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BIDMASAdding and subtracting

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Standard form

Adding and Subtracting Decimals

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ANSWERSa)0.5b)1.2c) 0.8d)1.3e)1.5

f) 1.47g)1.28h)1.66i) 0.97j) 1.68

• a)31.44b)70.81c) 39.46d)34.15e)50.8

• a)0.45b)0.54c) 0.49d)0.71e)0.7

• a)2.94b)39.02c) 67.25d)77.03e)54.11

Adding and Subtracting Fractions

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a) 7/8b) 8/12c) 7/9d) 7/10e) 2/3

f) 11/12g) 7/10h) 8/15i) 16/12 or 1 ¼j) 11/24

k) 1 7/12l) 1 5/56m) 29/30n) 29/52o) 1 1/10

p) 5/8q) 5/12r) 1/3s) 2/5t) 1/2

u) 7/20 v) 8/21w) 23/36x) 9/22y) 71/126

Adding and Subtracting Decimals

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Answers1.

a)0.5b)1.2c)0.8d)1.3e)1.5

2. a)1.47b)1.28c)1.66d)0.97e)1.68

3. a)31.44b)70.81c) 39.46d)34.15e)50.8

4. a)0.45b)0.54c) 0.49d)0.71e)0.7

5. a)2.94b)39.02c) 67.25d)77.03e)54.11

Direct Proportion

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1. If A is directly proportional to B, write an equation in the form A=kB linking the two variables if when A= 8 B= 4.

2. All of the variables below are directly proportional, write an equation linking them:1. V= 12 when M =42. T= 5 when S=13. Y= 34 when x=24. H=48 when M=45. P= 5 when N=10

3. B is directly proportional to C, when B is 18 C is 27.1. Write an equation linking B and C2. Find B when C= 663. Find C when B = 30

4. Z is directly proportional to Y, when Z =55, Y=51. Write an equation linking Z and Y2. Find Y when Z = 773. Find Z when Y=0.1

5. N is directly proportional to L, when N=1.8 L =0.61. Write an equation linking N and L2. Find L when N= 3.23. Find N when L=0.5

Answers1.A=2B2.

1.V=4M2.T=5S3.Y=17X4.H=12M5.N=2P

3. 1.C=1.5B2.B=443.C=45

4. 1.z=11y2.y=73.z=1.1

5. 1.N=3L2.L=1.23.N=1.5

Bidmas

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A)1. (3 + 3 ) x 42. 4 x 2 – 53. (5 + 7) ÷ 64. 5 x 3 + 55. (9 – 4 ) + 56. 1 + 1 – 17. 2 x (15 – 2)8. (5 x 4 ) + 29. (8 + 2 ) ÷ 1010. (21 x 1 ) – 2

B)1.(1 + 14) – (5 x 3 )2.(10 + 6 ) ÷ (4 x 2)3.(1 + 2 ) x (6 – 3)4.(2 x 6 ) – (14 ÷ 2)5.(7 x 2) ÷ ( 20 – 6)6.(3 x 10) – (2 x 2)7.(9 x 5) – ( 2 x 10)

C)1. (3 x 3 – 4 ) x (2 + 2)2. 2 x (13 – 4) – (23 ÷ 23)3. 3 x (1 + 4) – (5 x 2)4. 4 x (3 + 2) – ( 24 – 5)5. 7 x ( 4 ÷ 2 ) ÷ ( 3 x 5 -1 )6. ((9 + 7 x 3 ) ÷ 10) – 1

A. 1) 242) 33) 24) 205) 106) 17) 268) 229) 110)19

B. 1) 02) 23) 94) 55) 16) 267) 25

C. 1) 202) 173) 54) 15) 16) 2

Factors and HCF

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1) Find all the factors of the following numbers:1) 20 2) 24 3) 274) 325) 406) 507) 568) 1209) 200

2) 2 only has 2 factors (1 and 2), how many numbers can you find between 1 and 30 which have exactly 2 factors? (these are called prime numbers)

3) Find the highest common factors of the following pairs of numbers:1) 18 and 542) 25 and 453) 12 and 184) 27 and 1085) 30 and 75

4) Find the HCF of these pairs of numbers:1) 90 and 4502) 96 and 4803) 39 and 195

ANSWERS1.

