age 15 | 65 | ||
| Age 16 | 44 | ||
| Total | 70 | 120 |
Answer/Explanation
Ans:
| Girls | Boys | Total | |
| Age 15 | 26 | 39 | 65 |
| Age 16 | 44 | 11 | 55 |
| Total | 70 | 50 | 120 |
(ii) One child is selected at random.
Find the probability that it is a girl aged 16.
Give your answer as a fraction in its lowest terms.
Answer/Explanation
Ans: \(\frac{11}{30}oe\)
(iii) Write down the ratio number of girls aged 15: number of boys aged 15.
Give your answer in its simplest form.
Answer/Explanation
Ans: 2 : 3 cao
(b) Here are the distances, in metres, recorded in the boys’ shot putt.
9.23 6.21 9.86 8.64 7.15 7.72 9.01 7.34 6.53 6.89
(i) Find the median.
Answer/Explanation
Ans: 7.53 m
(ii) Find the range.
Answer/Explanation
Ans: 3.65 m
(iii) Another boy was a late entry to the competition.
After his attempt, the range increased by 20cm.
Work out the two possible distances of his attempt.
Answer/Explanation
Ans: 10.06 m or 6.01 m
Question
Javier went to a carnival with his friends.
(a) He played five games of darts.
These are his scores.
160 58 45 82 125
(i) Work out his mean score.
(ii) Find the range.
(b) The 5000 tickets for the carnival are different colours.
The table shows the number of tickets of each colour.
| Colour of ticket | Red | Green | Blue | Pink | White |
| Number of tickets | 370 | 560 | 1800 | 1320 | 950 |
A ticket is picked at random.
Find the probability that this ticket is Blue.
(c) Five different types of food are sold at the carnival.
Javier chooses one of these types of food.
The table shows the probability that he chooses each type of food.
| Type of food | Curry | Fries | Pasta | Burger | Salad |
| Probability | 0.15 | 0.23 | 0.4 | 0.07 |
Complete the table.
(d) Javier hires a four-seater bike.
The hire cost is $8.50 for the first hour and then $7.75 for each extra hour.
Calculate the cost of hiring the bike for 5 hours.
$ …………………………………………
(e) The table shows the number of drinks sold by one stall at the carnival.
| Drink | Number sold |
| Tea | 70 |
| Orange | 60 |
| Water | 120 |
| Coffee | 180 |
| Smoothie | 40 |
Draw a bar chart to show this information.
Complete the scale on the frequency axis.
Answer/Explanation
Answer:
(a) (i) 94
(ii) 115
(b) \(\frac{1800}{5000}\) oe isw
(c) [0].15
(d) 39.5[0]
(e) Correct bar chart
Question
(a) Juan and his family fly from London to Rio de Janeiro.
(i) The plane departs at 10 20 and arrives in Rio de Janeiro 11 hours 40 minutes later.
The local time in Rio de Janeiro is 5 hours behind the local time in London.
Work out the time in Rio de Janeiro when the plane arrives.
(ii) The total cost of the plane tickets is 3500 pounds (£).
The exchange rate is £1 = 4.45 Brazilian Real.
Calculate the cost of the tickets in Brazilian Real.
………………………………… Real
(b) (i) Juan and his family go to a soccer match.
He buys 2 adult tickets and 2 child tickets.
The price of an adult ticket is 660 Brazilian Real.
The price of a child ticket is \(\frac{2}{3}\) of the price of an adult ticket.
Calculate the total cost of the tickets.
………………………………… Real
(ii) The length, x metres, of the soccer pitch is 105m, correct to the nearest metre.
Complete the statement about the value of x.
……………………………… \(\leq \) x < ………………………………
(c) The table shows how Juan and his family spent their time in Rio de Janeiro.
(i) Complete the table.
(ii) Complete the pie chart.
