Mathematics. Higher. Set A Paper 1: Non-Calculator Test A. Name Class. Date

Transcription

1 1 hour 30 minutes Mathematics Higher 80 marks Ch 1 Set A Paper 1: Non-Calculator Test A Name Class Date Materials For this paper you must have: mathematical instruments You may not use a calculator. Instructions Use lack or lue ink or all-point pen. Draw diagrams in pencil. Answer all the questions. Do all rough work in on this paper. Cross through any work that you do not want to e marked. In all calculations, show clearly how you work out your answer. Information The maximum mark for this paper is 80. The marks for each question are shown in rackets [ ]. - Use this as a guide as to how much time to spend on each question. Advice Read each question carefully efore you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Question Total Mark

2 1 What is the ratio 4 : 10 in the form 1 : n? Circle your answer. 2 : 5 1 : 2.5 1: : 1 2 Circle the numer that is square, even and a multiple of The length of a swimming pool is 50 metres. Jane swims 24 lengths of the pool. How far does she swim? Give your answer in kilometres. 4 Which of these is not a square numer? Circle your answer

3 5 Convert these areas to the units given. a 300 mm 2 to cm 2 5 m 2 to cm 2 c m 2 to km 2 d 0.3 m 2 to mm 2

4 6 Complete these calculations. a 7 Expand and simplify 2(2x + 4) + 4(3x + 2) Circle the correct answer 16x x x x Ellie and Jaffar oth worked out Ellie Jaffar Comment on their work.

5 9 Investigators test three coins for ias. They flip each coin several times and put their results in this tale. List the coins in order of ias, with the least iased first, giving a reason for each. [4 marks] 10 For a scatter graph with a line of est fit explain the meaning of these terms and comment on the reliaility of each technique. a Interpolation. Extrapolation.

6 11 The nth term of a sequence is 4n 3. a Is 75 a term of this sequence? Give a reason for your answer. ecause Write an expression for the (n + 1)th term of this sequence. c Write an expression for the sum of the nth and (n + 1)th terms d The sum of two consecutive numers in the sequence is 326. Work out the smaller of these numers.

7 12 Two triangles are shown on the grid. a Write down the column vector for the translation that moves triangle P to triangle Q. Translate triangle Q using the vector ( ). Lael your new triangle R. c Write down the vector for the single translation that moves triangle P to triangle R. d Show the connection etween the vectors in parts a and and your answer to part c.

8 13 When two ordinary coins are spun the only possile outcomes are two heads, two tails or one head and one tail a Explain why the proaility of each outcome is not 1 3. What is the proaility of getting two heads? 14 The graph shows the height in metres, h, of a all thrown into the air against time, t, seconds. a What is the maximum height of the all? Circle your answer. 10m 2 m 12m 4 m For how long was the all in the air? Circle your answer. 12 seconds 3 seconds 5 seconds 4 seconds

9 15 Zak wants to go from London to York and ack in the same day. This journey is a distance of 205 miles each way. He can hire a car or go y train. A small car costs per day and 10.2 p per mile. A large car costs per day and 19.2p per mile. A one-way train costs and takes 2 hours 14 minutes. By car, his average speed will e aout 50 mph (including rests). a Estimate how much more a large car will cost than a small car. [3 marks] Use the estimates you found in part a to compare the total costs of the three possiilities and advise Zak on how to travel. Give a reason for your answer. 16 a A square has side length x. Khalid says, The area of my square has the same numerical value as its perimeter. List the side lengths of all the squares that fit this description. A cue has side length y. Mia says, The volume of my cue has the same numerical value as its surface area. List the side lengths of all the cues that fit this description.

10 17 PQRS is a square and PQT is an equilateral triangle. Not drawn accurately Work out the size of angle STR. You must show your working. [6 marks] 18 a Factorise x 2 49 Given that 4095 = write 4095 as a product of its prime factors. [3 marks]

11 19 A line has gradient 3. M and N are two points on this line. M is (5, k) and N is (6, ). Circle the expression for the y-coordinate of N. k - 3 k + 5 k + 3 k A, B, C and D are four points on the circumference of a circle. BC and AD are extended to meet at E. Angle ABC = 85 and angle CED = 36. a Complete the statement. ABCD is a quadrilateral. Work out the value of x. Give a reason for each step of your working. [4 marks]

12 21 Solve 22 Sphere A has a 5 cm radius and sphere B has a 10 cm radius. a Surface area of a sphere = 4πr 2 Calculate the surface area of sphere A, giving your answer in terms of π. Write the ratio surface area of A : surface area of B in its simplest terms.

13 23 In triangle OAB, = a and =. a Express in terms of a and. M is the midpoint of AB. Express in terms of a and. c N is the midpoint of OM. Express in terms of a and. [3 marks]

14 24 The half-life of a drug is the time it takes for a dose to reduce to half its initial amount. A doctor prescries a 4 mg sleeping pill with a half-life of 24 hours. a How many times does the dose halve to reduce to 0.25 mg? How many hours does it take for the dose to reduce to mg? c Write down a formula connecting the mass, m, of drug remaining with its half -life, t. Total for paper is 80 marks