Cambridge Essentials Mathematics Extension 7 A1.1 …essentials.cambridge.org/media/CEMKS3_E7_A1_1_WS_HWS3.pdf · a x + 5 b 3x c 5x – 8 d 13 – 4x e 3(x + 5) f (x – 1)2 g 17

Cambridge Essentials Mathematics Extension 7 A1.1 Homework 1

Original material © Cambridge University Press 2008 1

A1.1 Homework 1

1 Each symbol stands for a number. Find the value of each symbol.

a ☺ – 8 = 17 b ☼ × ☼ = 64 c ♦ ÷ 4 = 24 d 5∇+∇ = 6

2 ♥ = 3 and ☼ = 8. Find the value of each expression.

a ♥ + ☼ b 7 – ♥ c 48 ÷ ☼ d ☼ × ♥

3 ▲ = 7

Find a quick way to work out 90 – (▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲ + ▲).

Explain how you got your answer.

4 ☻ = 15

Write down the number that is

a 6 more than ☻ b 8 less than ☻ c 4 times ☻ d ☻ less than 40

5 ● – □ = 4 and ● × □ = 12. Write a pair of values for ● and □.

6 Paula has ◊ sweets. Write how many sweets each of Paula’s friends has.

a Jack has 6 more than Paula.

b Asif has half as many as Paula.

c Clare has 3 times as many as Paula.

d Kelly has 41 less than Paula.

7 Each letter stands for a number. Find the value of each letter.

a p + 4 = 7 b t – 5 = 5 c f × 3 = 21 d k ÷ 2 = 9 e m + m = 24

8 g = 20 and h = 4. Find the value of each expression.

a g + 6 b h × 3 c g – h d g ÷ 2 e g × h f 60 ÷ h

9 a × b = 72. Write four different values for a and b.



10 x + 5 can be written in words as ‘five more than x’.

Write these in words.

a x – 7 b x + 2 c 3x d 4x

e 8 + x f 6 – x g x × 2 h 2x + 1

11 n stands for a number. ‘4 more than n’ is written with symbols as n + 4.

Write these with symbols.

a 2 less than n b 5 times n c 10 more than n

d half of n e double n f 7 less than n

g 12 times n h 6 more than n i n less than 10

12 Look at this table. Age (in years)

Ahmed a

Brad b

Carla c

a Write each statement using the letters a, b, and c.

The first one has been done for you.

i Ahmed is 16 years older than Brad. Answer: a = b + 16

ii Carla is 13 years old.

iii Carla is three years younger than Brad.

iv Ahmed’s age is three years more than Brad’s age and Carla’s age added together.

b Write in words the meaning of each of these. The first one has been done for you.

i b = 16 Answer: Brad is 16 years old.

ii b + c = 29

iii a = 2 × b

iv a = c + 19



A1.1 Homework 2

1 Copy and complete each sequence.

Write the rule that tells you how to get from one term to the next.

a 13, 19, 25, , , 43 b 65, 53, , 29, , 5

c , 23, 32, 41, , 59 d , , 10.5, 14, , 21, 24.5

2 The first term of a sequence is 99 and the terms decrease by 13.

Write the first five terms of the sequence.

3 In a sequence, each term is half the term before. The second term is 56.

Write the first five terms of the sequence.

4 Here is a sequence of patterns made from circles.

Pattern 1 Pattern 2 Pattern 3

a Pattern 1 has 3 circles.

How many circles are there in Pattern 2? How many in Pattern 3?

b Draw the next two patterns in the sequence. How many circles are there in each one?

c Write the numbers of circles in the first five patterns as a sequence.

d What is the term-to-term rule for this sequence?

5 The sequence 6, 12, 18, 24, ... can be written like this.

1st term 2nd term 3rd term 4th term

6 × 1 6 × 2 6 × 3 6 × 4

Copy and complete.

The 5th term is 6 × = The 10th term is 6 × =

The 100th term is × = The nth term is ×



6 Write down the first five terms of the sequences with these nth terms.

a n + 8 b n + 20 c 4 × n + 7 d 100 – (6 × n)

7 The nth term of a sequence is 2 × n + 5. What is the 8th term of this sequence?

8 This is a sequence of patterns. Each pattern is made from hexagons.

Think of each pattern as one hexagon at the top with sets of three hexagons below it.

In this way, the number of hexagons in the patterns make a sequence.


