Answer ALL Questions s17
Instructions
· Use black ink or ball-point pen.
· Fill in the boxes at the top of this page with your name,
centre number and candidate number.
· Answer all questions.
· Answer the questions in the spaces provided
– there may be more space than you need.
· Calculators must not be used.
Information
· The total mark for this paper is 101
· The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
· Questions labelled with an asterisk (*) are ones where the quality of your
written communication will be assessed.
Advice
· Read each question carefully before you start to answer it.
· Keep an eye on the time.
· Try to answer every question.
· Check your answers if you have time at the end.
Suggested Grade Boundaries (for guidance only)
A* / A / B / C / D90 / 79 / 61 / 39 / 22
GCSE Mathematics 1MA0
Formulae: Higher Tier
You must not write on this formulae page.
Anything you write on this formulae page will gain NO credit.
Volume of prism = area of cross section × length Area of trapezium = (a + b)h
Volume of sphere πr3 Volume of cone πr2h
Surface area of sphere = 4πr2 Curved surface area of cone = πrl
In any triangle ABC The Quadratic Equation
The solutions of ax2+ bx + c = 0
where a ≠ 0, are given by
x =
Sine Rule
Cosine Rule a2 = b2+ c2– 2bc cos A
Area of triangle = ab sin C
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
You must NOT use a calculator.
1. Here is a list of ingredients for making 10 Flapjacks.
Ingredients for 10 Flapjacks80 g rolled oats
60 g butter
30 ml golden syrup
36 g light brown sugar
Work out the amount of each ingredient needed to make 15 Flapjacks.
...... g rolled oats
...... g butter
...... ml golden syrup
...... g light brown sugar
(Total 3 marks)
______
2. The scatter graph shows information about 10 apartments in a city.
The graph shows the distance from the city centre and the monthly rent of each apartment.
The table shows the distance from the city centre and the monthly rent for two other apartments.
Distance from the city centre (km) / 2 / 3.1Monthly rent (£) / 250 / 190
(a) On the scatter graph, plot the information from the table.
(1)
(b) Describe the relationship between the distance from the city centre and the monthly rent.
......
......
(1)
An apartment is 2.8 km from the city centre.
(c) Find an estimate for the monthly rent for this apartment.
£ ......
(2)
(Total 4 marks)
______
3. Louise spins a four-sided spinner and a five-sided spinner.
The four-sided spinner is labelled 2, 4, 6, 8
The five-sided spinner is labelled 1, 3, 5, 7, 9
Louise adds the score on the four-sided spinner to the score on the five-sided spinner.
She records the possible total scores in a table.
4-sided spinner
5-sided spinner / + / 2 / 4 / 6 / 81 / 3 / 5 / 7 / 9
3 / 5 / 7 / 9 / 11
5 / 7 / 9 / 11 / 13
7 / 9 / 11 / x / x
9 / 11 / 13 / x / x
(a) Complete the table of possible total scores.
(1)
(b) Write down all the ways in which Louise can get a total score of 11
One way has been done for you.
(2,9)......
(2)
Both spinners are fair.
(c) Find the probability that Louise’s total score is less than 6
......
(2)
(Total 5 marks)
______
4. (a) Expand 3(2 + t)
......
(1)
(b) Expand 3x(2x + 5)
......
(2)
(c) Expand and simplify (m + 3)(m + 10)
......
(2)
(Total 5 marks)
______
5.
Triangle T has been drawn on the grid.
Rotate triangle T 180° about the point (1, 0).
Label the new triangle A.
(Total 2 marks)
6. Work out an estimate for
......
(Total 2 marks)
______
7. Rita is going to make some cheeseburgers for a party.
She buys some packets of cheese slices and some boxes of burgers.
There are 20 cheese slices in each packet.
There are 12 burgers in each box.
Rita buys exactly the same number of cheese slices and burgers.
(i) How many packets of cheese slices and how many boxes of burgers does she buy?
...... packets of cheese slices
...... boxes of burgers
Rita wants to put one cheese slice and one burger into each bread roll.
She wants to use all the cheese slices and all the burgers.
(ii) How many bread rolls does Rita need?
...... bread rolls
(Total 4 marks)
______
8. The diagram shows a garden in the shape of a rectangle.
The scale of the diagram is 1 cm represents 2 m.
Scale: 1 cm represents 2 m
Irfan is going to plant a tree in the garden.
The tree must be
more than 3 metres from the patio
and more than 6 metres from the centre of the pond.
On the diagram, shade the region where Irfan can plant the tree.
