Calculator Practice Questions June 2017 GCSE Mathematics (OCR style) Foundation Tier Paper 3 Name Class INSTRUCTIONS TO CANDIDATES Answer all the questions. Read each question carefully. Make sure you know what you have to do before starting your answer. You are permitted to use a calculator in this paper. Do all rough work in this book. INFORMATION FOR CANDIDATES The number of marks is given in brackets at the end of each question or part question on the Question Paper. You are reminded of the need for clear presentation in your answers. The PiXL Club Limited 2017 This resource is strictly for the use of member schools for as long as they remain members of The PiXL Club. It may not be copied, sold nor transferred to a third party or used by the school after membership ceases. Until such time it may be freely used within the member school. All opinions and contributions are those of the authors. The contents of this resource are not connected with nor endorsed by any other company, organisation or institution. Page 1 of 42
OCR Foundation Paper 3 Revision List The following are the topics we feel are more likely to appear in Paper 3, based on the content that has been examined so far in Papers 1 & 2. This is not a guarantee that these topics will definitely come up nor is it a guarantee that the previously examined material won t be asked again! Algebra Substitution Rearranging equations (changing the subject) Sequences nth term Inequalities solving and drawing on a number line Using formulae in context Straight line graphs (y = mx + c) Drawing linear and quadratic graphs using a table of values Expanding double brackets Solving simultaneous equations Number HCF Estimation Use your calculator to Statistics Mean from grouped data (including explaining why it is an estimate) Two way tables Scatter diagrams, correlation and line of best fit Geometry Vectors Transformations (Translation, Reflection, Rotation, Enlargement) Trigonometry 3D Shapes names, properties, surface area & volume Converting units of measure Angles in polygons (interior/exterior) Density/mass/volume Arcs/Sectors Ratio & Proportion Direct proportion Inverse proportion Probability Venn diagrams Page 2 of 42
Answer all the questions 1 For each of the following write a number which satisfies the inequality 20 < x < 40 (a) A prime number (b) A square number. [1] (c) A multiple of 8. [1] (d) A factor of 125. [1] (e) A cube number. [1] (f) A number with four digits. [1]. [1] Page 3 of 42
2 (a) Here are all the entries on Gemma s bank statement for the week ending 15 April. Three of the values are missing. Complete the bank statement. Date Item Credit ( ) Debit ( ) Balance ( ) 8 April Starting balance 84.58 12 April Card payment 69.95 13 April Direct debit 56.87 15 April Salary 920.00 [3] (b) In May, Gemma received a pay rise. Her salary increased by 3.2%. What was Gemma s salary in May?. [2] Page 4 of 42
3 (a) Carly writes 252 as a product of its prime factors and gets 2 x 3 x 6 x 7. Explain what mistake she has made........... [1] (b) Write the number 120 as a product of its prime factors. [2] (c) Find the highest common factor of 120 and 252.. [2] Page 5 of 42
4 (a) Rebekah uses her calculator to find the value of She says the result is 11.56. Rebekah is wrong. 16.682 2.78 + 5.56. Calculate the correct result. Give your answer correct to one decimal place. [2] (b) What mistake did Rebekah make?......... [1] 5 Calculate the value to the equation below. Give your answer correct to 2 significant figures 6.25 0.8 0.42 3 6 (a) Convert this into a mixed number 21 5. [2] (b) Convert this into an improper fraction. [1] 2 3 5. [1] Page 6 of 42
