Calculator Questions June 2016
Q1.
Use your calculator to work out
Write down all the figures on your calculator display.
You must give your answer as a decimal.
..............................................................................................................................................
(Total for Question is 2 marks)
Q2.
* Talil is going to make some concrete mix.
He needs to mix cement, sand and gravel in the ratio 1 : 3 : 5 by weight.
Talil wants to make 180 kg of concrete mix.
Talil has
15 kg of cement
85 kg of sand
100 kg of gravel
Does Talil have enough cement, sand and gravel to make the concrete mix?
(Total for Question is 4 marks)
Q3. Here are the ingredients needed to make 16 gingerbread men.
Ingredients
to make 16 gingerbread men
180 g flour
40 g ginger
110 g butter
30 g sugar
Hamish wants to make 24 gingerbread men.
Work out how much of each of the ingredients he needs.
...........................................................g flour
...........................................................g ginger
...........................................................g butter
...........................................................g sugar
(Total for Question is 3 marks)
Q4.
t = x2 − 5y
x=6
y=4
Work out the value of t.
........................................................
(Total for Question is 2 marks)
Q5.
The diagram shows the front elevation and the side elevation of a prism.
(a) On the grid, draw a plan of this prism.
(2)
(b) In the space below, draw a sketch of this prism.
(2)
Q6. The table shows information about the heights, in centimetres, of 30 sunflower plants.
(a) On the grid, draw a frequency polygon for this information.
(2)
(b) Write down the modal class interval.
...........................................................
(1)
Q7. The table shows the average temperature on each of seven days and the number of units of gas used
to heat a house on these days.
(a) Complete the scatter graph to show the information in the table. The first 5 points have been plotted for
you.
(1)
(b) Describe the relationship between the average temperature and the number of units of gas used.
.............................................................................................................................................
(1)
(c) Estimate the average temperature on a day when 12 units of gas are used.
...........................................................°C
(2)
Q8. The table gives some information about the birds Paula sees in her garden one day.
Bird
Frequency
Magpie
Thrush
Starling
Sparrow
15
10
20
27
Complete the accurate pie chart.
(Total for Question is 3 marks)
Q9. The list below shows the weight, in grams, of 15 baskets of strawberries.
193
200
207
211
198
189
223
218
190
195
207
206
205
189
212
Show this information in an ordered stem and leaf diagram.
You must include a key.
(Total for Question is 3 marks)
Q10.
Describe fully the single transformation that maps shape P onto shape Q.
.............................................................................................................................................
(Total for Question is 3 marks)
Q11.*
CDEF is a straight line.
AB is parallel to CF.
DE = AE.
Work out the size of the angle marked x.
You must give reasons for your answer.
(Total for Question is 4 marks)
Q12.
Diagram NOT accurately drawn
Work out the total surface area of this triangular prism.
..............................................................................................................................................
(Total for Question is 4 marks)
Q13. The table gives information about the time it took each of 80 children to do a jigsaw puzzle.
Work out the mean time for all 80 children.
........................................................... minutes
(Total for Question is 3 marks)
Q14. Tom and Amy set the alarms on their phones to sound at 6.45 am.
Both alarms sound together at 6.45 am.
Tom's alarm then sounds every 9 minutes.
Amy's alarm then sounds every 12 minutes.
At what time will both alarms next sound together?
...........................................................
(Total for question = 3 marks)
Q15. Write 525 as a product of its prime factors.
..............................................................................................................................................
(Total for Question is 3 marks)
Q18.
The equation x3 + 27x = 90
has a solution between 2 and 3
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show all your working.
x = ...........................................................
(Total for question = 4 marks)
Q19. Make p the subject of the formula
y = 3p2 – 4
......................
(Total for Question is 3 marks)
Q20. Here are the first five terms of an arithmetic sequence.
(a) Write down an expression, in terms of n, for the nth term of this sequence.
..............................................................................................................................................
(2)
2
The nth term of a different number sequence is 3n + 7
(b) Find the 10th term of this sequence.
..............................................................................................................................................
(2)
Q21. The table shows information about the times taken by 100 people in a fun run.
(a) Complete the cumulative frequency table for this information.
(1)
(b) On the grid, draw a cumulative frequency graph for your table.
(2)
(c) Use your graph to find an estimate for the median time.
........................................................... minutes
(1)
(d) Use your graph to find an estimate for the number of people who took longer than 63 minutes.
