Problem 1 Expand x(x+5) Write an expression for: 6 less than x Calculate the surface area of the cuboid Simplify 5x + x 2 + 8x + 3 + x 2 half of x 5 cm 8 cm 3 cm A cuboid of length x, width 5 less than x and a height of half the length has a surface area of 250 cm 2. Show that 4x 2 15x 250 = 0 www.mathsbox.org.uk
Problem 2 Find the Lowest Common Multiple of 16 and 22 Divide 72 in the ratio 3:5 The sweets in a bag are orange, lemon and strawberry in the ratio 1:3:5. Given that there are more than 20 sweets in the bag, what is the smallest possible number of lemon sweets? At a film club the members can choose one of three types of film Drama, Action or Horror During the first week the members chose the films the in the ratio 2 : 5 : 8 During the second week the members chose the sports the in the ratio 5 : 7 : 6 If there are less than 100 members how many more chose Action in the second week than the first week? www.mathsbox.org.uk
Problem 3 Calculate the volume of a cylinder Make h the subject of the Calculate x (2 d.p.) r = 6 cm and height = 10 cm formula V = 1 3 πr2 h 9 cm 7 cm A solid metal cylinder has a base radius of 6cm and a height of 12cm. The cylinder was melted and recast into a solid cone with a circular base radius of 8cm. Find the total surface area of the cone. Curved Surface area = πrl (l is the slant height) www.mathsbox.org.uk
Problem 4 Decrease 50 by 10% There are four times as many red counters than blue counters in a bag. Express this as a ratio Fill in the blanks in the 2-way table Voucher No Voucher Total Adult 28 Child 82 Total 68 120 32 adults and 60 children visit a theme park. The admission price is 40 for an adult and 30 for a child. 36 of the visitors have a voucher, which gives them 10% off the admission. Twice as many children than adults do not have a voucher. Calculate the total paid for admission of the 32 adults and 60 children www.mathsbox.org.uk
Problem 5 Calculate the area of the trapezium What is 2 m 5 cm? Convert 3.5 m 3 to cm 3 The pool is filled with water at a rate of 10 litres per second to a depth 10 cm less than the top of the pool. How long will it take to fill the pool? 14 m 7 m www.mathsbox.org.uk
Problem 1 Expand x(x+5) x 2 + 5x Write an expression for: 6 less than x x - 6 ANSWERS Calculate the surface area of the cuboid Simplify half of x 5 cm 5x + x 2 + 8x + 3 + x 2 2x 2 + 13x + 3 ½x 8 cm 2 (5 8 + 5 3 + 8 3) 3 cm = 158 cm 2 A cuboid of length x, width 5 less than x and a height of half the length has a surface area of 250 cm 2. 2( x(x-5) + x(½x) + ½x(x-5) ) = 250 2x 2 10x + x 2 + x 2 5x 250 = 0 Show that 4x 2 15x 250 = 0
Problem 2 Find the Lowest Common Multiple of 16 and 22 16 = 2 2 2 2 22 = 2 11 LCM = 2 2 2 2 11 = 176 Divide 72 in the ratio 3:5 3 + 5 = 8 72 8 = 9 3 9 : 5 9 27 : 45 The sweets in a bag are orange, lemon and strawberry in the ratio 1:3:5. Given that there are more than 20 sweets in the bag, what is the smallest possible number of lemon sweets? 1 : 3 : 5 = 9 parts 3 : 9 : 15 = 27 9 lemon At a film club the members can choose one of three types of film Drama, Action or Horror During the first week the members chose the films the in the ratio 2 : 5 : 8 During the second week the members chose the sports the in the ratio 5 : 7 : 6 If there are less than 100 members how many more chose Action in the second week than the first week? 2 : 5 : 8 = 15 parts 5 : 7 : 6 = 18 parts LCM of 15 and 18 = 90 90 members Week 1 12 : 30 : 48 (90) Week 2 25 : 35 : 30 (90) 35 30 = 5 more
Problem 3 Calculate the volume of a cylinder Make h the subject of the Calculate x (2 d.p.) r = 6 cm and height = 10 cm V = π 6 2 10 = 1130.97 cm 3 formula V = 1 3 πr2 h πr 2 h = 3V h = 3V πr 2 7 cm 9 cm 9 2 + 7 2 = x 2 x 2 = 130 x = 130 = 11.40 cm A solid metal cylinder has a base radius of 6cm and a height of 12cm. The cylinder was melted and recast into a solid cone with a circular base radius of 8cm. Find the total surface area of the Volume of cylinder V = π 6 2 12 = 432π cm 3 Slant height of cone l 2 = 20.25 2 + 8 2 Cone 1 3 πr2 h = 432π cm 3 l = 474.0625 h = 3 432π 2 h = 20.25cm l = 22.77 cm π 8 Surface Area = π 8 2 + π 8 22.77 = 773.33 cm 2
Problem 4 Decrease 50 by 10% 10% = 5 50 5 = 45 There are four times as many red counters than blue counters in a bag. Express this as a ratio 4 : 1 Fill in the blanks in the 2-way table Voucher No Voucher Total Adult 28 10 38 Child 40 42 82 Total 68 52 120 30 adults and 60 children visit a theme park. The admission price is 40 for an adult and 30 for a child. 36 of the visitors have a voucher, which gives them 10% off the admission. Twice as many children than adults do not have a voucher. Calculate the total paid for admission of the 30 adults and 60 children Number without a voucher : 30 + 60 36 = 54 Dividing 54 in the ratio 2 : 1 = 36 : 18 Reduced prices Adult 36, Child 27 Voucher No Voucher Total Adult 12 18 30 Child 24 36 60 Total 36 54 90 Total = 12 36 + 24 27 + 18 40 + 36 30 = 3960
Problem 5 Calculate the area of the trapezium What is 2 m 5 cm? 2 0.05 = 1.95 m Convert 3.5 m 3 to cm 3 3.5 100 100 100 = 3500000cm 3 Area = ½ 6 (12 + 10) = 66 m 2 The pool is filled with water at a rate of 10 litres per second to a depth 10 cm less than the top of the pool. How long will it take to fill the pool? Area = ½ 1.9 (10 + 14) = 22.8 m 2 Volume = 22.8 7 = 159.6 m 3 1 litre = 1000 cm 3 10 litres = 10 000 cm 3 159.6m 3 = 159600000 cm 3 Time taken = 159600000 10000 = 15960 seconds 4 hours 26 minutes