1.1,2,4,5,10,20

2.1,2,3,4,6,8,12,24

3.1,3,9,27

4.1,2,4,8,16,32

5.1,2,4,5,8,10,20,40

6.1,2,5,10,25,50

7.1,2,4,6,7,8,14,28,56

8.1,2,3,4,5,6,10,12,20,24,30,40,60,120

9.1,2,4,5,10,20,40,50,100,200

2. 2,3,5,7,11,13,17,19,23,29 (10 of them)

3.

1.18

2.5

3.6

4.27

5.15

4.

1.90

2.96

3.39

Factor Trees

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1. Draw factor trees for the following numbers:a) 20b) 24c) 48d) 90e) 81f) 50g) 75h) 120i) 200j) 1800

2. Using your factor trees from question 1, write the numbers as products of their prime factors .

Answers1. 2.

a)22x5b)3 x 23

c)3 x 24

d)2 x 32 x 5e)34

f)2 x 52

g)3 x 52

h)23 x 3 x 5i)23 x 52

j)23 x 32 x 52

Directed Numbers

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Directed Numbers 2

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1) I am £250 into my overdraft () but then I get paid £535, how

much will I have in my bank account?

2) The temperature at the North Pole is -17°C; luckily the

temperature in my living room is 40°C warmer than that, what

is the temperature in my living room?

3) I have £32 and each month for 4 months I have to pay £15 to

my mobile phone, if I don’t put any money into my account,

how far will I be into my overdraft?

4) I jump out of a plane 125m above the ocean, I travelled 191m

before I stop, how far am I from the surface of the water?

5) I am playing air hockey with my friend, because I am amazing I

agree start on -9 points, we play first to 14, how many points

do I need to score?

Equivalent Fractions

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2.a)4b)15c)12d)20e)60f)8g)26h)32i)120j)15k)64l)154m)125n)400o)615p)9720

Ratio

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1. There are 10 girls and 15 boys in a class, what is the ratio of girls to boys in its simplest form?

2. There are 14 cats and 16 dogs in an animal shelter, what is the ratio of cats to dogs in its simplest form?

3. There 22 caramels and 55 fudges in a bag of sweets, what is the ratio of caramels to fudges in its simplest form?

4. Simplify these ratio to their simplest forms:a) 48:60b) 45:75c) 63:108d) 25:40:80e) 24:56:96f) 120:180:600g) 320:400:440

5. Archie and Charlie share their Thomas the tank engine toys in the ratio 1:4, how many do they each get if they have:

a. 10 toys b.30 toys c.45 toys6. Tom and Jerry share sweets in the ratio 2:3, how many do they each get if they share:

a. 20 sweets b.30 sweets c.55 sweets7. Sue and Linda share some money in the ratio 3:7, how many do they each get if they share:

a. £30 b.£60 c.£908. Mike, Dave and Henry share some little bits of blue tack in the ratio 1:2:3, how many do

they each get if they share:a. 60 pieces b.72 pieces c.300 pieces

Finding Percentages

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1) Some percentages I can find easily by doing a single sum, what single sums can I do to find:a. 10% b. 50% c.25%

2) If I know 10% how can I find:a. 5% b. 1% c. 20 % d. 90%

3) If I know 50% how can I find:a. 5% b. 25%

4) Find:a. 30% of 250 b. 40% of 500 c. 15% of 220 d. 75% of 84

5) Find:a. 35% of 440 b. 65% of 450 c. 16% of 220 d. 82% of 96

6) Find:a. 94% of 640 b. 8% of 520 c. 27% of 220 d. 53% of 96

7) Compare you methods for the questions above with a partner, where they the same ?

