GCSE Mathematics Paper 1F
Pearson Edexcel Level 1/Level 2 GCSE (9-1)
Foundation (Non-Calculator) | June 2019
Total: 80 marks | Time: 1 hour 30 minutes
Foundation (Non-Calculator) | June 2019
Total: 80 marks | Time: 1 hour 30 minutes
Mark Scheme Legend
- M1 = Method mark (correct method applied)
- A1 = Accuracy mark (correct answer)
- B1 = Independent mark (correct statement or value)
- P1 = Process mark (completing a process)
- C1 = Communication mark (clear explanation or reasoning)
📚 Table of Contents
- Question 1 (Unit Conversion)
- Question 2 (Decimals to Percentages)
- Question 3 (Order of Operations)
- Question 4 (Prime Numbers)
- Question 5 (Finding Midpoints)
- Question 6 (Multi-step Problems)
- Question 7 (Bar Charts and Mode)
- Question 8 (Ordering Fractions)
- Question 9 (Speed Distance Time)
- Question 10 (Solving Equations)
- Question 11 (Multiplication)
- Question 12 (Angles)
- Question 13 (Algebra Expressions)
- Question 14 (Fractions)
- Question 15 (Powers and Roots)
- Question 16 (Expand and Factorise)
- Question 17 (Probability)
- Question 18 (Problem Solving)
- Question 19 (Fraction Operations)
- Question 20 (Percentages and Area)
- Question 21 (Two-way Tables)
- Question 22 (Probability Tables)
- Question 23 (Ratio and Proportion)
- Question 24 (HCF)
- Question 25 (3D Shapes)
- Question 26 (Transformations)
- Question 27 (Complex Ratios)
- Question 28 (Rectangles and Area)
- Question 29 (Quadratic Graphs)
Question 1 (1 mark)
Write 180 minutes in hours.
Try Another One
Write 240 minutes in hours.
\(240 \div 60 = 4\)
Answer: 4 hours
Answer: 4 hours
Question 2 (1 mark)
Write 0.73 as a percentage.
Try Another One
Write 0.45 as a percentage.
\(0.45 \times 100 = 45\)
Answer: 45%
Answer: 45%
Question 3 (1 mark)
Work out \(10 \times (3 + 5)\)
Try Another One
Work out \(12 \times (4 + 3)\)
First, brackets: \(4 + 3 = 7\)
Then multiply: \(12 \times 7 = 84\)
Answer: 84
Then multiply: \(12 \times 7 = 84\)
Answer: 84
Question 4 (1 mark)
Write down a prime number that is between 20 and 30
Try Another One
Write down a prime number that is between 30 and 40
The prime numbers between 30 and 40 are: 31 and 37
Answer: 31 or 37
Answer: 31 or 37
Question 5 (1 mark)
Find the number that is exactly halfway between 7 and 15
Try Another One
Find the number that is exactly halfway between 12 and 28
\((12 + 28) \div 2 = 40 \div 2 = 20\)
Answer: 20
Answer: 20
Question 6 (4 marks)
Harry is planning a holiday for 4 people for 7 days.
Here are the costs for the holiday for each person:
Here are the costs for the holiday for each person:
- Travel: £150
- Hotel: £50 for each day
- Spending money: £250
Try Another One
Sarah is planning a holiday for 3 people for 5 days.
Here are the costs for the holiday for each person:
Here are the costs for the holiday for each person:
- Travel: £120
- Hotel: £60 for each day
- Spending money: £200
Travel: \(3 \times 120 = 360\)
Hotel: \(5 \times 3 \times 60 = 900\)
Spending: \(3 \times 200 = 600\)
Total: \(360 + 900 + 600 = 1860\)
Answer: £1860
Hotel: \(5 \times 3 \times 60 = 900\)
Spending: \(3 \times 200 = 600\)
Total: \(360 + 900 + 600 = 1860\)
Answer: £1860
Question 7 (3 marks)
In Adam’s garden, the flowers are only red or white or yellow or blue.
The chart shows the number of red flowers, the number of white flowers and the number of yellow flowers.
The total number of flowers is 30
(a) Work out the number of blue flowers.
(b) Write down the mode.
The chart shows the number of red flowers, the number of white flowers and the number of yellow flowers.
The total number of flowers is 30
(a) Work out the number of blue flowers.
(b) Write down the mode.
Try Another One
In Beth’s garden, there are 40 flowers that are only red or white or yellow or blue.
