Passport to grade C

Add, subtract, multiply and divide integers

• 382+674• 491-378• 23x74• 55212

Add, subtract, multiply and divide integers

• 382+674=1056• 491-378=113• 23x74=1702• 55212=46

Round to significant figures and estimate answers

Round to 1 significant figure• 356• 213• 4587• 35• 684• 12.7

Round to significant figures and estimate answers

Round to 1 significant figure• 356 400 check your answers• 213 200• 4587 5000• 35 40• 684 700• 12.7 10

Round to significant figures and estimate answers

Round to 1 significant figure• 356 400 check your answers• 213 200• 4587 5000• 35 40• 684 700• 12.7 10

Now use your rounded values to estimate answers. Step 1 round to 1 sig fig, step 2 calculate with your rounded values.

Eg 1) 4.6x1.4= 2) 12.3 – 3.5 3) (9.8+4.5)2.88

2.9x3.01=3x3=9

Round to significant figures and estimate answers

Round to 1 significant figure• 356 400 check your answers• 213 200• 4587 5000• 35 40• 684 700• 12.7 10

Now use your rounded values to estimate answers. Step 1 round to 1 sig fig, step 2 calculate with your rounded values.

Eg 1) 4.6x1.4= 5 2) 12.3 – 3.5=6 3) (9.8+4.5)2.88= 5

2.9x3.01=3x3=9

Find HCF and LCM of 2 numbers

Highest Common Factor

Lowest Common Multiple

Find HCF and LCM of 2 numbersHighest Common Factor

Lowest Common Multiple

Test question(a) Write each of the numbers 36 and 80 as a product of prime factors.36 = ...........................................80 = ........................................... [3] (b)(i)Find the least common multiple (LCM) of 36 and 80............................................ [2] (ii)Find the highest common factor (HCF) of 36 and 80............................................ [1]

Find HCF and LCM of 2 numbersHighest Common Factor

Lowest Common Multiple

Test question(a) Write each of the numbers 36 and 80 as a product of prime factors.36 = 2x2x3x3..............................80 = 2x2x2x2x5........................... [3] (b)(i)Find the least common multiple (LCM) of 36 and 80. 720............................. [2] (ii)Find the highest common factor (HCF) of 36 and 80. 4............................... [1]

Calculate the value of:

8

1

4

1

a:12

1 b: 12

2

c: 8

2 d: 8

3

Add, subtract, multiply and divide fractions

7 What is the value of:

5

1

3

2

a:2

1 b: 2

1

c: 15

7 d: 15

1

Add, subtract, multiply and divide fractions

b: 4

d: 8

a: 2

c: 6

8 Find the value of:

4

38

Add, subtract, multiply and divide fractions

b: 24

d: 6

a: 48

c: 12

10 What is the value of:

2

124

Add, subtract, multiply and divide fractions

Calculate percentage increase and decrease

Increase the following rail fares by 10%.

a) £9.20 b) £3.7010% = ………………… 10% = …………………New cost = ……………… New cost =

………………

c) £5.00 d) £9.8110% = ………………… 10% = …………………New cost = ……………… New cost =

………………

Calculate percentage increase and decrease

Increase the following rail fares by 10%.

a) £9.20 b) £3.7010% = 92p………………… 10% =

37p…………………New cost = £10.12…… New cost = £4.07……

c) £5.00 d) £9.8110% = 50p………………… 10% =

98p…………………New cost = £5.50………… New cost = £10.79……

Calculate percentage increase and decrease

decrease the following rail fares by 15%.

a) £9.20 b) £3.7010% = ………………… 10% = …………………5%= 5%=15%= 15%=New cost = ……………… New cost = ………………

c) £5.00 d) £9.8110% = ………………… 10% = …………………5%= 5%=15%= 15%=New cost = ……………… New cost = ………………

Calculate percentage increase and decrease

decrease the following rail fares by 15%.

a) £9.20 b) £3.7010% = 92p 10% = 37p5%= 46p 5%= 18.5p15%= £1.38 15%= 55.5pNew cost = £7.82 New cost =£3.15

c) £5.00 d) £9.8110% = 50p 10% = 98.1p5%= 25p 5%=49.05p15%= 75p 15%= £1.47New cost = £4.25 New cost = £8.34

Calculate the square root and cube root of a number

Match these values to their square roots49, 1, 81, 36, 25, 16, 41, 4, 7, 2, 6, 9, 5

Match these numbers to their cube roots125, 216, 1, 27, 64, 81, 5, 4, 2, 6, 3

Add, subtract, multiply and divide decimals

2.1+3.8=8.12-5.9=1.2x4=4.81.2=

Add, subtract, multiply and divide decimals

2.1+3.8=8.12-5.9=1.2x4=4.81.2=Now use your calculator to check

Add, subtract, multiply and divide decimals

2.1+3.8=8.12-5.9=1.2x4=4.81.2=Now use your calculator to check

Exam question. How many bottles of water at £1.27 can Amy buy with a £5 note? How much change will she have?

