Introduction to algebra — Paper 1 · IGCSE Mathematics 0580

12 z = 2x – y For Examiner's (a) Find z when x = –3 and y = 7. Use Answer(a) z = [1] (b) Make x the subject of the formula. Answer(b) x = [2]

3 marks

Mark scheme: 12 (a) (z =) − 13 1cao z + y z y (b) (x =) oe final answer 2 M1 for z + y = 2x or = x − or 2 2 2 –2x = –z – y ± z ± y SC1 for answer of form ± 2

This question in 0580/11 May/June 2009

10 When c = 10 and d = −2, find the value of the following expressions. (a) c + 2d Answer(a) [1] (b) 5c2 − cd Answer(b) [2]

3 marks

Mark scheme: 10 (a) 6 1 (b) 520 2 M1 for 5 × 102 − 10 × −2, or better If zero, SC1 for answer of 480 or 2520

This question in 0580/12 May/June 2010

19 Piet, Rob and Sam collect model aeroplanes. For Piet has x aeroplanes. Examiner's Rob has 7 more aeroplanes than Piet. Use Sam has three times as many aeroplanes as Piet. (a) Write down an expression, in terms of x, for (i) the number of aeroplanes Rob has, Answer(a)(i) [1] (ii) the number of aeroplanes Sam has. Answer(a)(ii) [1] (b) The total number of aeroplanes is 32. (i) Use the information in part (a) to write down an equation in x. Answer(b)(i) [1] (ii) Solve your equation. Answer(b)(ii) x = [2] (c) Write down the number of aeroplanes Rob has. Answer(c) [1]

6 marks

Mark scheme: 19 (a) (i) x + 7 1 (ii) 3x 1 (b) (i) x+their (a)(i)+their (a)(ii)=32 1ft ft dependent on 2 algebraic expressions in (a) or better (ii) (x =) 5 2ft M1 for 5x = 32 − 7 oe ft their (b)(i) with M1 for ax = b and A1 if answer is an integer. (c) 12 1ft ft their (b)(ii) substituted into their (a)(i) or their (b)(ii) + 7 evaluated correctly

This question in 0580/11 May/June 2011

1 Simplify the expression. p + p + p + p Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: Qu. Part Answers Mark Part Marks 1 4p 1

This question in 0580/12 May/June 2014

14 Find the value of 3a – 5b when a = –4 and b = 2 . Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 14 –22 2 M1 for 3×(–4) –5×2 or B1 for −12 or −10 seen in the working. IGCSE – May/June 2014 0580 13 13

This question in 0580/13 May/June 2014

14 To hire a bicycle it costs $6 for each day, plus a fi xed charge of $15. (a) Maria pays $39 to hire a bicycle. How many days does she hire it for? Answer(a) … days [2] (b) Write down a formula for the cost, C dollars, to hire a bicycle for d days. Answer(b) C = … [1] __________________________________________________________________________________________

3 marks

Mark scheme: 14 (a) 4 [days] 2 M1 for (39 − 15) ÷ 6 or 15 + 6 + 6 + 6 + 6 1 (b) [C=] 15 + 6d Final answer

This question in 0580/11 Oct/Nov 2014

19 Idris has c toy cars. Fadl has twice as many cars as Idris. Baasim has three more cars than Fadl. (a) Write down an expression, in terms of c, to complete each statement. Fadl has … cars. Baasim has … cars. [2] (b) Write down an expression, in terms of c, for the total number of cars the three children have. Give your answer in its simplest form. Answer(b) … [2] __________________________________________________________________________________________

4 marks

Mark scheme: 19 (a) 2c 1 2c + 3 1FT FT is their 2c + 3 provided linear (b) 5c + 3 2FT M1 for c + their 2c + their(2c+3) provided linear

This question in 0580/12 Feb/March 2015

19 (a) s = 4t + 3u Calculate s when t = 2.6 and u = –0.4 . Answer(a) s = … [2] (b) Solve 5x – 7 = 10. Answer(b) x = … [2] __________________________________________________________________________________________