Red: 12 flowers, White: 9 flowers, Yellow: 6 flowers
(a) Work out the number of blue flowers.
(b) Write down the mode.
Red: 12 flowers, White: 9 flowers, Yellow: 6 flowers
(a) Work out the number of blue flowers.
(b) Write down the mode.
(a) \(40 – 12 – 9 – 6 = 13\) blue flowers
(b) The mode is red (12 flowers)
Answer: (a) 13 (b) red
(b) The mode is red (12 flowers)
Answer: (a) 13 (b) red
Question 8 (2 marks)
Write the following fractions in order of size.
Start with the smallest fraction.
\(\frac{1}{3}\) \(\frac{3}{4}\) \(\frac{1}{4}\) \(\frac{7}{12}\) \(\frac{1}{2}\)
Start with the smallest fraction.
\(\frac{1}{3}\) \(\frac{3}{4}\) \(\frac{1}{4}\) \(\frac{7}{12}\) \(\frac{1}{2}\)
Try Another One
Write the following fractions in order of size. Start with the smallest fraction.
\(\frac{2}{5}\) \(\frac{1}{2}\) \(\frac{3}{10}\) \(\frac{7}{10}\) \(\frac{3}{5}\)
\(\frac{2}{5}\) \(\frac{1}{2}\) \(\frac{3}{10}\) \(\frac{7}{10}\) \(\frac{3}{5}\)
Converting to tenths: \(\frac{4}{10}\), \(\frac{5}{10}\), \(\frac{3}{10}\), \(\frac{7}{10}\), \(\frac{6}{10}\)
In order: \(\frac{3}{10}\), \(\frac{2}{5}\), \(\frac{1}{2}\), \(\frac{3}{5}\), \(\frac{7}{10}\)
Answer: \(\frac{3}{10}\), \(\frac{2}{5}\), \(\frac{1}{2}\), \(\frac{3}{5}\), \(\frac{7}{10}\)
In order: \(\frac{3}{10}\), \(\frac{2}{5}\), \(\frac{1}{2}\), \(\frac{3}{5}\), \(\frac{7}{10}\)
Answer: \(\frac{3}{10}\), \(\frac{2}{5}\), \(\frac{1}{2}\), \(\frac{3}{5}\), \(\frac{7}{10}\)
Question 9 (4 marks)
Ruth left her home at 9 am and walked to the library. She got to the library at 10 30 am. Ruth walked at a speed of 4 mph.
(a) Work out the distance Ruth walked.
Ruth got to the library at 10 30 am. She stayed at the library for 50 minutes. Then she walked home.
Ruth took \(1\frac{1}{4}\) hours to walk home.
(b) At what time did Ruth get home?
(a) Work out the distance Ruth walked.
Ruth got to the library at 10 30 am. She stayed at the library for 50 minutes. Then she walked home.
Ruth took \(1\frac{1}{4}\) hours to walk home.
(b) At what time did Ruth get home?
Try Another One
Tom left his home at 8 am and cycled to school. He got to school at 8:45 am. Tom cycled at a speed of 12 mph.
(a) Work out the distance Tom cycled.
Tom stayed at school for 6 hours 30 minutes, then cycled home. He took 1 hour to cycle home.
(b) At what time did Tom get home?
(a) Work out the distance Tom cycled.
Tom stayed at school for 6 hours 30 minutes, then cycled home. He took 1 hour to cycle home.
(b) At what time did Tom get home?
(a) Time = 45 minutes = 0.75 hours
Distance = \(12 \times 0.75 = 9\) miles
(b) Left school: 8:45 + 6 hours 30 minutes = 3:15 pm
Arrived home: 3:15 pm + 1 hour = 4:15 pm
Answer: (a) 9 miles (b) 4:15 pm
Distance = \(12 \times 0.75 = 9\) miles
(b) Left school: 8:45 + 6 hours 30 minutes = 3:15 pm
Arrived home: 3:15 pm + 1 hour = 4:15 pm
Answer: (a) 9 miles (b) 4:15 pm
Question 10 (4 marks)
(a) Solve \(t + t + t = 12\)
(b) Solve \(x – 2 = 6\)
(c) Solve \(6w + 2 = 20\)
(b) Solve \(x – 2 = 6\)
(c) Solve \(6w + 2 = 20\)
Try Another One
(a) Solve \(m + m + m + m = 20\)
(b) Solve \(y + 5 = 12\)
(c) Solve \(4p – 3 = 17\)
(b) Solve \(y + 5 = 12\)
(c) Solve \(4p – 3 = 17\)
(a) \(4m = 20\), so \(m = 5\)
(b) \(y = 12 – 5 = 7\)
(c) \(4p = 20\), so \(p = 5\)
Answer: (a) 5 (b) 7 (c) 5
(b) \(y = 12 – 5 = 7\)
(c) \(4p = 20\), so \(p = 5\)
Answer: (a) 5 (b) 7 (c) 5
Question 11 (2 marks)
Work out \(74 \times 58\)
Try Another One
Work out \(63 \times 47\)
\(63 \times 7 = 441\)
\(63 \times 40 = 2520\)
\(441 + 2520 = 2961\)
Answer: 2961
\(63 \times 40 = 2520\)
\(441 + 2520 = 2961\)
Answer: 2961
Question 12 (5 marks)
(a) AB and BC are perpendicular lines.