Answer/Explanation
Answer:
(a) (i) 1700 or 5pm
(ii) 15 575
(b) (i) 2200
(ii) 104.5
105.5
(c) (i) 30
20 72
(ii) Correct pie chart
Question
(a) The scatter diagram shows the scores for each student in class A for the written test and the speaking
test in French.
A line of best fit has been drawn.
(i) Each test is marked out of 60.
In which test did the class perform better?
Give a reason for your answer.
………………………………………. because ……………………………………………………………………………..
(ii) What type of correlation is shown in the scatter diagram?
(iii) One student is much better at speaking French than writing French.
Put a ring around the cross that represents this student.
(iv) One student scored 39 in the speaking test but was absent for the written test.
Use the line of best fit to estimate a score for this student in the written test.
(b) Here are the scores in the written test for class B.
21 14 48 32 8 29 41 39 30 23 17
Find
(i) the median,
(ii) the mean.
Answer/Explanation
Ans:
(a) (i) Written test and a valid reason
(ii) Positive
(iii) (45,10) indicated
(iv) 42
(b) (i) 29
(ii) 27.5 or 27.45 to 27.46
Question
(a) Write down the temperature shown by each arrow.
(i) 
………………………… °C
(ii) 
…………………………………….. °C
(b) The table shows the daily temperature in Hayville for one week in January.
(i) Which was the coldest day?
(ii) Find the difference between the temperature on Sunday and the temperature on Monday.
(c) In Grassington, the temperature recorded at 0735 was −3 °C.
(i) The temperature was recorded again \(8 \frac{1}{2}\) hours later.
At what time was this temperature recorded?
(ii) By this time, the temperature had risen by 7°C.
Find this temperature.
…………………………………….. °C
Answer/Explanation
Ans:
(a) (i) 16
(ii) -15
(b) (i) Friday
(ii) 6
(c) (i) 16 05 or 405 pm
(ii) 4
Question
Here is a sequence of diagrams made using identical rectangles.
A dot is shown at the junction of three lines.
A cross is shown at the junction of two lines.
(a) Write down the order of rotational symmetry of Diagram 1.
(b) Complete Diagram 4 using dots and crosses.
(c) Complete the table for Diagram 4 and Diagram 5.
| Diagram | 1 | 2 | 3 | 4 | 5 |
| Number of dots | 0 | 4 | 10 | ||
| Number of crosses | 4 | 6 | 8 |
(d) (i) Describe, in words, the rule for continuing the sequence for the number of dots.
(ii) The expression for the number of dots in Diagram n is \(n^2 + n – 2\).
Find the number of dots in Diagram 12.
(e) (i) Write down an expression for the number of crosses in Diagram n.
(ii) Diagram n has 100 crosses.
Find the value of n.
n = …………………………………………
Answer/Explanation
Answer:
(a) 2
(b) 3 dots correctly placed
4 crosses correctly placed
(c) 18 28
10 12
(d) (i) Add two more each time oe
(ii) 154
(e)(i) 2n + 2 oe final answer
(ii) 49
Question
Francis asks 30 families how many children they have.
The table shows the results.
| Number of children in each family | 0 | 1 | 2 | 3 | 4 | 5 |
| Number of families | 4 | 6 | 6 | 2 | 9 | 3 |
(a) (i) Write down the mode.
(ii) Find the median.
(iii) Calculate the mean.
(iv) Complete the bar chart, including the vertical scale.
(b) Francis also recorded the age group and gender of the children aged 12 or less.
The information is shown in the table.
| Age 4 and younge | Age 5 to 8 | Age 9 to 12 | Total | |
| Male | 9 | 36 | ||
| Female | 11 | |||
| Total | 30 | 20 | 75 |
Complete the table.
(c) Francis displays the results for the totals of each age group on a pie chart.
The sector angle for the group ‘Age 4 and younger’ is 120°.
Calculate the sector angle for
(i) age 5 to 8,
(ii) age 9 to 12.
(d) Complete the pie chart.
