Topic 1 - Decimals, Estimation, Best Buy and Exchange Rates

Insert brackets where necessary to make the following calculation correct: 12 + 3 x 14 - 2 = 180.

(12 + 3) (14 - 2) = 180

- 3 - 8 = ?

-11

- 10 x 14 = ?

-140

- 5 + ( - 10) = ?

-15

What are the next two terms in the sequence; 1, -4, -9, -14.........?

-19, -24

- 9 - ( - 9) = ?

0

248 ÷ 100 = ?

0.248

A shoe box has measurements 0.42 m by 0.18 m by 0.14 m. Miss Bartholomew wants to cover the box with pretty paper. Estimate the surface area of the box.

0.3192m

What are all the factors of 24?

1, 2, 3, 4, 6, 8, 12, 24

In a packet of 12 sweets 4 are red. You take a sweet without looking; what is the probability of choosing a red sweet?

1/3

7 - ( - 4) = ?

11

- 3 x - 4 = ?

12

A company need to package boxes into containers. Each small box weighs 12kg. The maximum weight a container can manage is 320kg. What is the maximum number of boxes they can pack in a container?

12 boxes

Simplify 3J + 9k - 2k + 9J

12J + 8k

Mr Robinson is buying carpet for his dining room. He requires 14.6 square metres of carpet and it is advertised at £6.79 per square metre. Work out roughly how much the carpet will cost.? Show all your working clearly.

14.6 x 6.79 = 99.134 so roughly, £99 (to 2 significant figures)

What is the product of 14 and 11?

154

159 x 100 = ?

15900

45 - 7 x 3 = ?

21

Expand 3(7x - 7)

21x-21

What are the next two terms in the sequence; 4, 9, 14, 19, .........?

24, 29

32 ÷ 10 = ?

3.2

0.381 x 10 = ?

3.81

Calculate 150 - (7 x (4 2 + 1))

31

Expand the bracket 3(a-7)

3a-21

Simplify 2x + 7y + 2x - 3y

4x+4y

In a class of 30 students the probability that a pupil has brown eyes is 1/6th. How many students should have brown eyes?

5

Write five thousand, three hundred and four in figures

5304

Expand and simplify 3(a+7) + 2(a+3)

5a + 27

In a class of 30 students 1/5th of the class are left handed. How many are left handed?

6

What is the highest common factor (HCF) of 12 and 30?

6

What is 5830 rounded to one significant figure?

6000

Round 7.65952 to two significant figures.

7

In a quadrilateral the angles are 125 0 , 45 0 , 110 0 and A. Find the value of A.

80 degrees

(18 x 3)/(2+4) = ?

9

Write down any three factors of 12

Any three from 1, 2, 3, 4, 6, 12

Sara is going to print 120 photos. Here is some information about the cost of printing in two shops. PHOTOBOX 15 prints £2.99. DIGITAL WORLD 10 prints £3.49, buy one pack get one free. Sara wants to buy the photos as cheaply as possible. Which shop should Sara buy the 120 photos from?

Digital World

Here is a method for multiplying a whole number by 101. Step 1: Put two zeros onto the right hand side of the number. Step 2: Add on the original number. Use an example to show that this method works by comparing your usual method with the method suggested above. Explain why this works.

Example 50 101 Step 1: 5000 Step 2: 5050. This method works as 50 x 101 is the same as saying (50 x 100) + (50 x 1)

The exchange rate in London is £1 = €1.17 The exchange rate in Paris is €1 = £0.76 Janet wants to change some pounds into euros. In which of these cities would Janet get the most euros?

Paris

Apples cost £1 for a 1.4 kg bag at Tesco. The same type of apples cost 87p for a 750g bag at ASDA. Where are the apples better value for money?

Tesco

A pack of 9 kitchen rolls costs £4.19. A pack of 4 kitchen rolls costs £1.76. Which pack gives the better value for money?

The pack of 4

Is 2 a prime number?