...........................................................
Q22. (a) Complete the table of values for y = x2 − 2x − 1
(2)
(2)
(b) On the grid, draw the graph of y = x2 − 2x − 1 for values of x from x = −2 = 3
(2)
Q23. A coach travels from Dronston to Luscoe. The travel graph for this journey is shown below.
(a) Work out the average speed of the coach, in kilometres per hour, for the first
10 minutes of the journey.
.......................................................... km/h
(2)
The coach stops in Luscoe for 15 minutes. The coach then returns to Dronston at a constant speed of
42km/h.
(b) Show this information on the travel graph.
(3)
Q24.
ABCDE is a regular pentagon.
ACFG is a square.
Work out the size of angle DCF.
You must show all your working.
...........................................................°
(Total for question = 4 marks)
Q25. Here is a scale drawing of a rectangular garden ABCD.
Jane wants to plant a tree in the garden
at least 5m from point C,
nearer to AB than to AD
and less than 3m from DC.
On the diagram, shade the region where Jane can plant the tree.
(Total for Question is 4 marks)
Q26. Bill's weight decreases from 64.8 kg to 59.3 kg.
Calculate the percentage decrease in Bill's weight.
Give your answer correct to 3 significant figures.
..............................................................................................................................................
(Total for Question is 3 marks)
Q27. * Viv wants to invest £2000 for 2 years in the same bank.
At the end of 2 years, Viv wants to have as much money as possible.
Which bank should she invest her £2000 in?
(Total for Question is 4 marks)
Q28. Claire is making a loaf of bread.
A loaf of bread loses 12% of its weight when it is baked.
Claire wants the baked loaf of bread to weigh 1.1 kg.
Work out the weight of the loaf of bread before it is baked.
........................................................... kg
(Total for question = 3 marks)
Q29. The table gives some information about the lengths of time, in hours, that some adults watched TV
last week.
(a) Work out an estimate for the mean length of time.
........................................................... hours
(4)
(b) Draw a histogram for the information in the table.
(3)
Q30.
The diagram shows a cuboid drawn on a 3-D grid.
Three of the vertices of the cuboid are P (3, 2, 0)
Q (3, 0, 0)
R (3, 0, 4)
(a) Label the vertex Q with a cross (×).
(1)
The vertex S is shown on the diagram.
(b) Write down the coordinates of the vertex S.
..............................................................................................................................................
(1)
(Total for Question is 2 marks)
Q31. Manchester airport is on a bearing of 330° from a London airport.
(a) Find the bearing of the London airport from Manchester airport.
...........................................................°
(2)
The London airport is 200 miles from Manchester airport.
A plane leaves Manchester airport at 10 am to fly to the London airport.
The plane flies at an average speed of 120 mph.
(b) What time does the plane arrive at the London airport?
...........................................................
(4)
(Total for question = 6 marks)
Q32.
Calculate the length of AB.
Give your answer correct to 1 decimal place.
..............................................................................................................................................
(Total for Question is 3 marks)
Q33.
* The diagram shows a ladder leaning against a vertical wall.
The ladder stands on horizontal ground. The length of the ladder is 6 m. The bottom of the ladder is 2.25
m from the bottom of the wall.
A ladder is safe to use when the angle marked y is about 75°. Is the ladder safe to use?
You must show all your working.
Q34.
ABCD and AEFG are mathematically similar trapeziums.
AE = 5 cm
EF = 12 cm
BC = 18 cm
(a) Work out the length of AB.
........................................................... cm
(2)
Trapezium AEFG has an area of 36 cm2.
(b) Work out the area of the shaded region.
........................................................... cm2
(3)
(Total for Question is 5 marks)
Q35.
Solve the simultaneous equations
3x + 2y = 4
4x + 5y = 17
x ...........................................................
y ...........................................................
(Total for Question is 4 marks)
Q36. Solve 5x2 + 6x – 2 = 0
Give your solutions correct to 2 decimal places.
..............................................................................................................................................
(Total for Question is 3 marks)
Q37.
(a) Given that x and y are integers such that
find all the possible values of x.
...........................................................
(2)
(b) On the grid below show, by shading, the region defined by the inequalities
Mark this region with the letter R.
(4)
Q38.
OAB is a sector of a circle, centre O. The radius of the circle is 15 cm. The angle of the sector is 30°.
Calculate the area of sector OAB.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question is 2 marks)
Q39. (a) Write down the equation of a straight line that is parallel to y = 5x + 6
..............................................................................................................................................