Answer/Explanation
Answer:
(a) (i) 4
(ii) 2
(iii) 2.5
(iv) 4 bars correct height, correct
width and correct gaps
Correct vertical scale shown
(b) 6 values correctly placed
14 16 [9] 39
[11] 14 11 [36]
25 [30] [20] [75]
(c) (i) 144
(ii) 144
(d) Correct line from centre to
circumference, angles 144° and
96°
Question
(a) The table gives some information about the numbers of visitors at a leisure centre one day.
(i) Complete the table.
(ii) Work out how many more child visitors than adult visitors there are.
………………………………………….
(iii) Write down the fraction of visitors that are adults.
Give your answer in its lowest terms.
………………………………………….
(iv) Write the ratio number of males : number of females.
Give your answer in its simplest form.
…………………. : ………………….
(v) One of these visitors is selected at random.
Find the probability that this visitor is a male child.
………………………………………….
(b) The number of people in each of 150 cars entering the leisure centre car park is recorded.
The table shows the results.
(i) Write down the mode.
………………………………………….
(ii) Calculate the mean.
………………………………………….
(c) In a survey of 50 visitors to the leisure centre, 18 used the gym.
One day, 1500 people visited the leisure centre.
Calculate an estimate for the number of people who used the gym on this day.
………………………………………….
Answer/Explanation
(a)(i) 96 144 240
129 131 260
225 275 500
(ii) 50
(iii)\frac{9}{20}
(iv) 12 : 13
(v)\frac{144}{500}
(b)(i) 1
(ii) 2.4
(c) 540
Question
Lena owns a café.
(a) One day, Lena records the drinks she sells in one hour.
(i) Complete the frequency table.
You may use the tally column to help you.
(ii) Draw a bar chart to show this information.
Complete the scale on the frequency axis.
(b) This table shows the opening hours of the café.
(i) Work out the total number of hours the café is open in one week.
………………………………… hours
(ii) Lena is in the café for 40 hours each week.
Ron is in the café when Lena is not there.
Calculate the percentage of the total opening hours that Ron is in the café each week.
………………………………………%
(c) Saddak buys 3 cups of tea and 2 cookies for \($6.95 .\)
A cup of tea costs \($1.75 .\)
Work out the cost of one cookie.
\($ …………………………………………\)
(d) The price of a cake is \($2.60 .\)
At the end of the day, Lena reduces the price of each cake by 35%.
Calculate the reduced price of a cake.
\($ …………………………………………\)
Answer/Explanation
(a)(i) 7, 3, 6, 8
(ii) Correct bar chart with scaled
frequency axis
(b)(i) 64
(ii) 37.5
(c) [0].85
(d) 1.69
Question
(a) Seven students want to join the school diving club.
Some information about these students is recorded in the table below. To join the diving club you must be
• at least 12 years old in March 2018
and
• at least 150 centimetres tall
and
• able to swim at least 0.5 kilometres.
Write down the names of the students who can join the club.
(b) The students dive off boards of different heights.
The speed, s m/s, that they enter the water from a board of height h metres, can be found using this
formula.
\(s=\sqrt{19.6h}\)
(i) Calculate the value of s when h = 10.
s = ………………………………………..
(ii) Make h the subject of the formula.
h = ……………………………………
Answer/Explanation
(a) Cala, Elu
(b)(i) 14
(ii)\(h=\frac{s^{2}}{19.6}\)
Question
(a) Some people go fishing and catch four types of fish.
Some information is shown in the table
(i) Complete the table.
(ii) Complete the pie chart.
(b) Records show that \(\frac{14}{3}\) of all mullet caught are underweight.
In one day, 168 mullet are caught.
Work out the expected number of mullet that are underweight.
Answer/Explanation
(a)(i)4
17 36
(ii)\(32^{\circ} \) sector drawn
(b) 36
Question
(a) 25 students go on a water sports trip.
The students each choose their favourite water sport.
These are the results.
(i) Complete the frequency table for the results.
You may use the tally column to help you.
(ii) Write down the mode.
