Foundation/Higher Crossover Questions Topics: Worded HCF and LCM Questions Equations with unknowns on both sides Unit Conversions Venn diagrams Worded two-way tables Basic Trigonometry Loci & Constructions Drawing cubic graphs Estimated mean from grouped data Compound measures Angles in parallel lines Simple and compound interest Subject of the formula Real-life graphs
Questions Q1. Michael writes down 4 different factors of 60 He adds the 4 factors together. He gets a number greater than 20 but less than 35 What 4 factors could Michael have written down?... (Total for Question is 3 marks) Q2. Write down three different factors of 18 that add together to give a prime number.......... (Total for question = 2 marks) Q3. Liz buys packets of coloured buttons. There are 8 red buttons in each packet of red buttons. There are 6 silver buttons in each packet of silver buttons. There are 5 gold buttons in each packet of gold buttons. Liz buys equal numbers of red buttons, silver buttons and gold buttons. How many packets of each colour of buttons did Liz buy?... packets of red buttons... packets of silver buttons... packets of gold buttons (Total for question = 3 marks)
Q4. (a) Make t the subject of the formula 2(a + t) = 5t + 7 (b) Solve the simultaneous equations 3x 4y = 8 9x + 5y = 1.5 t =...................... (3) x =...................... y =...................... (3) (Total for Question is 6 marks) Q5. Ali has x cards. Belinda has twice as many cards as Ali. Charlie has 5 more cards than Ali. They have a total of 33 cards. (a) Show that 4x + 5 = 33 (b) Work out the number of cards Ali has. (3)... (2) (Total for Question is 5 marks)
Q6. Stephanie is x years old. Tobi is twice as old as Stephanie. Ulrika is 3 years younger than Tobi. The sum of all their ages is 52 years. (a) Show that 5x 3 = 52 (b) Work out the value of x. (3) x =... (2) (Total for Question is 5 marks) Q7. Asha and Lucy are selling pencils in a school shop. They sell boxes of pencils and single pencils. Asha sells 7 boxes of pencils and 22 single pencils. Lucy sells 5 boxes of pencils and 2 single pencils. Asha sells twice as many pencils as Lucy. Work out how many pencils there are in a box.... (Total for question = 4 marks)
Q8. (a) Write down the inequality represented on the number line.... (1) (b) Solve 4y 9 3... (2) (c) 3 n < 2 2 < m < 4 n and m are integers. Given that n = m, write down all the possible values of n.... (2) (Total for question = 5 marks)
Q9. Solve the simultaneous equations 5x + 2y = 2 3x 5y = 11.2 x =... y =... (Total for question = 4 marks)
Q10. ABCD is a rectangle. EFGH is a trapezium. All measurements are in centimetres. The perimeters of these two shapes are the same. Work out the area of the rectangle.... cm 2 (Total for question = 5 marks)
Q11. (a) Solve 3(2p 5) = 21 (b) Solve 9x 11 = 5x + 7 p =.................... (3) x =.................... (3) (Total for Question is 6 marks) Q12. A sprinter runs a distance of 200 metres in 25 seconds. Work out the average speed of the sprinter.... m/s (Total for question = 1 mark)
Q13. Change 72 km/h into m/s.... m / s (Total for question = 3 marks) Q14. Change 2 m 3 to cm 3.... cm 3 (Total for question = 2 marks) Q15. Peter goes for a walk. He walks 15 miles in 6 hours. (a) Work out Peter's average speed. Give your answer in miles per hour.... 5 miles = 8 km. Sunita says that Peter walked more than 20 km. *(b) Is Sunita right? You must show all your working. (2) (2) (Total for Question is 4 marks)
Q16. Steve travelled from Ashton to Barnfield. He travelled 235 miles, correct to the nearest 5 miles. The journey took him 200 minutes, correct to the nearest 5 minutes. Calculate the lower bound for the average speed of the journey. Give your answer in miles per hour, correct to 3 significant figures. You must show all your working.... mph (Total for question = 4 marks) Q17. A rectangle has an area of 4 m 2. Write this area in cm 2.... cm 2 (Total for question = 2 marks)
Q18. (a) Write 2.3 kg in grams.... g (1) (b) Write 350 mm in centimetres.... cm (1) (c) Change 27 000 cm 3 to litres.... litres (1) (Total for question = 3 marks) Q19. Linda keeps chickens. She sells the eggs that her chickens lay. She has 140 chickens. Each chicken lays 6 eggs a week. Linda gives each chicken 100 g of chicken feed each day. The chicken feed costs 6.75 for a 25 kg bag. Work out the cost of the chicken feed for every 12 eggs. (Total for question = 5 marks)