Equivalent Fractions

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HCF and LCM

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Find the Highest Common Factor of these numbers:•18 and 30•15 and 20•16 and 24•12 and 36•20 and 30•28 and 70•39 and 65•38 and 57

Find the Lowest Common Multiple of these numbers•6 and 7•4 and 6•5 and 8•10 and 4•16 and 5•14 and 21•2.2 and 5•0.4 and 7

1.422.123.404.205.806.427.558.14

1.62.53.84.125.106.147.138.19

Indirect Proportion

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1. If A is indirectly proportional to B and when A= 5 B= 6 :1.Find k2.Write an equation linking A and B3.Find A when:

1. B=32.B=15

4.Find B when:1. A=12.A=-3

2. If A is indirectly proportional to B and when A= 7 B= 12 :1.Find k2.Write an equation linking A and B3.Find A when:

1. B=42.B=6

4.Find B when:1. A=102.A=2

3. If A is indirectly proportional to B and when A= -4 B= 10 :1.Find k2.Write an equation linking A and B3.Find A when:

1. B=-82.B=10

4.Find B when:1. A=-12.A=-0.5

4. If A is indirectly proportional to B and when A= 24 B= 0.5 :1.Find k2.Write an equation linking A and B3.Find A when:

a.B=6b.B= -3

4.Find B when:a.A= -2b.A= 100

Fractions, Decimals and Percentages

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1. a) 75%b) 10%c) 20%d) 35%e) 42%

2. a) 0.7b) 0.25c) 0.3d) 0.15e) 0.05

3. a) 60% b) 70%c) 8%d) 27%e) 80%

4. a) ¼b) 33/100c) 51/100d) 4/5e) 1/5

5. a) 0.4b) 0.9c) 0.74d) 0.03e) 0.05

6. a) 7/10b) 3/5c) 11/50d) 7/20e) 21/50

Limits

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1) These numbers have been rounded to the nearest 10, write down the largest and smallest values they could be:

1) 502) 803) 110

2) These numbers have been rounded to the nearest whole number, write down the upper and lower limits:

1) 32) 173) 234) 1005) -3

3) These lengths have been rounded to the nearest 10th of a cm, write the upper and lower limits:

1) 12.5cm2) 21.7cm3) 35.8cm4) 52.1cm5) 80.4cm

4) A field is 100m wide and 120m long, both lengths have been

rounded to the nearest metre.

a) Find the perimeter and area of the field if these

measurements are accurate

b) Find the largest and smallest possible perimeter

c) Find the largest and smallest possible area.

5) A rectangle has it’s area rounded to the nearest whole number,

it becomes 40cm2. One side of the rectangle is exactly 10cm; find

the maximum and minimum lengths the other length could have.

6) Two lengths of wood are stuck together and their combined

length is rounded to the nearest mm and it is 14.9cm, one length

is rounded to the nearest mm and is 7.1cm. Find the minimum

and maximum length of the other length.

Answers1.

1.45 and 54.9999999.. 2.75 and 84.999....3.105 and 114.9999...

2. 1.2.5 and 3.4999...2.16.5 and 17.4999...3.22.5 and 23.49999...4.99.5 and 100.4999..5. -3.499999 and -2.5

3. 1. 12.45 and 12.552.21.65 and 21.753.35.75 and 38.54.52.05 and 52.155.80.35 and 80.45

4.

a)p=44om and area= 12000m2

b)largest= 442m smallest=438m

c) largest= 12110.25m2 smallest=11890.25m2

5. smallest- 3.95cm largest- 4.05cm

6. largest- 7.9cm smallest- 7.7cm

Multiples

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A. List the first 5 multiples of:1. 52. 73. 124. 145. 19

B. What is the:6. 9th multiple of 87. 7th multiple of 68. 12th multiple of 129. 11th multiple of 1010. 13th multiple of 511. 5th multiple of 13

C. List 3 numbers which are in:1. 3 and 4 times tables2. 3 and 5 times tables3. 10 and 4 times tables4. 9 and 2 times tables5. 12 and 10 times tables

D. What is the lowest common multiple of:1. 5 and 62. 7 and 83. 4 and 84. 9 and 65. 10 and 6

E. What is the lowest common multiple of:6. 13 and 57. 15 and 128. 16 and 109. 14 and 2110. 21 and 70

a) 5,10,15,20,25b) 7.14.21.28.35c) 12,24, 36, 48, 60d) 14,28,42,56,70e) 19,38,57,76,95

f) 72g) 42h) 144i) 110j) 65k) 65

l) 12,24,36m)15,30,45n) 20,40,60o) 18,36,54p) 60,120,180

q) 30r) 56s) 8t) 18u) 30

v) 65w)60x) 80y) 42z) 210

Multiplying and dividing fractions

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Answers1.