7 Find the difference between the largest and the smallest of the below fractions. 2 6 3 10 6 15. [3] 8 In a word game, there is a bag of 80 tiles, each of which carries a letter that is either a vowel or a consonant. (a) 3 10 of the tiles have vowels on them. (i) How many tiles have vowels on them. [1] (ii) What percentage of the tiles have vowels on them?. [1] (iii) What is the ratio of tiles with vowels to tiles with consonants? Give your answer in its simplest form.. [2] (b) John finds some extra tiles, all of which are printed with a consonant. He adds them to the bag of 80 tiles. Now, 1 4 How many tiles did John add to the bag? of the tiles have vowels on them.. [2] Page 7 of 42
9 Pete lays bricks on Monday, Tuesday and Wednesday. On Monday, Pete lays 650 bricks. On Tuesday, he lays 14% more than he did on Monday. (a) How many bricks did he lay on Tuesday?. [2] (b) By the end of Wednesday, Pete had laid 2000 bricks. What percentage of these bricks did he lay on Wednesday?. [2] (c) Pete s wages are increased by 4%. After the increase, Pete is paid 572. How much was Pete paid before the increase?. [2] Page 8 of 42
10 Write each of these as a single power of a. (a) a x a x a x a x a. [1] (b) a 5 x a -4. [2] (c) a 8 a 4. [2] (d) (a 3 ) c. [1] (e) 2 a. [2] Page 9 of 42
11 (a) The angles in a quadrilateral are in the ratio 3 : 4 : 1 : 4 Find the size of the smallest angle in the quadrilateral.... [2] (b) Mark and James divide a cake in the ratio 2 : 3. What fraction of the cake does James get?... [1] (c) A drink is made by mixing orange juice and lemonade in the ratio 4 : 7. How much lemonade needs to be added to 6 litres of orange to create the correct mixture for the drink?... [2] Page 10 of 42
12 y is directly proportional to x. When x is 6, y is equal to 33. Calculate the value of y when x is 10.... [3] 13 F is inversely proportional to d. When F = 20, d = 3. (a) Find the value of F when d = 4.... [3] (b) Find the value of d when F = 5.... [2] 14 Show that 5(4x + 1) + 40 3x = 17x + 45... [1] Page 11 of 42
15 Simplify fully (a) 5a 2b 3a + 4b... [2] (b) 20a 5 4a... [2] 16 Expand and simplify (2x + 1)(x 3)... [2] 17 Factorise fully (a) 10g 2 f + 4g... [2] (b) x 2 2x 15... [2] 18 Tickets for bowling cost 9 per adult and 6 per child. Write a formula for the cost, C, when a family of n adults and k children go bowling. C =... [1] Page 12 of 42
19 Using the formula v = u + at, work out the value of v when u = 5.4, a = 6.2 and t = 1.7. Round your answer to 1 dp. [3] 20 Given that s = 1 (u + v)t 2 Find the value of s when u = 3.2, v = 5.7 and t = 8.... [2] Page 13 of 42
21 Here is a set of coordinate axes, with point A (3, 4). (i) Plot the point B ( 3, 2). [1] (ii) Work out the distance AB, giving your answer to 1 decimal place. [3] Page 14 of 42
22 The diagram below shows a triangle ABC. (i) Work out the length of BD. Give your answer to 1 decimal place. cm [3] (ii) Calculate the area of the triangle ABC. Give your answer to 2 significant figures. cm 2 [2] 23 Triangle ABC is a right angled triangle. Work out the size of angle ACB. Give your answer to 1 decimal place. [3] Page 15 of 42
24 The oven temperature of gas cookers is measured in Gas marks. This corresponds to a temperature in degrees Celsius, which can be found using the following flowchart. (a) David cooks a cake at Gas mark 5. What temperature is this in degrees Celsius? (b) Wendy needs to cook a casserole at 160 degrees Celsius. What gas mark does she need to set her oven at? Round this to the nearest whole number. degrees [1] [2] 25 (a) (i) Write down the next two terms of the following sequence. 4, 7, 10, 13, 16,., (ii) Write down an expression for the n th term of this sequence., [2] [2] (b) (i) Write down the next two terms of the following sequence. 4, 1, -2, -5, -8,.,, [2] (ii) Write down an expression for the n th term of this sequence. [2] Page 16 of 42
26 Electrical fuses fit inside plugs and they come in different sizes - 3 amp, 5 amp and 13 amp. The correct fuse size for an electrical appliance with power rating P watts, is given by the formula F = P 240 (a) What size fuse should be used for a table lamp of 720 watts? (b) An electric lawnmower needs a 13 amp fuse. What is the biggest power rating it could have? amp [1] watts [2] 27 a) Simplify fully the ratio 104 : 72... [1] b) Write these ratios in the form 1:n i) 8cm : 50cm... [1] ii) 40cm : 1.2m... [2] Page 17 of 42
