10F1 KPI Test - Solving Equations and Rearranging Formulae (PDF)

Name: KPI test 10F1 Solving Equations and Rearranging Formulae Score: /27 Foundation 1) a=b+c (Sparx U556) What is the subject of...

Name: KPI test 10F1 Solving Equations and Rearranging Formulae Score: /27 Foundation 1) a=b+c (Sparx U556) What is the subject of this formula? Circle the correct answer a b c b+c [1 mark] 2) d+e=f (Sparx U556) What is the subject of this formula? Circle the correct answer d e f d+e [1 mark] 3) v = u + at. Make u the subject. (Sparx U556) ……………………………………… [1 mark] 4) m = dv. Make d the subject. (Sparx U556) …………………………………….. [1 mark] 5) The formula for finding the area of a rectangle is 𝐴 = 𝑙 × 𝑤 (Sparx U556) If I know the area and the length, which formula would I use to find the width? Circle the correct answer. [1 mark] 𝑑 6) To find the speed of an object you divide the distance by the time: 𝑠= (Sparx U556) 𝑡 If I know the speed and distance of an object, which formula would I use to find the time? Circle the correct answer. 𝑑 𝑠 𝑡= 𝑡= 𝑡 =𝑑×𝑡 𝑠 𝑑 [1 mark] 1 7) The formula for the area of a triangle is 𝐴 = 𝑏ℎ. (Sparx U556) 2 Rearrange this formula to make b the subject. ……………………………………… [2 marks]  1 8) The formula for the area of a trapezium is 𝐴 = (𝑎 + 𝑏)ℎ. (Sparx U556) 2 Rearrange this formula to make a the subject. ……………………………………… [2 marks] 1 9) Rearrange 𝑦 = 𝑥 + 1, to make x the subject. (Sparx U556) 2 …………………………………….. [2 marks] 10) The area of this triangle is 20cm2. The base of the triangle is 5cm. What is the height of the triangle? ………………………. cm [2 marks] 11) The area of this trapezium is 40m2. Find the length of the missing side b. ………………………. m [3 marks) 12 a) The formula for the area of a circle is 𝐴 = 𝜋𝑟 2. (Sparx U556) Rearrange this formula to make r the subject. ………………………….. [2 marks] b) Hence or otherwise, find the radius of a circle which has an area of 50m2. Give your answer correct to 2 significant figures. ………………………. m [2 marks] 13) The length of the arc of this semi-circle is 40m. What is the length of the radius? Give your answer correct to 3 significant figures. ………………………… m [3 marks] 14) The area of this sector is 65m2. What is the length of the radius? ………………………… m [3 marks]  Name: KPI test Standard Form Score: /33 10F10* 1) Work out (Sparx U735) a) 5.2 x 10 b) 0.04 x 1000 c) 34.0205 x 100 ………………… …………………… …………………… [3 marks] 2) Work out (Sparx U735) a) 34 ÷ 10 b) 5.7 ÷ 1000 c) 356.34 ÷ 100 ………………… …………………… …………………… [3 marks] 3) Write the following standard form numbers as ordinary numbers. (Sparx U330) a) 5.2 × 104 b) 7.654 × 102 ………………… …………………… [2 marks] 4) Write the following standard form numbers as ordinary numbers. (Sparx U534) a) 3.4 × 10−3 b) 1.743 × 10−4 ………………….. …………………….. [2 marks] 5) Write the following ordinary numbers in standard form. (Sparx U330) a) 7650000 b) 20000 ………………….. …………………….. [2 marks] 6) Write the following ordinary numbers in standard form. (Sparx U534) a) 0.00005 b) 0.00345 ………………….. …………………….. [2 marks] 7) The number 0.6 x 104 can be written in standard form. Circle the correct answer. (Sparx U330) 6 x 104 6 x 105 6.6 x 104 6 x 103 60 x 102  [1 mark] 8) The number 52 x 10-5 can be written in standard form. Circle the correct answer. (Sparx U534) 5.2 x 104 5.2 x 105 5.2 x 10-6 5.2 x 10-4 5.2 x 10-5 [1 mark] 9) Write the following numbers in ascending order. (Sparx U330) 7.8 × 104 75000 79 × 103 0.82 × 105 ……………………………………………………………………………………………… [2 marks] 10) There are 66.5 million people in the UK. Write this number in standard form. (Sparx U330) Answer ……………………………. [1 mark] 11) A box weighs 5.2 × 103 grams. Write in standard form the weight of 100 boxes. (Sparx U264) Answer ……………………………. [1 mark] 12) Calculate the following giving your answer in standard form: (Sparx U264) (6 x 103) x (2 x 102) Answer ……………………………. [2 marks] 13) Calculate the following giving your answer in standard form: (Sparx U264) (6 x 104) ÷ (3 x 10-2) Answer ……………………………. [2 marks] 14) Calculate the following giving your answer in standard form: (Sparx U290) (5.1 x 106) + (2.3 x 105)  Answer ……………………………. [2 marks] 15) Calculate the following giving your answer in standard form: (Sparx U290) (4.2 x 105) - (3.3 x 104) Answer ……………………………. [2 marks] Use a calculator for the following questions. (Sparx U161) 16) The distance from the Earth to the Sun is 1.496 x 1011 metres. The speed of light is 3 x 108 metres per second. a) Show that, correct to 3 significant figures, light will take 0.139 hours to travel from the Sun to the Earth. [2 marks] b) 1 googol is 1 x 10100 Danesh says, “When I multiply 1.496 x 1011 by 6.68 x 109 I get nearly 1 googgol because 1.496 x 1011 by 6.68 x 109 = 9.99 x 1099 ” Is Danesh correct? Give a reason for your answer. …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… [1 mark] 17) The mass of a carbon atom is 2 x 10-23g. How many carbon atoms are there in one gram of carbon? (Sparx U161) Answer ……………………………. [2 marks]  Name KPI test Volume 2 Score: /33 10F4 1) Work out the volume of the cuboid. (Sparx: U786) Answer …………………..cm3 [2 marks] 2) Work out the volume of the prism. (Sparx: U174) Answer............................... cm3 [3 marks] 3) The dimensions of a cuboid are 7.1cm x 5.2cm x 7.9cm. Estimate the volume of the cuboid. (Sparx: U786) Answer............................... cm3 [2 marks] 4) Work out the volume of the triangular prism. (Sparx: U174) Answer............................... cm3 [3 marks] 5) A skip is in the shape of a prism with cross-section ABCD. (Sparx: U174) AD = 2.3 m, DC = 1.3 m and BC = 1.7 m. The width of the skip is 1.5 m. (a) Calculate the area of the shape ABCD. Answer............................... m2 [2 marks] (b) Calculate the volume of the skip. Answer............................... m3 [2 marks] 6) A can of drink is in the shape of a cylinder. (Sparx: U915) The can has a radius of 4 cm and a height of 15 cm. Calculate the volume of the cylinder. Give your answer correct to 3 significant figures. Answer............................... cm3 [2 marks] 7) The diagram shows a triangular prism. (Sparx: U174) BC = 4 cm, CF = 12 cm and angle ABC = 90º. The volume of the triangular prism is 84 cm3. Work out the length of the side AB of the prism. Answer............................... cm [3 marks] 8) Work out the volume of the cone. Give your answer in terms of π and to 3 significant figures (Sparx: U116) Answer............................... cm3 [3 marks] 9) Work out the volume of the square based pyramid. (Sparx: U484) Answer............................... cm3 [3 marks] 10) Work out the volume of the sphere. (Sparx: U617) Give your answer in terms of π Answer............................... cm3 [3 marks] 11) 4000cm3 is equivalent to: (Sparx: U468) Circle the correct answer. 4m3 0.4m3 0.04m3 0.004m3 [1 mark] 12) 200cm3 is equivalent to: (Sparx: U468) Circle the correct answer. 20ml 200ml 2000ml 20000ml [1 mark] 13) Work out the volume of the frustum. Give your answer in terms of π and to 3 significant figures. (Sparx: U350) Answer............................... cm3 [3 marks]  Name: 10 F7 Quadratics - algebraic Score: /20 1. Circle the correct factorisation of the following quadratics (Sparx U178, U963) a) x2 + 5x + 4 (x + 4)(x + 1) (x + 2)(x + 2) (x + 1)(x + 5) (x + 5)(x – 1) b) x2 – 4x – 12 (x + 2)(x + 6) (x + 2)(x – 6) (x – 3)(x – 4) (x + 1)(x – 12) c) x 2 – 9 (x + 1)(x – 9) (x – 3)(x – 3) x(x – 9) (x + 3)(x – 3) [3 marks] 2. Circle the roots for each quadratic (Sparx U228) a) (x + 3)(x + 2) = 0 x = 3 and x = 2 x = 3 and x = –2 x = –3 and x = 2 x = –3 and x = –2 [1 mark] b) (x + 1)(x – 5) = 0 x = –1 and x = –5 x = –1 and x = 5 x = 1 and 𝑥 = – 5 x = 1 and x = 5 [1 mark] c) x 2 – 4x – 12 = 0 x = 3 and x = 2 x = 6 and x = –2 x = –6 and x = 2 x = –3 and x = –2 [2 marks] 3. 