Problem 1. 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

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Trevor Freeman
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1 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 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

2 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?

3 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)

4 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 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

5 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

6 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 x 2 2x x + 3 ½x 8 cm 2 ( ) 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

7 Problem 2 Find the Lowest Common Multiple of 16 and = = 2 11 LCM = = 176 Divide 72 in the ratio 3: = = : : 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 = members Week 1 12 : 30 : 48 (90) Week 2 25 : 35 : 30 (90) = 5 more

8 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 = cm 3 formula V = 1 3 πr2 h πr 2 h = 3V h = 3V πr 2 7 cm 9 cm = x 2 x 2 = 130 x = 130 = 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 = 432π cm 3 Slant height of cone l 2 = Cone 1 3 πr2 h = 432π cm 3 l = h = 3 432π 2 h = 20.25cm l = cm π 8 Surface Area = π π = cm 2

9 Problem 4 Decrease 50 by 10% 10% = = 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 Child Total 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 : = 54 Dividing 54 in the ratio 2 : 1 = 36 : 18 Reduced prices Adult 36, Child 27 Voucher No Voucher Total Adult Child Total Total = = 3960

10 Problem 5 Calculate the area of the trapezium What is 2 m 5 cm? = 1.95 m Convert 3.5 m 3 to cm = cm 3 Area = ½ 6 ( ) = 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 ( ) = 22.8 m 2 Volume = = m 3 1 litre = 1000 cm 3 10 litres = cm m 3 = cm 3 Time taken = = seconds 4 hours 26 minutes

Problem 1. 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

Problem 1. 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 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