Module 5 Homework 1: Non-Calculator

Homework 16 (Calculator allowed) Name:

1) Adam has 12 counters. He puts them into threes like this.

a) How many threes can he make altogether? …………………………………. (1)

b) He puts the same number of counters into fours.

How many fours can he make altogether? …………………………………. (1)

2) Look at the clock in the box. a) Write this time down as a digital time ………………. : ………………. (1)

b) What time will the clock show two hours later? Tick (ü) it.

(1)

3) Tom is making 3-digit numbers with these cards. He can make this number.

Write down all the other 3-digit numbers he can make.

4) The tally chart shows the number of children in each class.

The total for Class 4 and the tally for Class 3 are covered up.

a) Complete the total for Class 4 and the tally for Class 3. (2)

b) How many children are there altogether?

…………………………………………………………………………….. (1)

5) Alice had some cherries.

She ate half of them.

These are the cherries she left.

How many cherries did she start with?

……………………………………………………………………………………………Answer: ………………….. cherries (1)

6) Judah’s dad washes some cars. He uses 12 buckets of water. Each bucket has 5 litres of water.

How many litres of water does he use altogether?

Show how you work it out.

…………………………………………………………………………………………………….. Answer: …………………… litres (2)

7 a) Draw a cross (×) on three numbers that are not even. (1)

b) Look at this number line.

Write the missing number in the 2 empty boxes. (1)

c) Write the total: 26 + 32 + 13 ………………………………………………………………………………. (1)

1) Each rule below makes a sequence. Use the rule to write the next two numbers for each sequence.

Rule: Add 4 to the last number 3 7 11 ………. ……… (1)

Rule: Double the last number and then add 1 3 7 15 ………. ……… (1)

Rule: Multiply the last number by 3 and take away 2 3 7 19 ………. ……… (1)

2) Here are some shapes.

They are drawn on a

centimetre square grid

Complete the

sentences below.

a) Shape …………………. is the only shape with no right angles. (1)

b) Shape ………...... and shape ……………………… have no lines of symmetry (1)

c) Shape …………………… is the only shape with no parallel sides (1)

3) Here is a diagram showing the results from a survey asking girls and

boys in a class of students for their favourite colour.

a) Which colour is least popular overall? …………………………… (1)

b) How many girls responded to the survey? …………………………….. (1)

4) The scale shown is used for weighing ingredients. All of the values are metric.

a) Write down the weight indicated by the arrow (including the unit of measure)

……………………………………………………………………………………………… (1)

b) 300 grams of weight is added to the scale. What it the total weight now?

……………………………………………………………………………………………… (1)

c) A chicken weighs 3.25 kilograms. Draw another arrow to

show this weight on the scale. (1)

5) A restaurant is offering the following prices:

a) A family of 2 adults and 5 children eat at the restaurant.

The adults have both starters and main courses, the children only

have main courses. Work out the total cost of the mean.

………………………………………………………………………………………………………………………………………………………………. (2)

b) Another family eats at the restaurant. The total cost of the meal where everyone has eaten both starters and main

courses is £108.50. How many people are there in this other family?

………………………………………………………………………………………………………………………………………………………. (2)

1) Look at the graph

a) Write the coordinates of points A, B and C

A is ( ….… , ….… ) B is ( ….… , ….… ) C is ( ….… , ….… ) (2)

b) Mark point D accurately on the graph so that

ABCD is a square. (1)

c) Point B is reflected in the x axis to form B′.

Write the coordinates of point B′.

B′ is ( ….… , ….… ) (1)

2) A green box contains 50 packs of salt and vinegar crisps. There are 12 green boxes. A blue box contains 30 packs

of cheese and onion crisps. There are 15 blue boxes. Each packet of crisps costs £0.75.

a) Match each question with the correct calculation.The first one has been done for you. (2)

b) Ben calculates 50 × 0.75 – 30 × 0.75. Write a possible question that Ben is answering.

