KS4 2016 specimen papers OCR H3 specimen 14 A straight line goes through the points (p, q) and (r, s), where p + 2 = r q + 4 = s. Find the gradient of the line. AQA F3 H3 specimen 21 When x² = 16 the only value that x can be is 4. Is this true or false? Tick a box. (b) When n is a positive integer, the value of 2n is always a factor of the value of 20n. Reason Reason (c) When y is positive, the value of y² is always greater than the value of y. Reason AQA H2 specimen 18 In the formula T = (n 6)² + 1 n is a positive integer. (a) Kim says, The value of T is always greater than 1 because (n 6)² is always greater than 0 Comment on her statement. (b) What is the only value of T that is a square number? OCR F1 specimen 17 Six equations are shown below, each labelled with a letter. Choose the correct letters to make each statement true. (a) Equation B and equation... are equivalent. (b) Equation... and equation... each show x is inversely proportional to y. OCR F2 specimen 18 Amin is attempting to solve the following equation. (x + 1)(x + 4) = (x - 2)(x - 3) His incorrect solution is shown below. (a) Identify the step in which Amin made his first error and explain why this step is incorrect. (b) Write out a correct solution to the equation. AQA H1 2015 Nov 7 These expressions represent four numbers. The sum of the first two expressions is 36 Work out the value of the median of the four numbers.
OCR F1 specimen (b) Angus thinks of a number. If he cubes his number and then adds 9, he gets 17. What number is he thinking of? OCR H1 specimen 11 (a) Give one reason why 0 is an even number. OCR F3 specimen 4 Antonio works Monday, Tuesday and Wednesday. He starts work at 4.00 pm and finishes at 10.30 pm. Antonio is paid 10 per hour on weekdays. One week, he also works for 4 hours on Sunday. He is paid 50% more on Sundays. How much does Antonio earn altogether this week? AQA F2 H2 specimen 22 ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} S = square numbers E = even numbers (a) Complete the Venn diagram. (b) One of the numbers is chosen at random. Write down P (S E). AQA H1 specimen 15 a 10 4 + a 10 2 = 24 240 where a is a number. Work out a 10 4 a 10 2 Give your answer in standard form. OCR F2 specimen 3 Peter says The sum of an odd number and an even number is even. The example 3 + 4 = 7 shows that Peter is not correct. Write an example to show that each of these statements is not correct. (a) The sum of two prime numbers is always odd. (b) Squaring a whole number always results in an even number. AQA F3 specimen 13 Hayley and Tom have 2000 to spend on food at their wedding. Here are their two options. Work out the maximum number of people they can pay for. Show working to compare the maximum number of people for both options. AQA F1 specimen 10 Here are some properties of numbers. A Even B Odd C Prime D Square E Two-digit 10 (a) Which two properties does the number 4 have? Circle the correct letters. A B C D E AQA F2 specimen 9 Lucy says, 3 is odd and 2 is even, so when you add a multiple of 3 to a multiple of 2 the answer is always odd. 10 (b) Can one number have all of the properties? Tick a box. Give a reason for your answer. 10 (c) Write down a number with three of the properties. State which properties it has. Is she correct? Write down a calculation to support your answer.
AQA F2 specimen 11 Three boxes contain counters. There are 62 counters in total. The total number of counters in box A and box B is 34. The difference between the number of counters in box A and box C is 9 Work out the number of counters in each box. Edexcel F2 specimen 11 Adam says, When you multiply an even number by an odd number the answer is always an odd number. (a) Write down an example to show Adam is wrong. Edexcel F3 specimen 3 There are 6760 people at a rugby match. 3879 of the people are men. 1241 of the people are women. ¼ of the children are girls. Work out how many boys are at the rugby match. Edexcel F2 specimen 6 Jan writes down one multiple of 9 and two different factors of 40 Jan adds together her three numbers. Her answer is greater than 20 but less than 30. Find three numbers that Jan could have written down. Edexcel F1 specimen 3 Write down the 20th odd number. Betty says, When you multiply two prime numbers together the answer is always an odd number. (b) Betty is wrong. Explain why. Edexcel H3 specimen 6 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? OCR H2 specimen 19 The prices of two phones are in the ratio x : y. When the prices are both increased by 20, the ratio becomes 5 : 2. When the prices are both reduced by 5, the ratio becomes 5 : 1. Express the ratio x : y in its lowest terms. OCR F1 H1 specimen 19 Peter makes a large amount of pink paint by mixing red and white paint in the ratio 2 : 3. Red paint costs 80 per 10 litres. White paint costs 5 per 10 litres. Peter sells his pink paint in 10-litre tins for 60 per tin. Calculate how much profit he makes for each tin he sells. Edexcel F2 specimen 22 A tin of varnish costs 15 A rectangular floor has dimensions 6 m by 11 m. The floor is going to be covered in varnish. Edexcel H2 specimen 8 In a box of pens, there are three times as many red pens as green pens and two times as many green pens as blue pens. For the pens in the box, write down the ratio of the number of red pens to the number of green pens to the number of blue pens. AQA H3 specimen 16 During a game, players can win and lose counters. At the start of the game Rob, Tim and Zak share the counters in the ratio 5 : 6 : 7 At the end of the game Rob, Tim and Zak share the same number of counters in the ratio 7 : 9 : 8 Show that Rob ends the game with more counters than he started with. Helen assumes that each tin of this varnish covers an area of 12 m². (a) Using Helen s assumption, work out the cost of buying the varnish for this floor. Helen finds that each tin of varnish covers less than 12 m². (b) Explain how this might affect the number of tins she needs to buy.
