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**Questions and Worked Solutions for Edexcel GCSE Mathematics June 2019 Paper 2H (Calculator)**

Edexcel GCSE Mathematics June 2019 Past Paper 2H (Pdf)

Edexcel GCSE June 2019 Paper 2H (Calculator) Solutions

1. (a) Solve 14n > 11n + 6

(b) On the number line below, show the set of values of x for which –2 < x + 3 ≤ 4

2. On the grid below, draw the graph of y = 2x – 3 for values of x from -2 to 4

3. 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.

(i) Work out how many of the 195 students you think will want to go to the Theme Park.

(ii) State any assumption you made and explain how this may affect your answer.

4. A container is in the shape of a cuboid.

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?

5. ABC is a right-angled triangle.

Calculate the length of AB.

Give your answer correct to 2 decimal places.

6. 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.

7. £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.

8. (a) Write 0.00562 in standard form.

(b) Write 1.452 × 103 as an ordinary number.

9. 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.

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.

(b) Work out the ratio e : f

10. 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.

(b) Work out the probability that her train will be late on at least one of these two days.

11. The grouped frequency table gives information about the times, in minutes, that 80 office workers take to get to work.

(a) Complete the cumulative frequency table.

(b) On the grid, draw the cumulative frequency graph for this information.

(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.

12. OAB is a sector of a circle with centre O and radius 7 cm.

The area of the sector is 40 cm^{2}

Calculate the perimeter of the sector.

Give your answer correct to 3 significant figures.

14. 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.

(a) (i) Calculate an estimate of the gradient of the graph at t = 15

(ii) Describe what your answer to part (i) represents.

(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.

15. Make m the subject of the formula f = (3m + 4)/(m - 1)

16. The straight line L has the equation 3y = 4x + 7

The point A has coordinate (3, -5)

Find an equation of the straight line that is perpendicular to L and passes through A.

17. 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

All the small cubes are yellow.

(b) Work out the least possible number of large yellow cubes in the bag.

18. The points A, B, C and D lie on a circle.

CDE is a straight line.

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.

19.The diagram shows a triangular prism.

The diagram shows part of the graph of y = x^{2} – 2x + 3

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.

20. CDEF is a quadrilateral.

CD = a, DE = b and FC = a – b.

(a) Express FE in terms of a and/or b.

Give your answer in its simplest form.

M is the midpoint of DE.

X is the point on FM such that FX : XM = n : 1

CXE is a straight line.

(b) Work out the value of n.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More videos, activities and worksheets that are suitable for GCSE Maths

Edexcel GCSE Mathematics June 2019 Past Paper 2H (Pdf)

Edexcel GCSE June 2019 Paper 2H (Calculator) Solutions

1. (a) Solve 14n > 11n + 6

(b) On the number line below, show the set of values of x for which –2 < x + 3 ≤ 4

2. On the grid below, draw the graph of y = 2x – 3 for values of x from -2 to 4

3. 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.

(i) Work out how many of the 195 students you think will want to go to the Theme Park.

(ii) State any assumption you made and explain how this may affect your answer.

4. A container is in the shape of a cuboid.

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?

5. ABC is a right-angled triangle.

Calculate the length of AB.

Give your answer correct to 2 decimal places.

6. 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.

7. £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.

8. (a) Write 0.00562 in standard form.

(b) Write 1.452 × 103 as an ordinary number.

9. 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.

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.

(b) Work out the ratio e : f

10. 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.

(b) Work out the probability that her train will be late on at least one of these two days.

11. The grouped frequency table gives information about the times, in minutes, that 80 office workers take to get to work.

(a) Complete the cumulative frequency table.

(b) On the grid, draw the cumulative frequency graph for this information.

(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.

12. OAB is a sector of a circle with centre O and radius 7 cm.

The area of the sector is 40 cm

Calculate the perimeter of the sector.

Give your answer correct to 3 significant figures.

14. 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.

(a) (i) Calculate an estimate of the gradient of the graph at t = 15

(ii) Describe what your answer to part (i) represents.

(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.

15. Make m the subject of the formula f = (3m + 4)/(m - 1)

16. The straight line L has the equation 3y = 4x + 7

The point A has coordinate (3, -5)

Find an equation of the straight line that is perpendicular to L and passes through A.

17. 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

All the small cubes are yellow.

(b) Work out the least possible number of large yellow cubes in the bag.

18. The points A, B, C and D lie on a circle.

CDE is a straight line.

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.

19.The diagram shows a triangular prism.

The diagram shows part of the graph of y = x

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.

20. CDEF is a quadrilateral.

CD = a, DE = b and FC = a – b.

(a) Express FE in terms of a and/or b.

Give your answer in its simplest form.

M is the midpoint of DE.

X is the point on FM such that FX : XM = n : 1

CXE is a straight line.

(b) Work out the value of n.

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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