……………………………………………………………………………………………………………………………………………………… (1)

3) Look at this equation

Write a pair of values for x and y to make the equation true. x = ………….. y = …………… (1)

Now write a different pair of values for x and y to make the equation true. x = ………….. y = …………… (1)

4 a) Here is a percentage bar chart.

It shows the results from a survey

where people were asked,

“Do you like cheese?” 80 people said, “No”. How many people said, “Yes”? …………………………………………… (1)

b) Sally asked 20 people whether

they like custard. 10 people

said, “yes”, 8 people said, “no”

and 2 people said, “I don’t know”. Fill in the percentage bard chart with this information. (2)

5) Henry cycles 10 laps of a track and records his times for each lap to the nearest second.

Lap 1 Lap 2 Lap 3 Lap 4 Lap 5 Lap 6 Lap 7 Lap 8 Lap 9 Lap 10

316 298 290 302 317 328 330 317 335 345 Complete each of the sentences.

a) Henry’s quickest time was lap ……………… (1)

b) The range in lap times was …………………………………………………………………………………………………….. (1)

c) The median lap time was …………………………………………………………………………………………………….. (1)

1) Sam and Ann measure the amount of water that they each drink in an hour.

Sam drinks 0.5 litres. Ann drinks 700 millilitres. Who drinks the most and by how much more?

Sam Ann ………………………………………………………………………… millilitres more (1)

2a) The diagram shows a triangle. b) A triangle is right angled and isosceles.

Write the ratio of the angles write down the size of the three angles in the triangle

A : B : C in their simplest form.

………………………………………………. ……………………………………………………………………….

……….. : ……….. : ……….. (2) Answer: ………….. , ………….. and ………….. (2)

4) Here are two shapes, a rectangle and a square, with

the same perimeter. They are not drawn accurately.

a) Work out the side length of the square.

………………………………………………………………………. cm (1)

b) A different square has the same area as the rectangle shown. What is the side length of this square?

……………………………………………………………………………………………………………………………………………………. (1)

5) Solve these equations

16x + 74 = 33 52 – x = 100 + 23x

……………………………………………………………………… …………………………………………………………………………….

……………………………………………… x = ……………….. (1) ……………………………………… x = ……………….. (2)

6) Daniel needs to buy 30 pens. Pens can be bought in packs of 5 costing £1.20 per pack, or in packs of 6 costing

£1.40 per pack. Work out the difference in cost between buying 30 pens in packs of 5 and in packs of 6.

…………………………………………………………………… ……………………………………………………………………………………………

………………………………………………………………………………………………………………………………………………… (2)

1) The pie chart shows results of an experiment where 1000 people

were asked to taste different types of crisp and to choose their

favourite. 20% chose type A, 4% chose type B, 11% chose type C

and 49% chose type D. The remaining people couldn’t decide.

a) What angle was used to represent Type B in the pie chart?

………………………………………………………………………………………….. (1)

b) How many people chose Type C? ……………………………………. (1)

Alderney has a population of 9 500. Using the pie chart, how many

people would you expect to choose Type B in Alderney? ………………………………………………… (1)

2) Look at the information: x = 3 and y = 20. Complete the rules to show different ways to get y using x.

The first one is done for you.

To get y, multiply x by …………….. and add …………….. This can be written as y = …………………………………..

To get y, multiply x by …………….. and add …………….. This can be written as y = ………………………………… (1)

To get y, multiply x by …………….. and subtract …………… This can be written as y = ………………………………….. (1)

To get y, divide x by …………….. and add …………….. This can be written as y = ………………………………….. (1)

3) The diagram shows a trapezium drawn inside a rectangle. The diagram is not drawn accurately.

Work out the shaded area. You must give the correct unit in your answer.

………………………………………………………………………………………………………………….

……………………………………………………………………………………………………….. (3)

4) Write the missing numbers:

5x + 3 = 11 so 5x + 1 = …………………… (1) 2 – 3y = 6 so (2 – 3y)2 = …………………… (1)

5) Henry has investigated how people working in a bank

travel to work.