AQA F1 H1 specimen 10 White paint costs 2.80 per litre. Blue paint costs 3.50 per litre. White paint and blue paint are mixed in the ratio 3 : 2 Work out the cost of 18 litres of the mixture. Edexcel F1 H1 specimen 25 In a company, the ratio of the number of men to the number of women is 3:2. 40% of the men are under the age of 25 10% of the women are under the age of 25 What percentage of all the people in the company are under the age of 25? OCR F3 specimen 3 (a) How many 20p coins would you need to make up 7000? (b) Each 20p coin weighs 5 g. AQA F2 specimen 14 Luke saves 10p coins and 20p coins. He has three times as many 10p coins as 20p coins a total of 17 How many 10p coins does he have? Edexcel F2 H2 specimen 23 Frank, Mary and Seth shared some sweets in the ratio 4 : 5 : 7 Seth got 18 more sweets than Frank. Work out the total number of sweets they shared. AQA H2 specimen 21 A company makes boxes of cereal. A box usually contains 450 grams of cereal. Here are two options for a special offer. Lizzie says I can lift 7000 worth of 20p coins. Is Lizzie s claim reasonable? Show your working and state any assumptions you have made. (c) How have any assumptions you have made affected your answer to part (b)? Which option is the better value for the customer? You must show your working. Edexcel F3 specimen 23 A and B are two companies. The table shows some information about the sales of each company and the number of workers for each company in 2004 and in 2014. (a) Work out the percentage increase in sales from 2004 to 2014 for Company A. (b) Which company had the most sales per worker in 2014, Company A or Company B? You must show how you get your answer. OCR H1 Applications of Maths 2015 May 1 Logos can be very expensive to design. It can also be very expensive to change them. Here are some famous logos and their cost, in dollars ($) and pounds ( ). AQA F2 specimen 17 Mr Jones works for five days each week. If he uses his car to travel to work, each day he drive a total distance of 24.2 miles his car travels 32.3 miles per gallon of petrol petrol costs 1.27 per litre. If he uses the bus to travel to work, he can buy a weekly ticket for 19.50. Use 1 gallon = 4.5 litres The Next logo cost 10% of the cost of the Pepsi logo. Work out the cost in pounds of the London Olympics logo. Use only the information given above. Is it cheaper if he uses his car or the bus to travel to work? You must show your working.
AQA H2 specimen 26 Two boxes are made with card. The boxes are similar cuboids. The smaller box has height 32 cm It takes 44% more card to make the larger box. Work out the height, h, of the larger box. Edexcel F2 specimen 22 A tin of varnish costs 15 A rectangular floor has dimensions 6 m by 11 m. The floor is going to be covered in varnish. Helen assumes that each tin of this varnish covers an area of 12 m². (a) Using Helen s assumption, work out the cost of buying the varnish for this floor. Helen finds that each tin of varnish covers less than 12 m². (b) Explain how this might affect the number of tins she needs to buy. AQA F1 H1 specimen 30 ABCH is a square. HCFG is a rectangle. CDEF is a square. They are joined to make an L-shape. Not drawn accurately Show that the total area of the L-shape, in cm², is x² + 9x + 27. OCR F3 specimen 19 The perimeter of the triangle is the same length as the perimeter of the square. Find an expression for the length of one side of the square in terms of a. Give your answer in its simplest form. Edexcel H2 specimen 9 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. OCR F2 specimen 6 (b) The area of the parallelogram is three times the area of the triangle. Show that the perpendicular height h of the parallelogram is 4cm.