Find the value of \(x\).
(b) RS and TU are parallel lines. PQ is a straight line.
An angle of size 125° is shown on the diagram.
(i) Write down the letter of one other angle of size 125°. Give a reason for your answer.
(ii) Explain why \(a + b + c = 235°\)
Find the value of \(x\).
(b) RS and TU are parallel lines. PQ is a straight line.
An angle of size 125° is shown on the diagram.
(i) Write down the letter of one other angle of size 125°. Give a reason for your answer.
(ii) Explain why \(a + b + c = 235°\)
Try Another One
(a) CD and DE are perpendicular lines. If one part of the angle is 35° and another is 20°, find the remaining angle \(y\).
(b) In a diagram with parallel lines and a 110° angle marked, write an equation for the sum of three angles on a straight line if one is 110°.
(b) In a diagram with parallel lines and a 110° angle marked, write an equation for the sum of three angles on a straight line if one is 110°.
(a) \(35 + 20 + y = 90\), so \(y = 35°\)
(b) If the angles are \(p + q + r\) and one angle is 110°, then on a straight line: \(p + q + r = 180 – 110 = 70°\)
Answer: (a) 35° (b) 70°
(b) If the angles are \(p + q + r\) and one angle is 110°, then on a straight line: \(p + q + r = 180 – 110 = 70°\)
Answer: (a) 35° (b) 70°
Question 13 (1 mark)
The length of a line is \(x\) centimetres.
Write down an expression, in terms of \(x\), for the length of the line in millimetres.
Write down an expression, in terms of \(x\), for the length of the line in millimetres.
Try Another One
The mass of an object is \(m\) kilograms. Write down an expression, in terms of \(m\), for the mass in grams.
1 kilogram = 1000 grams
Expression: \(1000m\) grams
Answer: \(1000m\)
Expression: \(1000m\) grams
Answer: \(1000m\)
Question 24 (2 marks)
Find the highest common factor (HCF) of 72 and 90
Try Another One
Find the highest common factor (HCF) of 48 and 60
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Common factors: 1, 2, 3, 4, 6, 12
Answer: 12
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Common factors: 1, 2, 3, 4, 6, 12
Answer: 12
Question 29 (3 marks)
Here is the graph of \(y = x^2 – 2x – 3\)
(a) Write down the coordinates of the turning point on the graph of \(y = x^2 – 2x – 3\)
(b) Use the graph to find the roots of the equation \(x^2 – 2x – 3 = 0\)
(a) Write down the coordinates of the turning point on the graph of \(y = x^2 – 2x – 3\)
(b) Use the graph to find the roots of the equation \(x^2 – 2x – 3 = 0\)
Try Another One
A graph of \(y = x^2 + 2x – 8\) has its turning point at (-1, -9) and crosses the x-axis at two points.
(a) What are the coordinates of the turning point?
(b) If the graph crosses the x-axis at \(x = -4\) and \(x = 2\), what are the roots of \(x^2 + 2x – 8 = 0\)?
(a) What are the coordinates of the turning point?
(b) If the graph crosses the x-axis at \(x = -4\) and \(x = 2\), what are the roots of \(x^2 + 2x – 8 = 0\)?
(a) The turning point is (-1, -9)
(b) The roots are \(x = -4\) and \(x = 2\)
Answer: (a) (-1, -9) (b) -4 and 2
(b) The roots are \(x = -4\) and \(x = 2\)
Answer: (a) (-1, -9) (b) -4 and 2