The table shows the results.

a) What percentage of the people do not travel to work by car? …………………………………………………………………… (1)

b) 22 people travel to work by car. Some of these people

share a car.

Write the missing frequency in the table. (1)

c) Calculate the mean number of people in each car.

…………………………………………………………………………………………

……………………………………………………………………………………………………………………………………………………. (2)

1) Multiply out the brackets

a) 5(3x + 2) b) (y + 3)(y + 4)

………………………………………………………………… ……………………………………………………………………….

………………………………………………………………… (1) ………………………………………………………………………. (1)

2) Harry has worked out the

probability of randomly choosing

a certain type of number from the

values 1 to 100.

a) What is the probability of not choosing a prime number? ………………………………………………………………………. (1)

b) One of the probabilities has been rounded. Which one? ………………………………………………………………………. (1)

c) Explain why the probability of choosing a square or cube number is not 0.14

……………………………………………………………………………………………………………………………………………………………… (1)

d) Work out the probability of choosing a number which is a multiple of both 3 and 4

………………………………………………………………………………………………………………………………………………… (1)

3) This shaded shape is made using two semicircles. One semicircle

has a diameter of 10 cm. This forms the radius of the other semicircle.

Calculate the perimeter of the shaded shape.

4) A raffle consists of white tickets and pink tickets. The number of each type of ticket

sold is shown in the table including whether the ticket is even or odd numbered

A raffle ticket is taken at random from each colour. In which colour is it more likely

to choose an even number? You must show your working.

………………………………………………………………………………………………………………………………………………………………

……………………………………………………………………………………………… Answer: …………………………………… (2)

5) Triangle A has side lengths, 6cm, 8cm and 10cm.

a) Use Pythagoras’ theorem to explain why triangle A must be right angled.

……………………………………………………………………………………………………………………………………………………………… (1)

b) Triangle A is enlarged to form a second triangle with a side length of 9cm. One of the possible set of lengths for

triangle B is 9cm and 12cm and 15cm and the scale factor of the enlargement is 32. Work out the other two

possible sets of lengths and in each case, write the scale factor of the enlargement.

………………………………………………………………………………………………………………………………………………………………

Answer 1: Lengths: ………… cm and …………… cm and …………… cm Scale factor = …………………..

Answer 2: Lengths: ………… cm and …………… cm and …………… cm Scale factor = ………………….. (3)

1) A magazine article reports that the population of the Shetland Islands has fallen by 20% over the last twenty

years. The population of the Shetland Islands is now estimated to be around 23 000. About how many people

were living in the Shetland Islands 20 years ago?

………………………………………………………………………………………………………………………………………………………………

……………………………………………………………………………………………… Answer: ………………………… people (2)

2) A regular octagon is made by cutting a triangle from each corner of a square. The

perimeter of the octagon is 24 cm. Work out the length of x, writing your answer to 2 d.p.s.

…………………………………………………………………………………………………………………………….

……………………………………………………………………………………………………………………………

………………………………………………………………………………….. x = …………………….. (2)

3) There are 100 families in a survey. 50 are English, 30 are Welsh and the rest are Scottish. The table shows

the mean number of children for the families. What is the overall mean number of children for the 100 families?

4) The average distance between Pluto and the Sun is 3660 million miles.

a) Write this distance in standard form. …………………………………………………………………………………….... miles (1)

b) Given that 5 miles = 8 kilometres, how many metres is the average distance between Pluto and the Sun?

Write your answer in standard form.

………………………………………………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………………………………….... (2)

5) I am thinking of a number. When I subtract 9 from my number and square the answer, I get the same result as

when I square my number and subtract 9 from the answer. Use an algebraic method to work out my number.

………………………………………………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………………………………….... (2)

3) Here are some simultaneous equations.

a) Write an expression for y in terms of a and b ………………………………………………………………………………………….

……………………………………………………………………………………………………………………………………………………….... (2)

b) Solve the simultaneous equations given that a = 2 and b = 7

………………………………………………………………………………………………………………………………………………………………

…………………………………………………………………………………………………… x = ………..….. y = …………… (2)