4 marks

Mark scheme: 19 (a) 9.2 2 M1 for 4 × 2.6 + 3 × (–0.4) or better (b) 3.4 2 M1 for one correct step in a 2-step method

This question in 0580/11 Oct/Nov 2015

12 y = mx + c Find the value of y when m = −2, x = −7 and c = −3. y = … [2]

2 marks

Mark scheme: 12 11 2 M1 for −2 × −7 − 3 soi

This question in 0580/11 May/June 2016

21 (a) Simplify. 3p + 5p + p … [1] (b) Multiply out the brackets. 4(q – 3) … [1] (c) Factorise completely. 10t + 15t2 … [2] (d) Solve the simultaneous equations. You must show all your working. 3x + y = 7 5x – y = 17 x = … y = … [2]

6 marks

Mark scheme: 21 (a) 9p final answer 1 (b) 4q – 12 final answer 1 (c) 5t(2 + 3t) final answer 2 M1 for t(10 + 15t) or 5(2t + 3t2) (d) [x = ] 3, [y = ] –2 2 B1 for one correct with working with supporting working If zero scored, SC1 for 2 values satisfying one of the original equations or SC1 if no working shown, but 2 correct answers given

This question in 0580/12 Oct/Nov 2016

6 Find the value of 7x + 3y when x = 12 and y = -6. … [2]

2 marks

Mark scheme: 6 66 2 B1 for 84 or −18 seen

This question in 0580/11 May/June 2018

4 Work out. - 2 - 1 (a) - e 5o e 1o [1] f p - 3 (b) 7 e 4o [1] f p

2 marks

Mark scheme: 4(a)  − 1  1    4  4(b)  − 21  1    28 

This question in 0580/12 Oct/Nov 2018

8 T = a 2 + 4b Find the value of T when a = 5 and b = 3. T = … [2]

2 marks

Mark scheme: 8 37 2 B1 for 25 or 12

This question in 0580/12 Oct/Nov 2018

3 (a) The temperature on Monday was -7 °C. The temperature on Tuesday was 5 °C lower than on Monday. The temperature on Wednesday was 8 °C higher than on Tuesday. Find the temperature on Wednesday. … °C [2] (b) Kyra has a faulty thermometer. It always shows the temperature as 2 °C higher than the actual temperature. The temperature on the thermometer is T °C. Write an expression, in terms of T, for the actual temperature. … °C [1]

3 marks

Mark scheme: 3(a) −4 2 B1 for −12 seen or M1 for −7 − 5 + 8 or better 3(b) T – 2 cao 1

This question in 0580/12 Feb/March 2020

9 (a) Write down the gradient of the line y = 2x - 3 . … [1] (b) Complete the table of values for y = 2x - 3 . x -2 0 3 y [2] (c) On the grid, draw the graph of y = 2x - 3 for - 2 G x G 3 . y 4 2 – 2 – 1 0 1 2 3 x – 2 – 4 – 6 – 8 [1]

4 marks

Mark scheme: 9(a) 2 1 9(b) – 7 – 3 3 2 B1 for 2 correct 9(c) Correct ruled graph 1 FT their (b) provided it is a single ruled straight line

This question in 0580/12 Feb/March 2020

7 Work out. - 3 (a) 2 e 7o [1] f p 8 - 5 (b) + e- 6o e 2o [1] f p

2 marks

Mark scheme: 7(a)  − 6  1    14  7(b)  3  1    −4 

This question in 0580/12 Feb/March 2021

5 The formula for changing a temperature measured in Celsius (°C) to Fahrenheit (°F) is 9C F = + 32 . 5 Use this formula to change 65°C to Fahrenheit. … °F [2]

2 marks

Mark scheme: 5 149 2 M1 for 9 × 65 ÷ 5 [+32]