…………………………………………
(iii) Work out the percentage of students whose favourite water sport is snorkelling.
…………………………………….. %
(b) The table shows the times of the high and low tides.
(i) Write down the time of the 2nd high tide on Wednesday using the 12-hour clock.
…………………………………………
(ii) Work out the time between the two low tides on Thursday.
………….. h ………….. min
(iii) The surfing activity starts \(1\frac{1}{2}\) hours before the high tide on Tuesday afternoon.
Write down the time that the surfing activity starts.
…………………………………………
Answer/Explanation
(a)(i)5, 8, 4, 2, 6
(ii)Surfing
(b)(i)3.37pm
(ii)12h 26min
(iii)12:52pm
Question
Mrs. Verma has a restaurant.
In the restaurant each table has 8 chairs.
Sometimes she puts tables together.
The diagrams show how the tables are put together and the position of each chair (X).
The pattern of tables and chairs forms a sequence.
(a) Draw the diagram for 4 tables. [1]
(b) Complete the table. [2]
(c) Find a formula for the number of chairs, c, in terms of the number of tables, t.
c = [2]
(d) 18 tables are put together in this way.
Work out the number of chairs needed.[2]
(e) Work out the number of tables, put together in this way, when 80 chairs are needed.[2]
Answer/Explanation
Ans:
5(a) 4 tables and 14 chairs correctly drawn
5(b) 14, 16, 18
5(c) 2 6 t + oe final answer
5(d) 42 cao
5(e) 37 cao
Question
Here is part of the menu for Jamie’s café.
(a) Sue has one tea and one cake.
Calculate how much she pays.
\($\)[1]
(b) Derrick has one coffee and two biscuits.
How much change does he receive from a $10 note?
\($\)[2]
(c) Harriet works at the café for 34 hours each week.
She is paid \($\)8.25 for each hour.
(i) Work out the amount she is paid each week.
\($\)[1]
(ii) One week she works 8 hours extra.
The extra hours are paid at 1.5 times her usual rate of \($\)8.25 for each hour.
Work out the total amount she is paid for that week.
\($\)[2]
(d) Peter works these hours each week at the café.
Work out the number of hours he works in one week.
hours [2]
(e) Jamie buys a clock for the café from Japan for 9395 yen.
The exchange rate is \($\)1 = 110.27 yen.
Work out the cost of the clock in dollars, correct to the nearest cent.
\($\) [3]
(f) Jamie invests $12000 at a rate of 5% per year compound interest.
Calculate the value of his investment at the end of 3 years.
\($\) [3]
Answer/Explanation
Ans:
1(a) 6.8[0]
1(b) 4.9[0]
1(c)(i) 280.5[0]
1(c)(ii) 379.5[0]
1(d) 33
1(e) 85.20 cao
1(f) 13 891.5[0]
Question
(a) Jon spins this 6-sided spinner.
The probability that the spinner lands on any of the six sides is equally likely.
Write down the probability that the spinner lands on
(i) the number 6,
Answer/Explanation
Ans: \(\frac{1}{6}oe\)
(ii) a prime number,
Answer/Explanation
Ans: \(\frac{2}{6}oe\)
(iii) a number less than 11.
Answer/Explanation
Ans: 1
(b) Felix has a 12-sided spinner with the numbers 2, 4, 5, 7 and 9 written on it.
It is equally likely to land on any side.
The table shows the probability of the spinner landing on each number.
The diagram of the spinner has been completed for the number 2.
Complete the diagram for the numbers 4, 5, 7 and 9.
Answer/Explanation
Ans: (2,2,2), 4,4,4,4,5,5,7,7,9 seen on spinner
(c) Felix says that his spinner is more likely to land on a 2 than Jon’s spinner.
Explain why he is wrong.
Answer/Explanation
Ans: Felix’s probability is \(\frac{3}{12}\) which is
less than Jon’s probability \(\left (of\frac{2}{6} \right )\) which is \(\frac{4}{12}oe\)
(d) Felix spins his 12-sided spinner 60 times and records the results.