1 + 1 × 3 = 4 1 + 2 × 3 = 7 1 + 3 × 3 = 10

Copy and complete.

a The number of hexagons in Pattern 4 is 1 + × 3 =

b The number of hexagons in Pattern 10 is + × =

c The number of hexagons in Pattern n is 1 + ×

9 What is the nth term of each sequence?

a 7, 14, 21, 28, 35, ..., b 5, 9, 13, 17, 21, ...,

c 10, 18, 26, 34, 42, ..., d 70, 65, 60, 55, 50, ...

10 Sharif is making ‘houses’ with arrows.

1 house 2 houses 3 houses 6 arrows

a Find the number of arrows in the pattern with n houses.

b How many arrows will be needed for 20 houses?

Cambridge Essentials Mathematics Extension 7 A1.2 Homework


A1.2 Homework

1 Copy and complete these function machines.

a 2 13

□ → + → 19

17 □

b n n – 7

□ → − → 18

□ n – 3 c 3 45

□ → × → 75

n □

d 30 6

□ → ÷ → 10

15n □

2 Draw a function machine for x → x + 2.5. Use the input values 0, 4, 13 and 25.

3 Copy and complete these function machines.

a 3 □

□ → 2 + → 4 × → 10

n □

b □ 1

2n → 2 ÷ → 6 − → □

□ 5n – 6

4 8 → → → →

Arrange the operations 6 + , 3 × and 4− in different ways in the function machine.

a Make the output 18. b Make the output 26. c Make the largest possible output.

5 1

2→ 3 × → →

3

Copy and complete the function machine

so that these are the outputs.

a 1

2

3

b 4

7

10

c 1.5

3

4.5



6 Copy and complete the function machine in two different ways.

2 8

□ → → 20

9 □

7 Copy and complete.

x → → 4 × → 3x

8 Copy and complete this function machine in two different ways.

x → → 1 − → → 2x

9 Copy and complete this function machine so that the output is always the same as the input.

x → → 6 − → → 4 × → 2 ÷ → x

Check your answer using the input values 2, 3 and 4.

10 a Copy and complete the table of x and y values for this function machine.

x → 3 × → 2 + → y

x 1 2 3 4 5 6

y

b Copy and complete this mapping diagram using values from your table.

11 A function uses the rule n → ?

Here are some inputs and outputs

for this function.

What is the function?

1 → 2

2 → 6

3 → 10

4 → 14



A2.1 Homework 1

1 Work these out.

a 3 + 5 × 2 b 17 – 2 × 8 c 3(4 + 6) d 4 × 2 + 3 × 5

e 9 + 8 ÷ 4 f (10 – 3) ÷ 2 g 20 ÷ 4 + 21 ÷ 7 h 11 – (8 + 5)

i 32 + 42 j 2 × (12 + 5) k 102 ÷ 22 l (10 ÷ 2)2

2 Find the value of each of these expressions when x = 4.

a x + 5 b 3x c 5x – 8 d 13 – 4x

e 3(x + 5) f (x – 1)2 g 17 – 3(x + 2) h (x + 2)2

i x

40 j 2

3x k 7

22+x

l x5

100

3 Find the value of each of these expressions when p = 6 and q = 3.

a p + q b p – q c pq d 3p – 6q

e p + 2q f 18 – (p + q) g q(p + 1) h p2 – q2

i qp +

45 j 1

6+qp k

pq−33 l

qp −24

m pq2 n p2q o 5 – pq p p2 + q2

4 Simplify these expressions.

a x + 4 + 9 b x + 7 – 3 c x + 4 × 5

d x + x + x + x e 3x – x f 4x – 7x

g 10x – 4x – x h x + y + y + y i 3x – x + 2y + y

j 3xyz + 4xyz k 3k + m + 2k – m l x – 5x + 3 – 8m + 4 + 10m

m x2 – 1 + x + 7 + 2x2 n 5k2 – 6 – k2 – 4 o p2 + 7p – 3 + 2p2 + 3p – 4

5 Write these expressions in words.

a 3n + 6 b 2(n + 6) c

36+n d

362 +n



A2.1 Homework 2

1 Write a formula for the perimeter P of each shape.

Write your formula in its simplest form.

a

b

c

d

e

f

g

h

i

2 Guy thinks of three different rectangles, A, B and C. Each one has a perimeter of 6x + 10.

Use the information below to draw the three rectangles. Label the sides.

a One of the side lengths of rectangle A is 2x.

b One of the side lengths of rectangle B is x.

c One of the side lengths of rectangle C is 2x + 3.