(Total for Question 8 is 3 marks)
______
9.
ABC is an equilateral triangle.
ACD is a straight line.
(a) Work out the size of the angle marked x.
...... °
(2)
(b) Give a reason for your answer.
......
......
(1)
(Total 3 marks)
______
10. (a) Simplify 3a + 4c – a + 3c
......
(2)
(b) Expand y(2y – 3)
......
(1)
(c) Factorise x2 – 4x
......
(2)
(d) Expand and simplify 2(x + 3) + 3(2x – 1)
......
(2)
(e) Solve 3(x + 2) = 8
x = ......
(2)
(Total 9 marks)
11. Ria is going to buy a caravan.
The total cost of the caravan is £7000 plus VAT at 20%.
Ria pays a deposit of £3000.
She pays the rest of the total cost in 6 equal monthly payments.
Work out the amount of each monthly payment.
£......
(Total 4 marks)
______
12. 5 schools sent some students to a conference.
One of the schools sent both boys and girls.
This school sent 16 boys.
The ratio of the number of boys it sent to the number of girls it sent was 1 : 2
The other 4 schools sent only girls.
Each of the 5 schools sent the same number of students.
Work out the total number of students sent to the conference by these 5 schools.
......
(Total 4 marks)
______
13. (a) Write in standard form 213 000
......
(1)
(b) Write in standard form 0.00123
......
(1)
(Total 2 marks)
14.
P is the point with coordinates (2, 3).
Q is the point with coordinates (12, 7).
Work out the coordinates of the midpoint of the line PQ.
( ...... , ...... )
(Total 2 marks)
______
15. Express 180 as a product of its prime factors.
......
(Total 3 marks)
______
16. (a) Simplify (m–2)5
......
(1)
(b) Factorise x2 + 3x – 10
......
(2)
(Total for Question 16 is 3 marks)
______
17. (a) Write down the value of 100.
......
(1)
(b) Write down the value of 10–2.
......
(1)
(c) Write these numbers in order of size.
Start with the smallest number.
2.73 × 103 27.3 × 10–3 273 × 102 0.00273
......
(2)
(Total for Question 17 is 4 marks)
______
18. The cumulative frequency graph shows information about the times 80 swimmers take to swim 50 metres.
(a) Use the graph to find an estimate for the median time.
...... seconds
(1)
A swimmer has to swim 50 metres in 60 seconds or less to qualify for the swimming
team.
The team captain says,
“More than 25% of swimmers have qualified for the swimming team.”
*(b) Is the team captain right?
You must show how you got your answer.
(3)
For these 80 swimmers
the least time taken was 28 seconds
and the greatest time taken was 96 seconds.
(c) Use the cumulative frequency graph and the information above to draw a box plot for
the times taken by the swimmers.
(3)
(Total 7 marks)
______
19. Arwen buys a car for £4000
The value of the car depreciates by 10% each year.
Work out the value of the car after two years.
£ ......
(Total 3 marks)
______
20. Solve the simultaneous equations
5x + 2y = 11
4x – 3y = 18
x = ......
y = ......
(Total for Question 20 is 4 marks)
______
21. Solve the simultaneous equations
3x + 2y = 8
2x + 5y = –2
x = ......
y = ......
(Total 4 marks)
22. The table gives some information about the delays, in minutes, of 80 flights.
0 < n £ 20 / 16
20 < n £ 30 / 26
30 < n £ 40 / 23
40 < n £ 50 / 10
50 < n £ 60 / 5
(a) Write down the modal class interval.
......
(1)
(b) Complete the cumulative frequency table.
Delay (n minutes) / Frequency0 < n £ 20
0 < n £ 30
0 < n £ 40
0 < n £ 50
0 < n £ 60
(1)
(c) On the grid opposite, draw a cumulative frequency graph for your table.
(2)
(d) Use your graph to find an estimate for
(i) the median delay,
...... minutes
(ii) the interquartile range of the delays.
...... minutes
(3)
(Total 7 marks)
______
23. (a) Expand and simplify (x − 3)(x + 5)
......
(2)
(b) Solve x2 + 8x − 9 = 0
......
(3)
(Total 5 marks)
______
24. There are three different types of sandwiches on a shelf.
There are
4 egg sandwiches,
5 cheese sandwiches
and 2 ham sandwiches.
Erin takes at random 2 of these sandwiches.
Work out the probability that she takes 2 different types of sandwiches.
......
(Total 5 marks)
______
25. (a) Rationalise the denominator of
......
(2)
(b) Work out the value of (√2 + √8)2
......