a)3/32b)5/48c)1/9d)4/25e)7/16

2. a)65/18 b)11c) 8d)1e)1/2

3. a)4/24 or 1/6b)20/12 or 5/3c)1d)1e)24/42 or 4/7

4. a)39/30 or 13/10b)22/18 or 11/9c) 32/36 or 8/9d)63/28e)50/16 or 25/8

Multiplying and dividing decimals

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1 a) 0.8 x 7 =b) 0.5 x 7 =c) 0.1 x 6 =d) 0.6 x 4 =e) 0.3 x 3 =

2 a) 0.2 x 0.5 =b) 0.4 x 0.7 =c) 0.8 x 0.1 =d) 0.9 x 0.9 =e) 0.6 x 0.1 =

3 a) 1.9 x 0.3 =b) 1.6 x 0.5 =c) 1.6 x 0.5 =d) 1.7 x 0.2 =e) 1.3 x 0.7 =

4 a) 5.4 x 0.11 =b) 5.2 x 0.97 =c) 8.3 x 0.73 =d) 4.6 x 0.11 =e) 8.2 x 0.75 =

Multiplying Dividing1

a)3.2 ÷ 4b)4.8 ÷ 8c) 7.2 ÷ 9d)2.4 ÷ 6e)1.8 ÷ 3

2 f)5.6 ÷ 0.7g)6.3 ÷ 0.7h)2.7 ÷ 0.3i)4.9 ÷ 0.7j)2.8 ÷ 0.7

3 k) 1.65 ÷ 0.15l) 24 ÷ 0.12m) 27.3 ÷ 1.3n) 0.03 ÷ 0.005o) 0.99 ÷ 0.0009

Answers1.

a) 5.6b) 3.5c) 0.6d) 2.4e) 0.9

2. a) 0.1b) 0.28c) 0.08d) 0.81e) 0.06

3. a) 0.57

b)0.8c) 0.75d)0.34e)0.91

4. a)0.594b)5.044c) 6.059d)0.506e)6.15

1. f)0.8g) 0.6h)0.8i)0.4j)0.6

2. k)8l)9m)9n)7o)4

3.p) 11q)200r)21s)6t)1100

Ordering Fractions

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ANSWERS1. 1/4 3/8 ½ and 4/8

3/42. 2/5 ½ 3/5 and 6/10

2/293. 1/3 5/12 1/1 4/6

3/44. 1/4 1/2 2/3 5/6

7/85. 1/4 2/5 1/2 6/10

3/46. 1/3 4/9 1/2 2/3

5/67. 2/6 1/4 5/12 2/3

7/98. 2/7 2/4 5/8 11/14

3/2

Percentage Increase/Decrease

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1. Explain how you would use a calculator to increase an amount by a given percent.

2. Increase the following amounts by 42%a)£225b) £306c)£125d)£448e)£512

3. A TV costs £120, how much will it cost if its price is increased by:

a) 12%b)31%c)55%d)62.5%e)99.9%

4. Simon puts £70 in a bank, each year the money in his bank increase by 5.5%, how much does he have in:

a) 1 yearb)2 yearsc)5 years?

5. Explain how you would use a calculator to decrease an amount by a given percent.

6. Decrease the following amounts by 28%a) £225b) £306c) £125d) £448e) £512

7. A TV costs £120, how much will it cost if its price is decreased by:

f) 19%g) 32%h) 79%i) 73.5%j) 42%

8. A car bought for £6, 500 depreciates in value by 12.5% each year, how much will it be worth after:

k) 1 yearl) 2 yearsm) 5 years?