3 ygx

=

a Find g when y = 20 and x = 4. b Find g when y = 25 and x = 10.

c Find g when y = 10 and x = 50. d Find y when g = 6 and x = 1.3.

y

y

y

3y

3x

x

x

x

x + 3

x + 3

2y + 1 2y + 1

2y + 1 2y + 1

2t + 1

2t + 1

t + 1t + 1

3y

3y 3y

3y

2m + 1

m + 6

m

p

p

p + 5p + 5

x x

x + 1

8

xx

8

3x

3 3

x x

2x + 1 2x + 1

x



4 In these diagrams, lines are drawn from each square to each circle.

3 squares 4 squares 3 squares

2 circles 2 circles 3 circles

6 lines 8 lines 9 lines

a i In another diagram, there are 5 squares and 2 circles.

How many lines do you predict can be drawn?

ii Draw a line diagram for 5 squares and 2 circles.

How many lines have you drawn? Was your prediction in part i correct?

b Write a formula to work out the number of lines.

Use s for the number of squares

c for the number of circles

l for the number of lines.

c i Use your formula to find l when s = 5 and c = 4.

ii Use your formula to find l when s = 10 and c = 6.

iii Use your formula to find s when l = 28 and c = 7.

5 This formula converts a temperature in degrees Celsius (°C) to degrees Fahrenheit (°F).

F = 5

1609 +C

C is the temperature in degrees Celsius, and F is the temperature in degrees Fahrenheit.

a Use the formula to convert 100 °C to degrees Fahrenheit.

b Use the formula to convert 10 °C to degrees Fahrenheit.

c Use the formula to convert 0 °C to degrees Fahrenheit.



A2.2 Homework

1 Write an expression for the output of each function machine.

a x → 6 + → b x → 7 ÷ → c x → 10 × →

d x → 1 − → e x → 4 × → 3 − → f x → 5 ÷ → 2 + →

g x → 5 + → 2 × → h x → 5 × → 2 + → i x → 4 − → 7 ÷ →

2 Draw a function machine to represent each expression.

a 3x + 2 b 3(x + 2) c 2 + 3x

d 2

9−m e 3y + 1 f

31+y

g 5(d + 4) h 4m + 5 i 2k − 7

3 Here are reverse function machines. Write the value of x for each.

a x ← 3 − ← 7 b x ← 6 ÷ ← 8 + ← 10

4 Write the inverse of each operation.

a Add 6 b Multiply by 7 c Divide by 3 d Subtract 2

e – 1 f × 4 g ÷ 6 h – 11

i × 100 j – 5.6 k + 2.1 l ÷ 4.8

5 This function machine represents the equation 5x – 1 = 7.

x → 5 ÷ → 1 − → 7

a Copy and complete the reverse function machine.

x ← ← ← 7

b Use the reverse function machine to solve the equation 5x – 1 = 7.



6 For each equation below i draw a function machine

ii draw the reverse function machine

iii use the reverse function machine to solve the equation

a 3x – 8 = 4 b 7t + 8 = 15 c 3(d + 2) = 9

d 6(m + 5) = 72 e 2p – 4 = 11 f 2(c – 4) = 3

g 5t – 1 = 6 h

915−k = 11 i

312 +y = 5

7 Look at these equations.

5x + 1 = 7

51+x = 7

Sita says that x has the same value in each equation.

a Is she correct?

b Draw function machines to explain your answer.

8 Use algebra to solve these equations. The first one is done for you.

2

510

105

195

915

=

=

=

+=

=−

p

p

p

p

pa

b 2d + 7 = 9 c 6z – 17 = 25 d 5q – 1 = 4

e 2g – 4 = 13 f 4m + 11 = 19 g 3t + 4 = 9

h 4(x – 1) = 24 i 7(p + 3) = 49 j 2

13 −y = 4



A3.1 Homework 1

1 a Write an expression for these instructions.

Start with n, subtract 5 and multiply the answer by 3.

b Write this expression in words. 4

9+x

c Find the value of x

x−−

10)4(3 when x = 8.

