Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level21. Simultaneous Equations 11) 2x + 2y = 10x + 2y = 62) 3x + y = 182x + y = 133) 4x + 2y = 22x + 2y = 04) 5x + 3y = 185x + y = 165) x + y = 1x – y = 56) 3x + 4y = 29x – 4y = – 177) 3x – 2y = 10– 3x + y = – 118) 3x + 4y = 183x – 4y = – 69) 4x + 3y = 112x + y = 710) 5x + 2y = 332x + y = 1411) 6x + 2y = 104x + y = 712) 3x – 2y = 13x – y = 513) 2x + 3y = 283x – y = 914) 2x + 3y = 155x – y = 4615) 4x + 3y = 136x – 2y = 1316) 5x + 3y = 142x + 2y = 417) A family of 2 adults and 2 children go to the cinema. Their tickets cost a total of £14.00.Another family of 1 adult and 4 children go to the same cinema and their bill is £13.60.a) Letting x represent the cost of an adults ticket and y the cost of a childs ticket, write downtwo equations connecting x and yb) Solve for x and y.18) The sum of two numbers is 39 and their difference is 9.a) Letting x and y be the two numbers, write down two equations connecting x and y.b) Solve the equations.19) A rectangle has a perimeter of 42cm. Another rectangle has a length double that of the firstand a width one third of that of the first. The perimeter of the second is 57cm.Letting x and y represent the dimensions of the first rectangle, write down two equationscontaining x and y. Solve the equations and write down the dimensions of the secondrectangle.20) 4 oranges and 3 apples weigh 720 grams. 3 oranges and 4 apples weigh 750 grams. Let xand y represent their weights. Write down two equations containing x and y. Calculate theweights of each piece of fruit.21) Three mugs and two plates cost £7.20, but four mugs and one plate cost £7.90. Let xrepresent the cost of a mug and y the cost of a plate. Write down two equations involving xand y. Solve these equations and calculate the cost of seven mugs and six plates.22) Sandra withdrew £400 from the bank. She was given £20 and £10 notes, a total of 23altogether. Let x represent the number of £20 notes and y the number of £10 notes. Writedown two equations and solve them.23) A quiz game has two types of question, hard (h) and easy (e). Team A answers 7 hardquestions and 13 easy questions. Team B answers 13 hard questions and 3 easy questions. Ifthey both score 74 points, find how many points were given for each of the two types ofquestion.24) A man stays at a hotel. He has bed and breakfast (b) for three nights and two dinners (d).A second man has four nights bed and breakfast and three dinners. If the first man’s bill is£90 and the second man’s bill is £124, calculate the cost of a dinner.25) Four large buckets and two small buckets hold 58 litres. Three large buckets and five smallbuckets hold 68 litres. How much does each bucket hold?26) Caroline buys three first class stamps and five second class stamps for £1.94. Jeremy buysfive first class stamps and three second class stamps for £2.06. Calculate the cost of eachtype of stamp.