Q20. Sue is driving home from her friend's house. Sue drives Sue 10 miles from her friend's house to the motorway 240 miles on the motorway 5 miles from the motorway to her home takes 20 minutes to drive from her friend's house to the motorway drives at an average speed of 60 mph on the motorway takes 25 minutes to drive from the motorway to her home Sue stops for a 30 minute rest on her drive home. Sue leaves her friend's house at 9.00 am. What time does Sue get home? You must show all your working.... (Total for Question is 3 marks)
Q21. * Anne wants to fill 12 hanging baskets with compost. Each hanging basket is a hemisphere of diameter 40 cm. Anne has 4 bags of compost. There are 50 litres of compost in each bag. Has Anne got enough compost to fill the 12 hanging baskets? (Total for question = 4 marks)
Q22. Zahra mixes 150g of metal A and 150g of metal B to make 300g of an alloy. Metal A has a density of 19.3g/cm 3. Metal B has a density of 8.9g/cm 3. Work out the density of the alloy.... cm 3 (Total for question = 4 marks)
Q23. * The diagram shows a solid wooden sphere. The radius of the sphere is 2 cm. The mass of the sphere is 45 grams. Wood will float on the Dead Sea only when the density of the wood is less than 1.24 g/cm 3. Will this wooden sphere float on the Dead Sea? (Total for Question is 4 marks)
Q24. The graph shows the distance travelled by two trains. (a) Work out the gradient of the line for train A.... (2) (b) Which train is travelling at the greater speed? You must explain your answer.......... (1) (c) After how many minutes has train A gone 10 miles further than train B?... minutes (1) (Total for Question is 4 marks)
Q25. On an activity day students play one sport. They play football or hockey or tennis. 120 students are on the activity day. 30 of the students are boys. 12 of the boys and 26 of the girls play hockey. 45 of the students play football. 35 of the 45 students who play football are girls. Work out the number of girls who play tennis.... (Total for Question is 4 marks) Q26. There are 130 adults at a language school. Each adult studies one of French or Spanish or German. 96 of the adults are women.12 of the women study French. 73 of the adults study Spanish.55 of the women study Spanish. 9 of the men study German. How many of the adults study French?... (Total for Question is 4 marks)
Q27. * Toga wants to estimate the number of termites in a nest. On Monday Toga catches 80 termites. He puts a mark on each termite. He then puts all 80 termites back in the nest. On Tuesday Toga catches 60 termites. 12 of these termites have a mark on them. Work out an estimate for the total number of termites in the nest. You must write down any assumptions you have made.... (Total for question = 4 marks) Q28. Henri is carrying out a survey of the people aged 65 and over in his village. The table shows information about these people. Henri is going to take a sample of 30 people stratified by age. How many people aged 75 79 should be in the sample?... (Total for Question is 3 marks)
Q29. Clive wants to estimate the number of bees in a beehive. Clive catches 50 bees from the beehive. He marks each bee with a dye. He then lets the bees go. The next day, Clive catches 40 bees from the beehive. 8 of these bees have been marked with the dye. (i) Work out an estimate for the number of bees in the beehive.... bees (ii) Write down any assumptions you have made.......... (Total for Question is 4 marks)
Q30. Sami asked 50 people which drinks they liked from tea, coffee and milk. All 50 people like at least one of the drinks 19 people like all three drinks. 16 people like tea and coffee but do not like milk. 21 people like coffee and milk. 24 people like tea and milk. 40 people like coffee. 1 person likes only milk. Sami selects at random one of the 50 people. (a) Work out the probability that this person likes tea.... (4) (b) Given that the person selected at random from the 50 people likes tea, find the probability that this person also likes exactly one other drink.... (2) (Total for question = 6 marks)
Q31. Here is a Venn diagram. (a) Write down the numbers that are in set (i) A B (ii) A B... One of the numbers in the diagram is chosen at random. (b) Find the probability that the number is in set A'... (2)... (2) (Total for question = 4 marks)