2 a Explain the difference between 3n and n + 3.

b Copy and complete.

i 3n → → n

ii n + 3 → → n

3 Copy and complete these function machines. The first one has been done for you.

a 5x – 7 → 7 + ⎯→⎯ x5 5 ÷ → x

b 3x + 4 → ⎯→⎯ → x

c 2(x – 3) → ⎯→⎯ → x

d 7

6x → ⎯→⎯ → x

4 Solve these equations.

a x + 23 = 71 b 9x = 72 c 11x = 22

d 2x + 8 = 32 e 4x + 6 = 11 f 3(x + 5) = 36



5 The perimeter of this triangle is 41 cm.

a Write an equation for the perimeter of the triangle.

Simplify your equation.

b Solve the equation.

c Find the lengths of the sides of the triangle.

6 Catrin, Laila and Zac are playing a game. Catrin has n points. Laila has 5 more points

than Catrin. Zac has half as many points as Laila. They have 40 points altogether.

a Write this information as an equation and simplify it.

b Solve the equation.

c How many points does Zac have?

7 The smallest of four consecutive odd numbers is n.

a The sum of the four consecutive odd numbers is 88.

Write this information as an equation and simplify it.

b Solve the equation to find n, the smallest of the consecutive numbers.

8 This is a pentagon. The angles of a pentagon add up to 540°.

a Write an equation for the total of the angles of this pentagon. Simplify it.

b Solve the equation to find x.

c Find the size of the largest angle in the pentagon.

x + 6 cm x – 1 cm

2x

x + 90°

3x

2x

3x – 40°

x + 70°



A3.1 Homework 2

1 Explain why a + b = b + a, but a – b is not equal to b – a.

2 If x = m + n, which of the following are always true?

m = x – n n = mx n = x – m n = m – x

3 Simplify these expressions.

a 7xy – 4yx b 4mx + 2my – xm c 3 + kt + 5tk

4 Expand the brackets in these expressions. Simplify where possible.

a 7(x + 2y + 3) b 4(2m – 3) + 5m c 5(a + 2b) – 2a + b d 2(x + 4) + 3(5 + 3x)

5 This regular hexagon has sides of length 2a + 3b.

a Write an expression for the perimeter. Use brackets.

b Multiply out the brackets.

6 Solve these equations by expanding the brackets first.

a 7(c – 3) = 28 b 5x + 3(x + 1) = 35

c 3(2y – 1) + 2(3y + 4) = 17 d 6 + 3 (x + 4) = 24

7 Look at these expressions. 67 −x 42 +x

a What value of x makes the two expressions equal? Show your method.

b What value of x makes the first expression three times as big as the second expression?

Show your method.

8 In the diagram, the value in each square is

found by adding the values in the circles on

either side.

a Write and solve an equation to find n.

b Copy the diagram.

Find the two missing numbers.

2a + 3b

2a + 3b2a + 3b

2a + 3b

2a + 3b

2a + 3b



A3.2 Homework

1 y = 3x – 2. Copy and complete this mapping diagram for the input numbers 2, 3 and 4.

2 Draw mapping diagrams like the one in question 1 for each of these functions.

Use values of x and y from 0 to 10.

a y = 2x – 1 b y = 2(x − 1) c y = x + 2 d y = 13 − x

3 a Which of these labels could match the partly completed mapping diagram?

b The correct function also maps 6 to 9. Which is the correct label?

4 This simple mapping diagram uses values of x from –3 to 4.

What function does the mapping represent?

5 Draw simple mapping diagrams, like those in question 4, for these functions.

Use x values from –3 to 4.

a y = 3(x – 2) b y = 5x – 1 c y = 2x + 4

x → 2x – 3 x → 3x – 7 x → 10 – x x → x + 1

x

−3−2−1

01234

y

0.51 1.52 2.53 3.54



A4.1 Homework 1

1 In the diagram, A and C are opposite vertices

of a rectangle ABCD. AB is horizontal.

Write the equation of the line through these

pairs of vertices.

a A and B

b A and D

c B and C

d C and D

2 Write the coordinates of the point where each pair of lines intersect.

a x = 2 and y = 5 b x = –1 and y = 10

c x = 4 and y = x d y = x and y = 10

e x = 6 and y = x + 1 f y = 17 and y = x – 2

3 Write the equation of each line.

a The line parallel to AB and

passing through (–10, 7).

b The line parallel to BC and

passing through (14, –9).

c The line parallel to AC and

passing through:

i (0, 2)

ii (0, –1)

iii (4, 7)

iv (–5, –9)



A4.1 Homework 2

1 a Copy and complete the table for the equation y = 2x + 1

x 0 1 2 3 4

y

b Sketch the graphs of y = 2x + 1, x = 4 and y = 5 on the same diagram.

c Find the coordinates of the points of intersection of each pair of lines.

i y = 2x + 1 and x = 4 ii x = 4 and y = 5 iii y = 2x + 1 and y = 5

2 a Copy and complete the table for the equation y = 2x – 3.

x 0 1 2 3 4

y –3

b Draw the line y = 2x – 3.

c i Write the coordinates of the point where the line crosses the x-axis.

ii Write the coordinates of the point where the line crosses the y-axis.