28 (a) What is the name of the shape shown?... [1] Pick two words or phrases from the box above to complete the following sentences. (b) The shape has.. pairs of parallel lines. Opposite angles in the shape.. [2] 29 This 3D shape is called a The shape has vertices. The shape has edges. The shape has faces. [4] Page 18 of 42
30 (a) Measure the angle shown.... [1] (b) Construct an equilateral triangle using the line below as a base. [2] Page 19 of 42
31 (a) Construct the perpendicular bisector of the line below. [2] (b) Construct the bisector of the angle shown. [2] Page 20 of 42
32 Construct the shortest line from point P to the line AB A B P [3] Page 21 of 42
33 102 o 156 o 81 o x o Calculate the size of angle x. [3] Page 22 of 42
34 (a) Describe the single transformation that maps shape A onto shape B. [2] (b) Reflect shape B in the line y=1. Label the image C. [2] (c) Describe the single transformation that maps shape A onto shape C. [3] Page 23 of 42
35 Gold has a density of 19.3 g/cm³. Silver has a density of 10.5 g/cm³. Which would have a greater volume; 50kg of silver or 90kg of gold? Show how you decide. [3] Page 24 of 42
36 ABCD is a quadrilateral. It has sides, in no particular order, 3x + 12, 6x 1, 7x and 5x + 2 and a perimeter of 76cm. (a) By calculating the value of x, name the 3 types of quadrilateral ABCD could be.......... [6] (b) If AB = 6x 1, BC = 3x + 12, CD = 7x and AD = 5x + 2, which type of quadrilateral is ABCD?.. [1] Page 25 of 42
37 Enlarge the shape below by scale factor 2 using (-1, -2) as a centre of enlargement. [2] Page 26 of 42
38 NOT TO SCALE (a) Show that the area of the sector is 26.2 cm 2 to 3 significant figures [2] (b) Find the perimeter of the sector [3] Page 27 of 42
39 ABCD is a parallelogram. Y is the midpoint of AD. X is the midpoint of AB. AX = a and AY = b. Find the following vectors. Give your answer in terms of a and b. (a) AB. [1] (b) BC. [1] (c) Z is the midpoint of the line BC Find DZ. [2] Page 28 of 42
40 Ali and Sasha are calculating the volume of the cylinder below 4cm 6cm They calculate the volume to be 302 cm 3, correct to 3 significant figures. Ali then says if you double the radius and keep the height the same, the volume doubles. Sasha says if you double the height, and keep the radius the same, the volume doubles. Who is correct? You must show your working. [4] Page 29 of 42
41 ABCDV is square based pyramid. AD = 4cm and the vertical height, VO = 3cm. O is the centre of the base. M is the midpoint of the side CD. (i) Work out the area of the base of the pyramid. cm 2 [1] (ii) Hence find the volume of the pyramid [Volume of pyramid = 1 area of base height] 3 cm 3 [2] 42 Is the following triangle right-angled? Show clearly how you decide. [4] 43 Jane stands 25 metres from the base of a tree, at the point S. Page 30 of 42
The angle of elevation of the top of the tree is 17. Calculate the height of the tree, TG, giving your answer to 1 decimal place. metres [3] Page 31 of 42
44 Wendy and Paul want to estimate the number of red sweets they have in a jar containing 500 sweets. They decide to do it by taking a sweet from the jar at random, noting the colour and then returning it to the jar. They recorded their results in the following table. Number of sweets taken out Number of Red sweets chosen Relative frequency Wendy 35 8 Paul 125 31 (a) Complete the table by calculating the relative frequency of getting a red sweet correct to 2dp for both Wendy and Paul. [2] (b) Whose estimate do you think is the most accurate? Give a reason for your answer.... because.... [1] (c) Estimate the number of red sweets in the jar. sweets [2] Page 32 of 42
