Edexcel GCSE Higher June 2019 Paper 2 (calculator)
20 questions · 80 marks. Every question from the paper, recreated, with the official mark scheme, an annotated worked solution and a shadow question (the same skill with new numbers). Open the paper in the Ultimate Exam Question Finder to present it, print it or build a set.
Question 1 (5 marks)
(a)
Solve 14n > 11n + 6
(2 marks)
(b)
On the number line below, show the set of values of x for which -2 < x + 3 ≤ 4
Diagram: A number line for x from -6 to 6.
(3 marks)
Question 2 (3 marks)
On the grid below, draw the graph of y = 2x – 3 for values of x from –2 to 4
Diagram: A graph.
(3 marks)
Question 3 (3 marks)
Hannah is planning a day trip for 195 students.
She asks a sample of 30 students where they want to go.
Each student chooses one place.The table shows information about her results.
Place Number of students Theme Park 10 Theatre 5 Sports Centre 8 Seaside 7 (i)
Work out how many of the 195 students you think will want to go to the Theme Park.
(2 marks)
(ii)
State any assumption you made and explain how this may affect your answer.
(1 mark)
Question 4 (4 marks)
A container is in the shape of a cuboid.
Diagram: A cuboid 30 cm long, 6 cm deep and 19 cm high.
The container is 2/3 full of water.
A cup holds 275 ml of water.What is the greatest number of cups that can be completely filled with water from the container?
(4 marks)
Question 5 (2 marks)
ABC is a right-angled triangle.
Diagram: A right-angled triangle ABC. The right angle is at B. A is straight above B and C is to the right of B. AC, the sloping side, is 16 cm. The angle at C is 38°.
Calculate the length of AB.
Give your answer correct to 2 decimal places.(2 marks)
Question 6 (2 marks)
Sally used her calculator to work out the value of a number y.
The answer on her calculator display began
8.3
Complete the error interval for y.
……… ≤ y < ………
(2 marks)
Question 7 (4 marks)
£360 is shared between Abby, Ben, Chloe and Denesh.
The ratio of the amount Abby gets to the amount Ben gets is 2 : 7
Chloe and Denesh each get 1.5 times the amount Abby gets.Work out the amount of money that Ben gets.
(4 marks)
Question 8 (2 marks)
(a)
Write 0.00562 in standard form.
(1 mark)
(b)
Write 1.452 × 10³ as an ordinary number.
(1 mark)
Question 9 (4 marks)
The circumference of circle B is 90% of the circumference of circle A.
(a)
Find the ratio of the area of circle A to the area of circle B.
(2 marks)
(b)
Square E has sides of length e cm.
Square F has sides of length f cm.The area of square E is 44% greater than the area of square F.
Work out the ratio e : f
(2 marks)
Question 10 (5 marks)
Mary travels to work by train every day.
The probability that her train will be late on any day is 0.15(a)
Complete the probability tree diagram for Thursday and Friday.
Diagram: A probability tree diagram for Thursday and Friday. Thursday: late (0.15) or not late (a blank). After each, Friday: late or not late, with a blank, a blank, a blank, a blank on the four branches.
(2 marks)
(b)
Work out the probability that her train will be late on at least one of these two days.
(3 marks)
Question 11 (6 marks)
The grouped frequency table gives information about the times, in minutes, that 80 office
workers take to get to work.Time (t minutes) Frequency 0<t≤20 5 20<t≤40 30 40<t≤60 20 60<t≤80 15 80<t≤100 8 100<t≤120 2 (a)
Complete the cumulative frequency table.
Time (t minutes) Cumulative frequency 0<t≤20 0<t≤40 0<t≤60 0<t≤80 0<t≤100 0<t≤120 (1 mark)
(b)
On the grid, draw the cumulative frequency graph for this information.
Diagram: A blank grid for a cumulative frequency graph: Time (t minutes) from 0 to 140 across, cumulative frequency from 0 to 80 up.
(2 marks)
(c)
Use your graph to find an estimate for the percentage of these office workers who
take more than 90 minutes to get to work.(3 marks)
Question 12 (4 marks)
OAB is a sector of a circle with centre O and radius 7 cm.