(1)
(b) Find an equation of the line that is perpendicular to the line y = 5x + 6 and passes through the point (–2,
5).
..............................................................................................................................................
(3)
Q40. Make t the subject of the formula
..............................................................................................................................................
(Total for Question is 4 marks)
Q41. Here are some graphs that show relationships. A curve or line of best fit has been drawn on each
graph.
The equation of each graph is one of the equations in the following list.
y= 10 − 2x
y = 2x
y = 2x − 10
y = 8x − 2x2
y = 3x2
Give the equation of each graph.
Graph A ...........................................................
Graph B ...........................................................
Graph C ...........................................................
Q42.
V = 250 correct to the nearest 5
R = 3900 correct to the nearest 100
Work out the lower bound for the value of I.
Give your answer correct to 3 decimal places.
You must show your working.
..........................................................
(Total for question = 3 marks)
Q43.(a)
Expand and simplify (y − 2)(y − 5)
...........................................................
(2)
*(b) Prove algebraically that
(2n + 1)2 − (2n + 1) is an even number
for all positive integer values of n.
(3)
(Total for Question is 5 marks)
Q44.
(a) Simplify fully
..............................................................................................................................................
(3)
(b) Write
as a single fraction in its simplest form.
..............................................................................................................................................
(3)
(Total for Question is 6 marks)
Q45.
Express the recurring decimal
as a fraction in its simplest form.
..............................................................................................................................................
(Total for Question is 3 marks)
Q46.
Solve the simultaneous equations
x2 + y2 = 25
y = 2x + 5
x = . . . . . . . . . . . . . . and y = . . . . . . . . . . . . . .
or
x = . . . . . . . . . . . . . . and y = . . . . . . . . . . . . . .
(Total for Question is 6 marks)
Q47.
On the grid, enlarge the triangle by scale factor − , centre (0, −2).
(Total for Question is 2 marks)
Q48. 148 students went to Brighton.
Each student went to the Aquarium or the Brighton Wheel or the Royal Pavilion.
The table gives information about these students.
The teacher takes a sample of 40 of these students.
The sample is stratified by gender and by place visited.
Work out the number of students in the sample who are female and went to the Brighton Wheel.
...........................................................
(Total for question = 2 marks)
Q49. Here are some cards.
Each card has a letter on it.
Rachel takes at random two of these cards.
Work out the probability that there are different letters on the two cards.
..............................................................................................................................................
(Total for Question is 4 marks)
Q50.
Diagram NOT accurately drawn
ABC is a triangle.
AB = 8.7 cm. Angle ABC = 49°.
Angle ACB = 64°.
Calculate the area of triangle ABC.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question is 5 marks)
Q51. ABC is a triangle.
(a) Work out the area of triangle ABC.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . . cm2
(2)
(b) Work out the length of the side AB.
Give your answer correct to 3 significant figures.
..............................................................................................................................................
(3)
(Total for Question is 5 marks)
Q52.
(a) On the grid, draw the graph of x2 + y2 = 4
(2)
(b) On the grid, sketch the graph of y = cos x for 0° ≤ x ≤ 360°
(2)
Q53.
A frustrum is made by removing a small cone from a similar large cone.
The height of the small cone is 20 cm.
The height of the large cone is 40 cm.
The diameter of the base of the large cone is 30 cm.
Work out the volume of the frustrum.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . . . .cm3
(Total for Question is 4 marks)
Q54.
The expression x2 − 8x + 6 can be written in the form (x − p)2 + q for all values of x.
(a) Find the value of p and the value of q.
p = ...........................................................
q = ...........................................................
(3)
The graph of y = x − 8x + 6 has a minimum point.
2
(b) Write down the coordinates of this point.
(............................. , .............................)
(1)
(Total for question = 4 marks)
Q55.
The diagram shows part of the curve with equation y = f(x).
The coordinates of the maximum point of the curve are (3, 5).
(a) Write down the coordinates of the maximum point of the curve with equation
(i) y = f(x + 3)
(ii) y = 2f(x)
(iii) y = f(3x)
(............................................. , .............................................)
(............................................. , .............................................)
(............................................. , .............................................)
(3)
The curve with equation y = f(x) is transformed to give the curve with equation y = f(x) − 4
(b) Describe the transformation.
.............................................................................................................................................
(1)
(Total for question = 4 marks)