(2)
(Total 4 marks)
TOTAL FOR PAPER IS 100 MARKS
20
Practice Paper: Bronze 2 of 4
1 / 15 ÷ 1080 × 1.5
60 × 1.5
30 × 1.5
36 × 1.5 / 120, 90, 45, 54 / 3 / M2 for any one of 80 + 40 or 60 + 30 or 30 + 15 or 36 + 18 or 120 or 90 or 45 or 54 seen
A1 cao
OR
M1 for 15 ÷ 10 or 3 ÷ 2 or sight of 1.5
M1(dep) for 80 × '1.5' or 60 × '1.5' or 30 × '1.5' or
36 × '1.5'
A1 cao
OR
M1 for 80 ÷ 10 or 60 ÷ 10 or 30 ÷ 10 or 36 ÷ 10 or 8 or 6 or 3 or 3.6
M1(dep) for '8' × 15 or '6' × 15 or '3' × 15 or '3.6' × 15
A1 cao
OR
M1 for 80 ÷ 2 or 60 ÷ 2 or 30 ÷ 2 or 36 ÷ 2 or 40 or 30 or 15 or 18
M1 (dep) for '40' × 3 or '30' × 3 or '15' × 3 or '18' × 3
A1 cao
2 / (a) / Plot (2, 250) and (3.1, 190) / Plot points / 1 / B1 for both points plotted accurately
(b) / Relationship / 1 / B1 for “As the distance from the centre increases the monthly rent
decreases” or the nearer you are to the centre the more you have to pay oe (accept negative correlation)
(c) / 200 to 260 / 2 / M1 for attempting a correct method, eg a line of best fit
or any other indication, on a line that could be used as a line of best fit eg line to graph at x = 2.8or a mark on the line at 2.8
A1 for value in the range 200 to 260
3 / (a) / 13 / 15
15 / 17
/ 1 / B1 cao
(b) / (4, 7), (6, 5), (8, 3) / 2 / B2 for all 3 pairs (numbers in any order in each pair, condone use of addition sign) and no extra pairs
(B1 for one or two or three correct pairs and no more than three extra pairs given, ignoring repeats)
(c) / oe / 2 / B2 ft accept answer as fraction or decimal or percentage
(B1 for , x < 20, x ≠ 3 or , x > 3, x ≠ 3)
SC: If no marks scored award B1 for ‘3 out of 20’ as final answer or other use of incorrect notation
4 / (a) / 6 + 3t / 1 / B1 for 6 + 3t
(b) / 6x2 + 15x / 2 / B2 for 6x2 + 15x
(B1 for 6x2 or 15x)
(c) / m2 + 10m + 3m + 30 / m2 + 13m + 30 / 2 / M1 for all 4 terms (and no additional terms) correct with or without signs or 3 out of no more than four terms correct with
signs
A1 for m2 + 13m + 30
6 / / 4 / 2 / M1 for rounding at least one of the numbers to 1 significant figure correctly
A1 for answer between 3 and 4 inclusive
7 / (i) / 20, 40, 60
12, 24, 36, 48, 60
20 = 4×5 = 2×2×5
12 = 4×3 = 2×2×3 / 3 and 5
or
any multiple
of 3, 5 / 4 / M1 attempts multiples of both 20 and 12
(at least 3 of each shown but condone errors if intention is clear) or identifies 60 or a multiple of 60
M1 (dep on M1) for a division by 20 or 12
or counts up ‘multiples’ or identifies a common multiple
(implied if one answer is correct or answers reversed)
A1 cheese slices (packets) 3, burgers (boxes) 5
or any multiple of 3, 5
(ii) / 60 / B1 for 60 or ft from their correct answer in (i) or ft ‘common multiple’
8 / Correct region / 3 / B1 for full line drawn 1.5 cm from edge of patio and parallel to it
B1 for full arc of circle radius 3 cm centre the centre of the pond
B1 ft for shading region to the right of their vertical line and outside the arc of their circle with correct centre
9 / (a) / 180º - 60º
or
60º + 60º / 120º / 2 / M1 for 180 ÷ 3 or 60 as angle of triangle or 180 – 60 or 60 + 60
A1 cao
/ (b)
/ Reason / 1 / B1 for at least one correct reason and no incorrect reasons (ignore irrelevant reasons)
‘angles on a straight line add to 180º’ or ‘angles in a triangle add up to 180o’ or ‘angles in an equilateral triangle are equal’ or
‘exterior angle of a triangle is equal to the sum of the interior angles at the two other vertices’