(i) Complete the table by working out the sector angles for the numbers 7 and 9 .
Answer/Explanation
Ans: (90°, 120°, 30°), 72°, 48°
(ii) Complete the pie chart.
Answer/Explanation
Ans: 30° angle correct 72°, 48°
(iii) Write down the mode.
Answer/Explanation
Ans: 4
(iv) Calculate the mean.
Answer/Explanation
Ans: 4.85
Question
The number of crosses in each Diagram forms a sequence.
(a) On the grid draw Diagram 4.
Answer/Explanation
Ans: Correct diagram: 4 rows & 6 columns
(b) Write down the number of crosses needed to draw Diagram 5.
Answer/Explanation
Ans: 35
(c) Diagram 1 has 1 row of 3 crosses.
Diagram 2 has 2 rows of 4 crosses.
(i) Complete this statement for Diagram n.
Diagram n has n rows of crosses.
Answer/Explanation
Ans: n + 2 cao
(ii) Write down, in terms of n, how many crosses are needed to draw Diagram n.
Answer/Explanation
Ans: n (n + 2) oe
(iii) Find the number of crosses needed to draw Diagram 20.
Answer/Explanation
Ans: 440
Question
A sequence of diagrams is made from black counters and white counters.
The first four diagrams in the sequence are shown.
(a) Complete the table.
Answer/Explanation
Ans: 9 16 25
7 10 13
(b) Complete the statement.
The numbers of black counters are all numbers.
Answer/Explanation
Ans: square
(c) How many white counters are needed for
(i) Diagram 8,
Answer/Explanation
Ans: 22
(ii) Diagram n?
Answer/Explanation
Ans: 3n – 2 oe final answer
(d) Diagram p contains 58 white counters.
(i) Find the value of p.
Answer/Explanation
Ans: 20
(ii) Find the number of black counters in Diagram p.
Answer/Explanation
Ans: 400
Question
The diagrams show a sequence of shapes.
(a) On the grid, draw Diagram 4.
(b) Complete the table showing the number of lines in each diagram.
(c) Work out the number of lines in Diagram 8.
(d) Write down an expression, in terms of n, for the number of lines in Diagram n.
(e) Work out the number of lines in Diagram 100
(f) The number of lines in Diagram p is 66.
Find the value of p.
Answer/Explanation
(a) 
(b) 
(c) 48-7=41
(d) \(6 \times n-(n-1)\)
= 6n-n+1
= 5n+1
(e) \(500\times 100+1\)(5n+1)
=501
(f) 5n+1= no. of lines in diagram n
5p+1 = 66
5p= 65
p=13
Question
Each of the diagrams above shows one small shaded square and a number of small unshaded squares.
The diagrams form a sequence.
(a) Complete Diagram 5.
(b) Complete the table.
(c) Diagram p has 9999 small unshaded squares. Find p.
▶️Answer/Explanation
(a) 5 by 5 shape
(b) First row $25 \quad 2500 \quad n^2$ Second row $\quad 1 \quad 1 \quad 1$ Third row $24 \quad 2499 \quad n^2-1$
(c) 100
Question
The table below shows the age and price of 20 used cars in a showroom.
(a) Use this information to complete the following table.
(b) (i) Complete the frequency table for the price, $x, of the cars.
(ii) Draw a histogram to show this information.
(c) (i) On the grid below complete the scatter diagram showing the age and price of each car.
The first 10 points from the original table have been plotted.
(ii) What correlation is there between the price of a car and its age?
(iii) A car is chosen at random. Using your scatter diagram, find the probability that the car is more than 4 years old and the price is more than $5000.
▶️Answer/Explanation
(a) 5 , $126, \quad 90$
(b) (i) $3,5,6,4,2$
(ii) Blocks ‘correct’ heights No gaps.
(c) (i) 10 points plotted correctly
(ii) Zero oe
(iii) $\frac{3}{20}$ oe or 0.15 or $15 \%$