AQA F2 specimen 24 A Big Wheel is modelled as a circle with centre O and radius 15 metres. The wheel turns in an anticlockwise direction. The lowest point on the wheel is always 2 metres above horizontal ground. (a) C is a point on the wheel, h metres above horizontal ground. Angle COB = x Show that h = 17 15 cos x (b) D is a point on the wheel. Angle DOB = 120 Work out the height of D above horizontal ground. AQA F2 specimen 26 Two boxes are made with card. The boxes are similar cuboids. The smaller box has height 32 cm. It takes 44% more card to make the larger box. Work out the height, h, of the larger box. AQA F2 specimen 16 A company s logo is a pentagon has exactly one line of symmetry has sides with whole number lengths has a perimeter of 15 cm Draw a sketch of a possible logo. Label each side with its length. AQA F3 H3 specimen 29 ABC is a triangle with AB = AC. BA is parallel to CD. Show that angle x = 30 AQA H2 2015 Nov 15 A cycle track has two identical semi-circular ends and two straight sides as shown. A cyclist completes one lap. Her average speed is 18 m/s. Her target time to complete one lap is 30 seconds. Does she beat her target? You must show your working.
OCR F2 specimen 6 (b) The area of the parallelogram is three times the area of the triangle. Show that the perpendicular height h of the parallelogram is 4cm. AQA H3 specimen 6 A bag contains counters that are red, blue, green or yellow. A counter is chosen at random. The probability it is red is 9%. Work out the probability it is green. OCR F3 specimen 14 This frequency diagram summarises the number of minutes Astrid s train was late over the last 50 days. Frequency (a) Use information from this diagram to estimate the probability that her train will be 4 minutes late tomorrow. (b) Explain whether your answer to part (a) gives a reliable probability. AQA H2 specimen 14 A prime number between 300 and 450 is chosen at random. The table shows the probability that the number lies in different ranges. (a) Work out the value of x. (b) Work out the probability that the prime number is greater than 390. (c) There are four prime numbers between 300 and 330 How many prime numbers are there between 300 and 450? OCR F1 specimen 6 Here is a Venn diagram. 30 students are asked if they have a dog or cat. 21 have a dog. 16 have a cat. 8 have a dog, but not a cat. Complete the Venn diagram.
OCR F2 specimen 16 Abi, Ben and Carl each drop a number of identical drawing pins, and count how many land with the pin upwards. The table shows some of their results. (a) Abi says As a drawing pin can only land with its pin up or with its pin down, the probability of a drawing pin landing pin up is ½. Criticise her statement. (b) Carl s results give the best estimate of the probability of a drawing pin landing pin up. Explain why. (c) Two pins are dropped. Estimate the probability that both pins land pin up. AQA H2 F2 specimen 7 A coin is rolled onto a grid of squares. It lands randomly on the grid. To win, the coin must land completely within one of the squares. Meera and John each roll the coin a number of times and record their results. (a) Work out two different estimates for the probability of winning. Edexcel F1 specimen 17 100 students had some homework. 42 of these students are boys. 8 of the 100 students did not do their homework. 53 of the girls did do their homework. (a) Use this information to complete the frequency tree. One of the girls is chosen at random. (b) Work out the probability that this girl did not do her homework. (b) Which of your estimates is the better estimate for the probability of winning? Give a reason for your answer. AQA F1 specimen 18 The table shows the sales of food and drink for three days at a market stall. Sales ( ) Sales of food and drink Hannah uses this information to draw a composite bar chart. Write down three different mistakes that she has made. Day
AQA F1 specimen 22 The diagram shows information about the scores of Class 3A in a spelling test. Frequency Class 3A This diagram shows information about the scores of Class 3B in the same test. Frequency Class 3B (a) A student is chosen at random from Class 3A. Work out the probability that the student s score was the mode for the class. (b) Show that Class 3A had more consistent scores than Class 3B. Use the data from both diagrams. (c) Lucy is one of the 29 students in Class 3B. Her score was the same as the median score for her class. Work out her score. OCR H2 specimen 13 One day a museum monitored the time spent by visitors at six exhibitions. The visitor times are summarised in the box plots below. (a) Work out the range in visitor times at the Fantastic Frogs exhibition. (b) At which exhibition were visitor times the most consistent? Give a reason for your answer. (c) Give one similarity and one difference between the distributions of the visitor times for Origins of the Steam Engine and The Philippine Revolution. (d) Is it possible to work out from the box plots which exhibition had the most visitors? Justify your answer.
OCR H3 specimen 6 John wants to investigate whether men in the UK are better at estimating a time interval of 10 seconds than women in the UK. He decides to sample the population by asking his work colleagues to take the test. The diagrams below summarise John s results. (a) What information from the diagrams can be used to support each of these statements? (i) The older John s colleagues are, the lower their estimate is. (ii) Males in the sample tend to underestimate the interval and females in the sample tend to overestimate the interval. (b) Comment on whether any conclusions can be drawn for the UK population from the results of this sample.