45 Andrew has three cards and three discs. The cards are numbered 1, 3 and 4 and discs are numbered 2, 4 and 5. He picks one card at random and one disc at random and calculates the difference between them. (a) Complete the table to show all the possible outcomes. Disc 2 4 5 Card 1 3 4 [2] (b) Calculate the probability that Andrew gets a score which is odd. [1] 46 Alex has three cards, each with a different number on them. She can arrange them in any order but each card can only be used once. (a) List all of the possible three-digit numbers she can make. [2] (b) Alex arranges them without looking at the numbers on the cards. Calculate the probability that Alex arranges them to give a number which is even. [1] Page 33 of 42
47 Gemma has a box of red, blue and green pencils. She chooses a pencil at random. The probability that she chooses a red pencil is 0.5. The probability that she chooses a blue pencil is 0.2. (a) What is the probability that Gemma chooses a pencil that is either red or blue? [2] (b) What is the probability that Gemma chooses a pencil that is green? [2] (c) There were 40 pencils in the box originally. How many pencils were green? [2] 48 A group of 100 people were asked if they owned particular smartphones SAMSONG or NOCIA. 54 owned SAMSONG 37 owned NOCIA. 15 owned neither. (a) Complete the Venn diagram to show this information. [3] (b) Given that a person chosen at random owns a NOCIA, what is the probability that the person also owns a SAMSONG? [2] Page 34 of 42
49 Katie and Jenny are competing to swim for the school team. They both swim some trials and record their times. Katie completes 5 trials and she does the following times in secs. 26.2, 26.3, 26.5, 26.7, 26.3 Jenny completes 6 trials and she does the following times, in secs. 26.1, 26.3, 26.9, 26.2, 26.6, 26.5 Who should the teacher select? Show the calculations you have used and give reasons for your decisions.... because...... [2] Page 35 of 42
50 The pie chart shows the languages studied by 504 students in a school. All students study one language. The angles for the pie chart are shown. Calculate the actual numbers of students who study each language. Chinese German French Spanish [4] Page 36 of 42
51 The graph below shows the price of apples in three different cities in the USA in 2010. Explain why the graph is misleading. Give reasons for your answer and suggest a graph that would show the data more effectively................... [3] Page 37 of 42
52 (a) Complete the table of values for the equation y = 3x 2 from -3 x 3 x -3-2 -1 0 1 2 3 y -11-2 4 [2] (b) Plot the graph on the axes below. [2] (c) Give the equation of a line parallel to the equation y = 3x 2 [2] Page 38 of 42
53 (a) Complete the table of values for the equation y = x 2 2x from -2 x 3 x -2-1 0 1 2 3 y 8-1 [2] (b) Plot the graph on the axes below. [2] (c) Use your graph to find out the solutions to the equation x 2 2x = 1.5 x =., x =. [2] Page 39 of 42
54 Solve simultaneously. 5x + 3y = 14 2x y = 10 x =., y =. [3] 55 (a) Solve the inequality. 2x + 5 11 (b) Show your solution on the number line. [2] [1] Page 40 of 42
56 The scatter diagram below shows the test data from a science test and maths test for a class of students. (a) One of the results is an outlier. Write down the scores this student achieved for maths and science. Science Maths [2] (b) Another student sits the science test and scores 40 marks. Estimate the score they are likely to achieve in maths.... [2] (c) One final student sits the maths test and scores 70. Estimate the score they are likely to achieve in science.... [1] (d) Which of these two estimates is likely to be most accurate? Explain your reasoning. because.......... [3] (e) Which subject has the most consistent results? Explain your reasoning. because..... [2] Page 41 of 42
57 The table below shows the weights, w kg, of 50 packages in a post office. Weight (kg) Frequency 0 < w 5 19 5 < w 10 15 10 < w 15 10 15 < w 20 4 20 < w 25 2 (a) Calculate an estimate of the mean of this data. (a)... kg [4] (b) Explain why your answer is an estimate....... [1] Page 42 of 42