𝑦 = 𝑥 2 + 5𝑥 − 3 (Sparx U228) If x = 2, find the value of y. y = ………………… [2 marks] 4. Factorise fully 4𝑥 2 − 12𝑥 (Sparx U228) …………………………………… [2 marks] 5. Factorise (Sparx U228) 2 𝑥 − 81 …………………………………… [1 mark] 6. Factorise (Sparx U228) 2 𝑥 + 14𝑥 + 49 …………………………………… [1 mark] 7. Factorise (Sparx U228) 2 𝑥 + 6𝑥 + 8 …………………………………… [2 marks] 8. Solve (Sparx U228) 2 𝑥 − 36 = 0 …………………………………… [2 marks] 9. Solve (Sparx U228) 2 𝑥 − 5𝑥 − 24 = 0 …………………………………… [3 marks]  Name: Score: /38 KPI test 10H13 Ratio 2 1) Fully simplify the ratios: (Sparx U687) a) 5 : 10 b) 24 : 16 c) 24 : 48 : 60 …………………… ………………………. ……………………………. [3 marks] 2) Split £80 in the following ratios: (Sparx U577) a) 3:5 b) 5:4:7 …………………… ……………………………. [3 marks] 3) Before an election, (Sparx U577, U753) 26% said they would vote for A 12% said they would vote for B 30% said they would not vote. The rest of the population voted for A and B in the ratio 1:3. a) Who got the most votes? You must show your working. Answer ………………………………… [3 marks] b) 630 people did not vote. How many people did vote? Answer ………………………………… [2 marks] 4) a:b:c=3:4:5 (Sparx U176) Circle the value of a as a fraction of a + b + c 3 1 3 1 9 3 4 4 [1 mark] 5) Which ratio is not equivalent to the ratio 3 : 4 (Sparx U176) Circle your answer. 3 4 :1 1: 3 1: 1.3 6: 8 4 [1 mark] 6) Write in the form 1 : n, the ratio 6 : 4 (Sparx U687) Answer ………………….. [1 mark] 1 2 7) : = 𝑥 ∶ 1, what is the value of x? (Sparx U687) 2 3 1 3 3 4 3 5 4 3 [1 mark] 8) Carol and Amy throw darts at a target. (Sparx U577, U753) Carol’s ratio of hits to misses is 5:1 Amy’s ratio of hits to misses is 4:1 Carol says, “5 is bigger than 4, so I must have more hits than Amy.” Give an example to show that this might not be true. [2 marks] 9) Green paint is made by mixing blue paint and yellow paint in the ratio 7 : 4. (Sparx U753) Archie has 35 litres of blue paint and 18 litres of yellow paint. What is the maximum amount of green paint he can make? Answer ………………………….. [3 marks] 10) CD and PQ are lines of length 12cm (a) CE : CD = 1 : 2 Mark point E on the line with a cross. (b) PR : RQ = 1 : 3 Mark point R on the line with a cross. [2 marks] 11) White paint costs £4.60 per litre. (Sparx U753) Yellow paint costs £5.80 per litre. White and yellow paint are mixed in the ratio of 3 : 2 Work out the cost of 17 litres of the mixture. Answer ………………………….. [3 marks] 12) At a school the numbers of boys to girls is in the ratio 11:9 (Sparx U577) There are 70 more boys than girls. Work out the total number of students at the school. Answer ………………………….. [2 marks] 13) On a school trip the ratio of the number of teachers to students is 1 : 15 (Sparx U753, U176) The ratio of the number of male students to female is 7 : 5 The ratio of the number of male teachers to female is 1 : 3 Work out what percentage of all the people on the trip are female. Round your answer to the nearest integer. Answer ………………………….. [3 marks] 14) On Friday, some adults and children were in a cinema. (Sparx U176) The ratio of the number of adults to children was 3:1 Each person had a seat on the right or left side of the cinema. 2 of the children had a seat on the left side. 3 115 children had a seat on the right side. The cinema has 2000 seats. What percentage of the seats were empty? Answer ………………………….. [4 marks] 15) There are 600 cakes in a shop. The shop only sells fruit, chocolate, cream and lemon cakes. 3 of the cakes are fruit cakes. (Sparx U176) 8 45% of the cakes are chocolate cakes. The ratio of cream to lemon cakes is 3 : 4 How many lemon cakes are there? Answer ………………………….. [4 marks]  Name: Score: /92 KPI test 10H2 Linear Graphs 1. (Sparx U789) (a) (i) Write down the coordinates of point A. (……………,………….) [1 mark] (ii) Write down the coordinates of point B. (……………,………….) [1 mark] (b) (i) On the grid, mark the point (6, 4) with the letter P. [1 mark] (ii) On the grid, mark the point (3, 0) with the letter Q. [1 mark] 2. (Sparx U789) (a) Write down the coordinates of point P. (.......... ,..........) [1 mark] (b) (i) On the grid, plot the point (–1, 0). Label the point Q. [1 mark] (ii) On the grid, plot the point (–2, –3). Label the point R. [1 mark] 3. (Sparx U933) P has coordinates (1, 2). Q has coordinates (7, 10) Find the coordinates of the mid-point of the line PQ. (............ ,............) [2 marks] 4. A square ABCD has sides of length 5 units. (Sparx U889) Find the coordinates of point C. C (............ ,............) [2 marks] 5. Find the midpoint of the line AB where A is (2, 8) and B is (4, 16) (Sparx U933) (............ ,............) [2 marks] 6. On the grid below draw the following graphs. Clearly label your lines. (Sparx U741) a) x = 5 b) y = x c) y = -2 d) y = -x [4 marks] 7. The midpoint of CD is (6, 10). (Sparx U933) The coordinates of C are (-2, 3). What are the coordinates of D? (............ ,............) [2 marks] 8. (a) Complete the table of values for y = 2x + 1 (Sparx U741) x -2 -1 0 1 2 3 y [2 marks] (b) On the grid below, draw the graph of y = 2x + 1 [2 marks] (c) Use your graph to find (i) the value of y when x = –1.5 y =.................. [1 mark] (ii) the value of x when y = 6 x =.................. [1 mark] 9. On the grid below, draw the graph of y = 3 – 2x from x = −2 to x = 4 (Sparx U741) [3 marks] 10. Does the point A (–2, 5) lie on the line y = –2x + 1? Give a reason for your answer.  [2 marks] 11. On the grid, draw the graph of x + y = 4 (Sparx U741) [3 marks] 12. Two straight lines are shown. (Sparx U933) A is the midpoint of OB. B is the midpoint of TS. Work out the coordinates of T.  T ( …… , ……. ) [3 marks] 13. Here is a conversion graph between pounds (£) and Australian dollars. (Sparx U638) a) Change 20 Australian dollars to pounds …………………. [1 mark] b) Change £7 to Australian dollars. …………………. [1 mark] c) Change £400 to Australian dollars …………………. [2 marks] 14. Samir cleans carpets of different areas. (Sparx U638) He uses this graph to work out the cost of cleaning a carpet. A carpet has an area of 30m2. a) Use the graph to work out the cost of cleaning this carpet. ………………… [1 mark] b) It costs £150 to clean another carpet. Use the graph to work out the area of this carpet. ………………… [1 mark] c) A rectangular carpet has a length of 8.6m and a width of 5m. Work out the cost of cleaning this carpet. ………………… [2 marks] 15. (a) Complete the table of values for 4x + 3y = 12 (Sparx U741) x -1 0 1 2 3 1 2 y 5 2 3 3 [2 marks] (b) On the grid, draw the graph of 4x + 3y = 12 [2 marks] 16. The equation of a line is y = 2x + 3. What is the gradient of this line? (Sparx U669) Circle the correct answer. y x 2 3 2x [1 mark] 17. The equation of a line is y + 2x = 5. What is the gradient of this line? (Sparx U669) Circle the correct answer. y 2x 5 -2x -2 [1 mark] 18. The equation of a line is y = 2x + 3. What are the coordinates of the y-intercept? (Sparx U669) Circle the correct answer. ( 0, y ) ( 2, 0 ) ( 0, 2 ) ( 0, 3 ) ( 3, 0 ) [1 mark] 19. The equation of a line is y + 5 = 3x. What are the coordinates the y-intercept? (Sparx U669) Circle the correct answer. ( 0, y ) ( 3x, 0 ) ( 5, 0 ) ( 0, 5 ) ( 0, -5 ) [1 mark] 20. (Sparx U669, U377) (a) The line y = 3x + 5 crosses the y axis at P. What is the value of y at P?..................................... [1 mark] (b) Write down the equation of another line which is parallel to y = 3x + 5..................................... [1 mark] 21. A straight line has equation y = 5 – 3x (Sparx U669) (a) Write down the gradient of the line. ………………… [1 mark] (b) Write down the coordinates of the point where the line crosses the y-axis.  (…..… , …..