This question in 0580/12 May/June 2021

9 Work out. 6 4 (a) + e- 3o e- 5o [1] f p 3 (b) 6 e- 2o [1] f p

2 marks

Mark scheme: 9(a)  10  1    −8  9(b)  18  1    −12 

This question in 0580/12 Oct/Nov 2022

25 At a cinema, an adult ticket costs $a and a child ticket costs $c. (a) Farah buys 3 adult tickets and 4 child tickets for $38.50 . Complete the equation. 3a + 4c = … [1] (b) Hana buys 6 adult tickets and 5 child tickets for $65.00 . Write down another equation in terms of a and c. … [1] (c) Solve the two simultaneous equations to find the value of a and the value of c. You must show all your working. a = … c = … [3]

5 marks

Mark scheme: 25(a) 38.5 1 25(b) 6a + 5c = 65 1 If 0 scored in part(a) and part(b), SC1 for 3850 in part(a) and 6a + 5c = 6500 in part(b) 25(c) Correctly eliminating one variable M1 Follow through their linear equations [a =] 7.5 A1 [c =] 4 A1 If M0 or M0 FT scored, SC1 for 2 values which satisfy one correct equation or one of their equations

This question in 0580/11 May/June 2023

18 A bar of chocolate costs $3 and a bag of sweets costs $5. Write down an expression for the total cost, in dollars, of x bars of chocolate and y bags of sweets. $ … [2]

2 marks

Mark scheme: 18 3x + 5y final answer 2 B1 for 3x or 5y in final answer or for 3x + 5y seen then spoilt

This question in 0580/13 Oct/Nov 2023

15 In a league, teams gain 4 points for each win, 2 points for each draw and bonus points. A team has x wins, y draws and b bonus points. Write down an expression, in terms of x, y and b, for the total number of points the team has. … [2]

2 marks

Mark scheme: 15 4x + 2y + b final answer 2 B1 for two correct terms in 4x + 2y + b as final answer or correct answer seen and spoilt

This question in 0580/12 Oct/Nov 2024

14 (a) Complete the table of values for y = ( x + 3 )( x - 2 ) . x -4 -3 -2 -1 0 1 2 3 y 6 -4 -4 [3] (b) On the grid, draw the graph of y = ( x + 3 )( x - 2 ) for - 4 G x G 3 . y 6 5 4 3 2 1 - 4 -3 -2 -1 0 1 2 3 x -1 -2 -3 - 4 -5 -6 -7 [4] (c) Write down the coordinates of the lowest point of the graph. ( … , … ) [1] (d) Write down the equation of the line of symmetry of the graph. … [1] (e) Use your graph to solve the equation ( x + 3)( x - 2) = 3 . x = … or x = … [2]

11 marks

Mark scheme: 14(a) [6], 0, [−4], -6, -6, [−4], 0, 6 3 B2 for 3 correct B1 for 1 correct 14(b) Correct curve 4 B3FT for 7 points correctly plotted or B2FT for 5 points correctly plotted or B1FT for 3 points correctly plotted 14(c) ( −0.5 , k) where −6.6 k −6 1 14(d) x = −0.5 oe 1 14(e) −3.6 to −3.4 2.4 to 2.6 2 FT their curve B1 for each or B1 for y = 3 drawn

This question in 0580/12 May/June 2025

11 (a) Sam buys 3 apples at 40 cents each. He also buys 5 peaches. The total cost is $3.45 . Find the cost of 1 peach. … cents [3] (b) Pears cost 55 cents each. Bananas cost 36 cents each. Write an expression, in cents, for the cost of x pears and y bananas. … [2]

5 marks

Mark scheme: 11(a) 45 3 345 − ( 3  40 ) M2 for oe 5 or M1 for 345 – (3 × 40) or B1 for 120 11(b) 55x + 36y final answer 2 B1 for 55x or 36y in final answer or final answer seen and spoilt If 0 scored SC1 for 0.55x + 0.36y

This question in 0580/13 Oct/Nov 2025