Q32. Some students watched a film. James recorded the heart rates, in beats per minute, of the students after they had watched the film. The back-to-back stem and leaf diagram gives information about his results. (a) Compare the distribution of the heart rates of the female students and the distribution of the heart rates of the male students. (3) 13 of the 26 students like comedy films. 16 of the 26 students like science fiction films. 5 of the 26 students like both comedy and science fiction films. (b) Draw a Venn diagram to show this information. (3) (Total for question = 6 marks)
Q33. Draw a Venn diagram for this information. (Total for question is 4 marks) Q34. Triangle ABC has a right angle at C. Angle BAC = 48. AB = 9.3 cm. Calculate the length of BC. (Total for question = 3 marks)
Q35. * 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. (Total for Question is 3 marks)
Q36. ABCD is a parallelogram. DC = 5 cm Angle ADB = 36 Calculate the length of AD. Give your answer correct to 3 significant figures.... (Total for Question is 4 marks)
Q37. PQR is a right-angled triangle. Work out the size of the angle marked x. Give your answer correct to 1 decimal place.... (Total for question = 2 marks) Q38. DEF is a right-angled triangle. DE = 86 mm EF = 37 mm Calculate the size of the angle marked y. Give your answer correct to 1 decimal place....
(Total for Question is 3 marks) Q39. AB = 15 m BC = 24 m Angle BAD = 62 Work out the size of angle BCD. Give your answer correct to 1 decimal place.... (Total for question = 5 marks)
Q40. Here is a sketch of a triangle. In the space below, make an accurate drawing of the triangle. (Total for question = 3 marks)
Q41. Here is a scale drawing of an office. The scale is 1 cm to 2 metres. A photocopier is going to be put in the office. The photocopier has to be closer to B than it is to A. The photocopier also has to be less than 8 metres from C. Show, by shading, the region where the photocopier can be put. (Total for question = 3 marks)
Q42. Here is a triangle. Make an accurate drawing of triangle PQR. (Total for question = 2 marks)
Q43. The diagram shows the positions of two shops, A and B, on a map. The scale of the map is 1 cm represents 5 km. Yannis wants to build a warehouse. The warehouse needs to be less than 10 km from A, less than 20 km from B. Show by shading where Yannis can build the warehouse. (Total for Question is 3 marks)
Q44. (a) Complete the table of values for y = x 3 3x + 1 (b) On the grid, draw the graph of y = x 3 3x + 1 for values of x from 2 to 2 (2) (2) (Total for question = 4 marks)
Q45. 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 = 2 x y = 2x 10 y = 8x 2x 2 y = 3x 2 Give the equation of each graph. Graph A... Graph B... Graph C... (Total for question = 3 marks)
Q46. Here are three graphs. Here are four equations of graphs. y = x 3 y = x 2 + 4 y = 1 x y = 2 x Match each to the correct equation. A and y =..................... B and y =..................... C and y =..................... (Total for Question is 3 marks)
Q47. Helen went on 35 flights in a hot air balloon last year. The table gives some information about the length of time, t minutes, of each flight. On the grid below, draw a frequency polygon for this information. (Total for Question is 2 marks)
Q48. Bob asked each of 40 friends how many minutes they took to get to work. The table shows some information about his results. Time taken (m minutes) Frequency 0 < m 10 3 10 < m 20 8 20 < m 30 11 30 < m 40 9 40 < m 50 9 Work out an estimate for the mean time taken....................... minutes (Total for Question is 4 marks)
Q49. Jenny works in a shop that sells belts. The table shows information about the waist sizes of 50 customers who bought belts from the shop in May. (a) Calculate an estimate for the mean waist size.... inches (3) Belts are made in sizes Small, Medium, Large and Extra Large. Jenny needs to order more belts in June. The modal size of belts sold is Small. Jenny is going to order of the belts in size Small. The manager of the shop tells Jenny she should not order so many Small belts. (b) Who is correct, Jenny or the manager? You must give a reason for your answer....... (2) (Total for question is 5 marks)
Q50. The table shows information about the number of years 41 teachers have each taught at a school. (a) Write down the class interval that contains the median.... (2) (b) Calculate an estimate for the mean number of years. You must show all your working.... (4) (Total for question = 6 marks)
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