…) [1 mark] 22. A line passes through the point (0, 4). (Sparx U669) The gradient of this line is 2. Write down the equation of this line....................................... [2 marks] 23. (Sparx U315) Find the equation of line L …………………………… [3 marks] 24. Line A passes through the point ( 5, 9 ), and has a gradient of 2. What is the equation of line A? (Sparx U477) …………………………… [3 marks] 25. A straight line has equation 𝑦 = 3𝑥 + 1 (Sparx U477, U377) Write down the equation of the line that is parallel to 𝑦 = 3𝑥 + 1 and passes through the point (0,7)............................... [2 marks] 26. A Line passes through the points A ( 2, 4 ) and B ( 5, 13 ). What is the equation of the line? (Sparx U848) …………………………… [3 marks] 1 27. A straight line has equation 𝑦 = 2 𝑥 +1 The point P lies on the straight line. P has a y-coordinate of 5. Find the x-coordinate of P................................ [2 marks] 28. The straight line L1 has equation y = 2x + 3 (Sparx U477, U377) The straight line L2 is parallel to the straight line L1. The straight line L2 passes through the point (3, 2). Find an equation of the straight line L2...................................... [3 marks] 29. (Sparx U862) Phone calls cost £ y for x minutes. The graph gives the values of y for values of x from 0 to 5 (a) (i) Give an interpretation of the intercept of the graph on the y-axis.............................................................................................................................................................................................................................................................................................................................................. [1 mark] (ii) Give an interpretation of the gradient of the graph.............................................................................................................................................................................................................................................................................................................................................. [1 mark] (b) Find the equation of the straight line in the form y = m x + c [2 marks] 30. A straight line has equation 2y - 6x = 5 (Sparx U669) (a) Find the gradient of the line. ……………………….. [2 marks] The point (k, 6) lies on the line. (b) Find the value of k. k = ……………………….. [2 marks] 31. Which equation of a line is perpendicular to y = 2x + 1? (Sparx U898) Circle the correct answer. 1 2 1 y = 2x – 1 𝑦= 2 𝑥 −1 𝑦 = −2𝑥 + 1 𝑦 = −1𝑥 + 1 𝑦 = −2𝑥 + 3 [1 mark] 32. Line A has the equation y = 3x + 2. Line B is perpendicular to line A and passes through the point (6, 4). What is the equation of line B? (Sparx U898, U477) [2 marks] 33. ABCD is a rhombus. (Sparx U898, U477) The coordinates of A are (5, 11) 1 The equation of the diagonal DB is 𝑦 = 2 𝑥 + 6 Find the equation of the diagonal AC. ………………………. [3 marks] 34. P has coordinates ( -9, 7 ) (Sparx U848, U898) Q has coordinates ( 11, 12 ) M is the point on the line segment PQ such that PM : MQ = 2 : 3 Line L is perpendicular to the line segment PQ. L passes through M. Find an equation of L. ………………………. [4 marks]  Name: KPI test Linear Simultaneous Equations Score: /28 10H3 1) Solve the following simultaneous equations algebraically. (Sparx U760) 3x + 5y = 22 3x + 2y = 16 x = ………………….. y = ………………….. [3 marks] 2) Solve the following simultaneous equations algebraically. (Sparx U760) 4x + 3y = 7 2x – 5y = -29 x = ………………….. y = ………………….. [3 marks] 3) Solve the following simultaneous equations algebraically. (Sparx U760) 3x + 4y =11 2x + 6y = 9 x = ………………….. y = ………………….. [3 marks] 4) Solve the following simultaneous equations algebraically. (Sparx U760) 3x + y = - 4 3x – 4y = 6 x = ………………….. y = ………………….. [3 marks} 5) Use the graphs to solve the following simultaneous linear equations (Sparx U836) y = 8x + 2 and y = 7 – 2x x = ………… y = …………. [1 mark] 6) (Sparx U836) [3 marks] 7) (Sparx U836) x = …………………… y = …………………… [4 marks] 8) 5 adult tickets plus 1 child ticket costs £14 (Sparx U137) 3 adult tickets plus 2 child tickets cost £10.50 Work out the cost of 1 adult ticket and 1 child ticket. Adult ……………….. Child ………………… [4 marks] 9) Solve the following simultaneous equations algebraically. (Sparx U760) 1 4𝑦 + 5𝑥 = −3 3 5𝑦 − 3𝑥 = 5 4 x = ………………….. y = ………………….. [4 marks]