Rounding to Significant Figures

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Main1. When you are rounding to

decimal places you start counting after the decimal point, but with significant figures you start counting at the first non zero number

2. i. 1000 1500 1460ii. 200 160 157iii. 40 37 37.1 iv. 6 6.1 6.09v. 0.006 0.0064 0.00640

3. a) 4.7b) 0.058c) 0.19d) 540

Rounding to Decimal Places

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a) 1.463884266b) 1.572660902c) 3.783345228d) 6.3931313e) 0.640368898f) 0.326119942g) 4.249504359h) 4.44692939i) 1.447852851 j) 0.069143754

Work out the following on a calculator and give the answer to 2 decimal places;

a) 3.104 x 5.938b) 2.99 x 8.82c) 7.1537÷ 3.111d) 14.772

•Round the following numbers to a) 1 decimal place b) 2 decimals places c) 3 decimal places

ANSWERS

a)1.5 1.46 1.464b)1.6 1.57 1.573c)3.8 3.78 3.783d)6.4 6.39 6.393e)0.6 0.64 0.640f) 0.3 0.33 0.326g)4.2 4.25 4.250h)4.4 4.45 4.447i) 1.4 1.45 1.448j) 0.1 0.07 0.069

• a)18.43b)26.37c)2.30d)219.15e)3.67

Reverse Percentages

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1. What would you multiply an amount by to increase it by:

a) 15%b)25%c)4%d)0.5%e)13.5%

2. Find the original prices of these prices that have been increased by the given percentage:

a) Cost= £49.5 after 10% increaseb)Cost= £74.75 after 15% increasec)Cost= £61 after 22% increased)Cost= £104 after 30% increasee)Cost= £120 after 50% increase

3. I have £252 in my bank account; this is due to me earning 5% interest on what I originally had put in. How much money did I have originally in my bank account?

4. What would you multiply an amount by to decrease it by:

a) 15%b)25%c)4%d)0.5%e)13.5%

5. Find the original prices of these items that have been decreased by the given percentage:a) Cost= £72 after 10% decreaseb) Cost= £93.5 after 15% decreasec) Cost= £39 after 35% decreased) Cost= £4 9fter 40% decreasee) Cost= £67.50 after 55% decrease6. A Cars value has dropped by 11.5% it is now worth £3053.25, what was it worth when it was new?

Standard Form

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Answers1. a,e,f,g

2. 1. 474000000

2.1903.86200004.640005.350006.663000007.9090000008.60009.8710000000

3. 1.0.0000000001362.0.000000000953.0.000006384.0.00000007965.0.00000566.0.000000005437.0.0000000006328.0.000489.0.000161

4. 1.8.3 x 103

2.4.4 x 105

3.1.35 x 107

4.9.87 x 107

5.3.4 x 10-5

6.9.301 x 10-5

7.4.3 x 10-4

Two Brackets

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Answers1.

1.x2+12x+352.x2+10x + 213.x2 + 5x + 64.x2 + 6x + 85.x2 + 9x + 8

2. 1.x2 – 492.x2 + x – 123.x2 + 8x -204.x2 -17x + 725.x2 -10x + 24

3. 1.6x2+15x – 92.8x2 + 76x -403.9x2-71x – 84.6x2 – 48x + 425.9x2 – 37x + 4

4. 1.6x2 + 12x – 482.28x2 + 21x -493.12x2 -36x – 48

5. 15x2 + 10x – 25

Answers1.

1. x2+12x+352. x2+10x + 213. x2 + 5x + 64. x2 + 6x + 85. x2 + 9x + 8

2. a)x2 – 49b)x2 + x – 12c) x2 + 8x -20d)x2 -17x + 72e)x2 -10x + 24

3. a)6x2+15x – 9b)8x2 + 76x -40c) 9x2-71x – 8d)6x2 – 48x + 42e)9x2 – 37x + 4

4. a)6x2 + 12x – 48b)28x2 + 21x -49c) 12x2 -36x – 48

5. 15x2 + 10x – 25

3D Pythagoras

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Find the length of the longest diagonal of these cuboids

1) Answers2) 11.2cm3) 12.0cm4) 12.2cm5) 9.4cm6) 13.4cm7) 15.2cm

5cm

8cm

8cm

5cm

4cm

9cm 9cm

4cm

12cm

10cm3cm

15cm7cm

11cm

Find the Perimeter of these shapes

8cm8cm

5cm

4cm

9cm

4cm

8cm

3cm

5cm4cm 12cm

11cm

13cm

All of these shapes are regular

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Answers1. 26cm2. 26cm3. 30cm4. 25cm5. 36cm

Answers1. 21cm2. 17cm

Answers1. 16cm2. 25cm3. 72cm4. 39cm5. 96cm6. 110cm7. 42cm