Diagram: A sector OAB of a circle with centre O. OA and OB are both labelled 7 cm, and the arc AB joins A, at the top left, to B, at the right.
The area of the sector is 40 cm²
Calculate the perimeter of the sector.
Give your answer correct to 3 significant figures.(4 marks)
Question 13 (4 marks)
Show that 6 + [(x + 5) ÷ (x² + 3x – 10)/(x – 1)] simplifies to (ax – b)/(cx – d) where a, b, c and d are integers.
(4 marks)
Question 14 (7 marks)
A car moves from rest.
The graph gives information about the speed, v metres per second, of the car t seconds
after it starts to move.Diagram: A speed-time graph. Time is from 0 to 40 seconds and speed from 0 to 25 m/s. The curve starts at O, rises slowly then steeply through 4 m/s at 5 seconds, 12 at 10 and 18 at 15, levels off at about 20 m/s from 20 to 25 seconds, then falls to about 12.7 m/s at 40 seconds.
(a)(i)
Calculate an estimate of the gradient of the graph at t = 15
(3 marks)
(ii)
Describe what your answer to part (i) represents.
(1 mark)
(b)
Work out an estimate for the distance the car travels in the first 20 seconds of its journey.
Use 4 strips of equal width.(3 marks)
Question 15 (3 marks)
Make m the subject of the formula f = (3m + 4)/(m – 1)
(3 marks)
Question 16 (3 marks)
The straight line L has the equation 3y = 4x + 7
The point A has coordinates (3, -5)Find an equation of the straight line that is perpendicular to L and passes through A.
(3 marks)
Question 17 (4 marks)
There are some small cubes and some large cubes in a bag.
The cubes are red or the cubes are yellow.The ratio of the number of small cubes to the number of large cubes is 4 : 7
The ratio of the number of red cubes to the number of yellow cubes is 3 : 5(a)
Explain why the least possible number of cubes in the bag is 88
(1 mark)
(b)
All the small cubes are yellow.
Work out the least possible number of large yellow cubes in the bag.
(3 marks)
Question 18 (5 marks)
The points A, B, C and D lie on a circle.
CDE is a straight line.Diagram: A circle with the points A, B, C and D on it. B is at the top, A at the lower left, D at the lower right and C on the right between B and D. Chords AB, BD, AD and BC are drawn. The line from C goes through D and on to E, outside the circle. BA and BD are marked equal, CB and CD are marked equal, and angle ABD is 40°.
BA = BD
CB = CD
Angle ABD = 40°Work out the size of angle ADE.
You must give a reason for each stage of your working.(5 marks)
Question 19 (4 marks)
The diagram shows a triangular prism.
Diagram: A triangular prism. The base ABCD is a square of side 15 cm, lying flat: D at the front left, A at the front right, B at the back right and C at the back left. E is directly above B and F is directly above C, so the sloping face ADFE rises from the front edge DA up to the top edge FE. The right angle EBC is marked, and angle EAB is marked 35°. DC, CB and CF are hidden edges, drawn dashed.
The base, ABCD, of the prism is a square of side length 15 cm.
Angle ABE and angle CBE are right angles.
Angle EAB = 35°M is the point on DA such that
DM : MA = 2 : 3
Calculate the size of the angle between EM and the base of the prism.
Give your answer correct to 1 decimal place.(4 marks)
Question 20 (6 marks)
CDEF is a quadrilateral.
Diagram: The quadrilateral CDEF, with C at the top left, D at the top right, E at the bottom right and F at the bottom left. M is on the side DE, and a line joins F to M. X is a point marked on FM.
overrightarrowCD = mathbfa, overrightarrowDE = mathbfb and overrightarrowFC = mathbfa – mathbfb.
(a)
Express overrightarrowFE in terms of mathbfa and/or mathbfb.
Give your answer in its simplest form.(2 marks)
(b)
M is the midpoint of DE.
X is the point on FM such that FX : XM = n : 1
CXE is a straight line.Work out the value of n.
(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.