3 a Copy and complete the table for the equation y = 3x – 2.

x 0 1 2 3

y

b Plot the values from your table as coordinates on

a copy of the axes.

c Draw and label the lines y = 3x – 2 and y = 6 – x.

d Write down the coordinates of the point where

the lines cross.



A4.2 Homework

1 You can use this graph to work out the cost of a length of carpet.

a Find the cost of each length of carpet to the nearest pound.

i 6.5 m ii 5 m iii 2.5 m iv 7.1 m

b What length of carpet, to the nearest 0.1 m, can be bought for each price.

i £50 ii £20 iii £100 iv £72

2 a Copy and complete the table for y = 3x – 5.

x 0 1 2 3 4

y

Plot the values from your table as coordinates.

Draw the line y = 3x – 5.

b Use your graph to solve these equations.

i 3x – 5 = 1 ii 3x – 5 = 7 iii 3x – 5 = 4

iv 3x – 5 = 2.5 v 3x – 5 = –2 vi 3x – 5 = –3.5

c Copy and complete these steps to solve the equation 3x – 4.5 = –3.

3x – 4.5 = –3

3x – 5 =

x =



A5.1 Homework 1

1 This rectangle is 2a wide and 3b long.

Write a simplified expression for

a the area b the perimeter

2 a Look at these three cards. You can see two of the expressions. The third is hidden.

The mean of the three expressions is 5x. What is the hidden expression?

b Write a set of three expressions that has a mean value of 3x.

c

What is the mean value of these three expressions? Show your working.

Write your expression as simply as possible.

3 A teacher has a large pile of cards.

An expression for the total number of cards is 4n + 10.

a The teacher puts the cards into two piles. The number of cards in the first pile is 3n + 7.

Write an expression to show the number of cards in the second pile.

b The teacher uses all the cards to make two equal piles.

Write an expression to show the number of cards in each pile.

7x + 9 5x – 7 3x + 1

5x 5x – 7

3b

2a



4 This trapezium is made from two triangles and

a rectangle.

a Write an expression for length c using a and b.

b Write expressions for these.

i the area of the rectangle

ii the area of one triangle

iii the total area of the trapezium

5 a Write an expression x in terms of b.

b Write an expression y in terms of a.

Write your expressions as simply as possible.

6 The lowest of four consecutive even numbers is n.

a Write down, in terms of n, an expression for the second lowest even number.

b Write an expression for the sum of the four consecutive even numbers and simplify it.

c Find an expression for the number midway between the highest and the lowest

consecutive even numbers.

7 In this diagram, P has coordinates (n + 2, 3n)

a P is mapped to Q by a translation 3 right.

Find the coordinates of Q.

b P is mapped to R by a translation 5 right and

2 down. Find the coordinates of R.

c P is mapped to T by a reflection in the y-axis.

Find the coordinates of T.

8 A is the point (2m + 1, 5n – 3) and B is the point (6m – 5, 9n + 11).

Find the coordinates of the point midway between A and B.

4a + 3

y

5b − 3

2b + 1 x

7a + 5

b b

h

a

c



A5.1 Homework 2

1 Three equilateral triangles are drawn in the corners of a bigger

equilateral triangle forming the shaded regular hexagon.

The large triangle has side length a and each small triangle has

side length b.

Write a formula for P, the perimeter of the hexagon, in terms of a and b.

2 The cost of a raffle ticket at the school fair is 35p.

A customer buys n raffle tickets and gives the raffle-ticket seller x pounds.

Write a formula for C, the change given in pence.

3 Sacha is arranging square tables in rows for a children’s birthday party.

1 table 2 tables 3 tables

a Copy and complete this table. Number of tables 1 2 3 4 5

Number of children 4 6

b How many children can be seated in a row of 10 tables?

c Find a formula for c, the number of children that can be seated in a row of t tables.