True

Write 2,469,020 in words

Two million, four hundred and sixty-nine thousand and twenty

Work out these calculations. a) 3.2 ÷ 8 = ? b) 12.4 ÷ 6 = ? c) 34.83 ÷ 0.9 = ?

a) 0.4 b) 2.0 c) 38.7

Without using a calculator and given that 563 x 2.1 =1182.3 a) 56.3 x 2.1 b) 5630 x 2.1 c) 56.3 x 21

a) 118.23 b) 11823 c) 1182.3

Given 47 x 29 = 1363, work out, without using a calculator: a) 4.7 x 29 = ? b) b) 47 x 290 = ?

a) 136.3 b) 13630

Work out these calculations using a standard written method. a) 31.55 + 107.34 = ? b) 45.872 + 104.71 = ? c) 12.45 + 0.551 = ? d) 2.37 - 1.5 = ? e) 23.303 - 14.72 = ? f) 18.32 - 9.156 = ?

a) 138.89 b) 150.582 c) 13.001 d) 0.87 e) 8.583 f) 9.164

Work out these calculations. a) 3.2 x 8 = ? b) 12.4 x 0.6 = ? c) 6.3 x 2.4 = ? d) 12.6 x 27 = ? e) 55.27 x 3.64 = ?

a) 25.6 b) 7.44 c) 15.12 d) 340.2 e) 201.1828

Rounding all numbers to 1 sf write down and solve a calculation you would use to estimate answers to: a) 379 ÷ 19 b) 238 x 47 c) 1037 + 282 d) (462 x 79) ÷ 0.42

a) 40020 = 20 b) 200 x 50 = 10000 c) 1000 + 300 = 1300 d) = 100000

Round 456.009 to a. Nearest ten b. 1 decimal place c. 2 decimal places d. 2 sig fig e. 3 sig fig

a) 460 b) 456.0 c) 456.01 d) 460 e) 456

Calculate the following using a mental method a) 15 x 0.4 = ? b) 9 ÷ 0.5 = ? c) 1.2 x 0.008 = ? d) 21 ÷ 0.3 = ?

a) 6 b) 18 c) 0.96 d) 70

First estimate and then write down exact answers: (All estimations were done by rounding numbers to 1 sf) a) 2.16 - 1.08 b) 6.49 - 2.36 c) 14.46 - 9.88 d) 4.29 - 3.67

a) estimate = 1, exact = 1.08 b) estimate = 4, exact = 4.13 c) estimate = 4, exact = 4.58 d) estimate = 0, exact = 0.62

First estimate then write down exact answers: (All estimations were done by rounding numbers to 1 sf) a) 3.4 + 12.55 b) 6.92 + 0.04 c) 5.32 + 7.81 d) 3.58 + 2.7

a) estimate = 16, exact = 15.95 b) estimate = 7, exact = 6.96 c) estimate = 13, exact = 13.13 d) estimate = 7, exact = 6.28

Ann went to France. She changed £400 into Euros (€). The exchange rate was £1 = €1.34 (a) How many Euros did she get? (b) Ann went shopping in France. She bought: 2 scarves for €3.40 each 1 necklace for €16.40 1 bag for €10.50. The exchange rate was £1 = €1.34. Work out her total bill in pounds (£).

a) €536 b) £25 (to 2 sf)

Solve: 7p + 9 = 30

p=3

Solve: 5p - 4 = 31

p=7

A minibus cost £245 for the day to hire. There are 12 people. Estimate how much each person will need to pay.

£20

Adam's car does an average of 10.2 miles per litre of petrol. The cost of petrol is £1.09 per litre. Adam completes a journey of 289 miles. Estimate how much this will cost him.

£28.9

A coat costs £75, delivery costs a further 5%. What is the delivery charge?

£3.75

A train ticket that costs £48.80 is reduced by a ¼. What is the new cost?

£36.60

A box of chocolates priced at £6.00 is reduced by a third. What is the new price?

£4

A bunch of flowers priced at £9.60 is reduced by a third. What is the new price?

£6.40

An electricity bill is £82 plus VAT at 5%. Calculate the VAT charged.

£86.10