4 Here are some patterns made out of hexagons.


a Pattern 1 has 10 outside edges. How many outside edges are there in Pattern 2?

b How many outside edges are there in Pattern 3?

c How many will there be in Pattern 8?

d Find a formula for the number of outside edges in the nth pattern.

b

a



5 Black and white tiles are arranged to make patterns.


a Draw Pattern 4.

b Copy and complete the table for the number of white tiles.

Pattern numbers 1 2 3 4 5

Number of white tiles 8

c How many white tiles are in Pattern 10?

d Which pattern will contain 40 white tiles?

e Find a formula for the number of white tiles in the nth pattern.

6 a Write the next two terms in this sequence.

3, 10, 17, 24, . . .

b What is the 10th term of the sequence?

c Find a formula for the nth term of the sequence.

7 Write a formula for y in terms of x for each of these function machines.

a x → 3 + → 5 × → y b x → 2 ÷ → 4 − → y

c x → 3 × → 5 − → y d x → 1 − → 5 ÷ → y

8 a Copy and complete this function machine to show the formula y = 3

2−x .

x → → → y

b i Copy and complete this function machine to show the formula y = 7 – 3(x + 2).

x → + → × → 7 + → y

ii Simplify the formula y = 7 – 3(x + 2) as much as possible.

Draw another function machine to show your simplified formula.

It should contain just two operations.



A5.2 Homework 1

1 Solve these equations.

Give your answers as fractions or mixed numbers in their lowest terms.

a 3p + 5 = 30 b 4y + 2 = 5 c 2m – 5 = 4

d 36 – 10q = 27 e 33 = 8t + 7 f 52 = 100 – 20a

2 Solve these equations. Give your answers as decimals.

a 11 + 8x = 23 b 10m + 8 = 21 c 14 = 4n + 5

d 29 – 5q = 22 e 13 = 17 – 5a f 8c – 18 = 20

3 Find x. a

b

4 Write and solve an equation to find the value of a.

a

b

5 The sum of four consecutive multiples of 5 is 130.

The lowest of these numbers is x.

Write an equation and solve it to find x.

6 Peter, Melanie, April and Jack received a total of 38 chocolate eggs.

Jack had one less than Peter.

Peter had five less than Melanie.

April had half as many as Melanie.

How many eggs did each person have?

38° 6a + 5°

115° 8a – 7°

x

4x + 10°

x + 20°

x

2x

6x



A5.2 Homework 2

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31 32 33 34 35

36 37 38 39 40 41 42

1 The highlighted square contains the

numbers 9, 10, 16 and 17.

The sum of these numbers is 52.

Which numbers should the square

contain, so that the sum is 124?

43 44 45 46 47 48 49

n Begin by starting with a square like this

2 Solve these equations

a 2(x + 8) = 26 b 9(x – 3) = 99 c 12(14 – x) = 72

3 Solve these equations by expanding the brackets first.

a 8(x + 7.5) = 84 b 7(p + 5) – 13 = 71 c 47 = 12 + 4(c + 7)

4 Solve these equations

a 5m + 23 = 31 b 6 =

49+t c

8a + 3.5 = 6

5 The nth term of a sequence is 4

73 +n .

a Which term has value 16?

b How many terms have a value of less than 100?

c Show that there isn’t a term with value 20.



A5.3 Homework

1 This is a graph of Gail’s journey to the shops.

Gail starts by walking from home to the bus stop.

a How far is it to the bus stop from Gail’s house?

b How long does she wait for a bus?

c How long does the bus journey take?

Gail then walks the rest of the way to the shops.

d How long does the total journey from home to the shops take?

e What is the total distance that she walks?

f How far away from Gail’s home are the shops?

Gail gets lift home with a friend.

g How long does her return journey take from the shops to home?

h How long was she out of the house altogether?



2 William throws a ball up into the air and catches it on the way down.

One of these graphs shows the speed of the ball while it is in the air. Which one?

Give a reason for your answer.

3 Water is poured at a constant rate into each of the following beakers.

a Which beaker does each graph below represent? Explain your choice.

b Draw graphs for each of the other beakers.

Label each graph with the letter of the beaker it represents.

i ii iii

Documents

Cambridge Essentials Mathematics Extension 7 A1.1 …essentials.cambridge.org/media/CEMKS3_E7_A1_1_WS_HWS3.pdf · a x + 5 b 3x c 5x – 8 d 13 – 4x e 3(x + 5) f (x – 1)2 g 17