Write the prime factor decomposition of a number

• Also called the product of primes• 300• 600• 120• 60• 55• 550 check your results by multiplying the

together, you should get what you started with

Work with indices

Convert between fractions decimals and percentages

Fraction Decimal Percentage

= 0·9 = %

= = 3%

= 0·53 = 53%

Share an amount in a ratio4. Alan, Brendan and Chloe shared £768 in the ratio 5 : 4 : 3.

How much did each receive?Alan £ ....................................Brendan £ ....................................Chloe £ ....................................[3]

5. (a) A box contains 120 cubes.Some of the cubes are black, the rest are white.The black cubes and white cubes are in the ratio 2 : 3.Calculate the number of black cubes and the number of white cubes in the box.

black cubes ................................white cubes ................................[3]

(b) Another box also contains black cubes and white cubes in the ratio 2 : 3.There are 160 black cubes.How many white cubes are there?...................................[2]

Find the perimeter and area of a square, rectangle and triangle

Area and perimeter

• Perry the ant walks around the edge of a shape, when you calculate perimeter make sure you have used all the edges

• There are no formulas you have to know for perimeter except the circles one.

Area is the space a shape covers and we find it by multiplying

4cm

4.5cm

3.8cm

8cm

7cm

18mm 12cm

7cm

5cm

10cm

4cm

6cm

9cm

Area is the space a shape covers and we find it by multiplying

4cm

4.5cm

3.8cm

8cm

7cm

18mm 12cm

7cm

5cm

10cm

4cm

6cm

9cm

Factorise an expression

ExampleFactorise 36-3x

= 3(12-x)Now write and answer 5 of your own green

questions showing you can factorise an expression

Set up and solve a linear equationConstruct, and then solve, an equation for each situation given below: 1. Think of a number. Subtract 9. The result is 25. What is the number? 2. Think of a number. Multiply it by 5, then add 12. The result is 52. What is the

number?

3. A number is trebled and added to 11. The result is 50. What is the number? 4. The three angles in a triangle are c, c+20 and c+40. Find c.

5. A number added to twice the number gives an answer of 24. What is the number? 6. Three consecutive numbers added together make 48. What are they?

Round to decimal places

Round these numbers to one decimal place(a) 4.26 (b) 7.31 (c) 5.4377(d) 2.1804 (e) 12.5052 (f) 1.65(g) 0.95 (h) 4.352 (i) 7.857(j) 10.8501

Round to decimal places

Round these numbers to one decimal place(a)4.26 4.3 (b)7.31 7.3 (c)5.4377 5.4(d)2.1804 2.2 (e)12.5052 12.5 (f)1.65 1.7(g)0.95 1.0 (h)4.352 4.4 (i)7.857 7.9(j)10.8501 10.9Explain (g) to a friend

Solve an inequality

3x<18x>7 represent your solution on a number line2x+1≥11

Plot a quadratic graphFind the area of a compound shape

Calculate the area and circumference of a circle

• Write down the formulae you need• Calculate the area and perimeter of each shape

14cm3.5cm

9cm

You now have half a passport…

• Work down the 4th column and write green questions to convince your teacher you can do the topics in this column.

Expand brackets

• Remember there is no equals sign so you do not have to find an answer, just change the way it looks, in this case make it not have brackets.

• 3(a+2)• 7(b-4)• 3x(x+2)• 5x(y-4)

Expand brackets

• Remember there is no equals sign so you do not have to find an answer, just change the way it looks, in this case make it not have brackets.

• 3(a+2) 3a+6• 7(b-4) 7b-28• 3x(x+2) 3x2+6x• 5x(2y-4) 10xy-20x

Use trial and improvement

• Work to 1 decimal placea) x³+17=54b) 2x³+5x=200c) 5x²+60=120d) x³+6=20

Use trial and improvement

• Work to 1 decimal placea) X³+17=54 x=3.3b) 2x³+5x=200 x=4.5c) 5x²+60=120 x=3.5d) X³+6=20 x= 2.4

Write and use nth trem

• Use these nth terms to generate the next 5 terms of the sequences, the first one has been done for you

a)3n+1 4, _, _, _, _, …..b)2n-3 -1, _, _, _, _, …..c) n+10 11, _, _, _, _......d)n² 1, _, _, _, _, …..

Write and use nth trem

• Use these nth terms to generate the next 5 terms of the sequences, the first one has been done for you

a)3n+1 4, 7, 10, 13, 16, …..b)2n-3 -1, 1, 3, 5, 7, …..c) n+10 11, 12, 13, 15, 15......d)n² 1, 4, 9, 16, 25, …..

Now find the nth terms of these sequences

a) 4, 6, 8, 10, …..b) 3, 6, 9, 12, ….c) 1, 5, 9, 13, …..d) 10, 7, 4, …..e) 20, 24, 28, …..

Now find the nth terms of these sequences

a) 4, 6, 8, 10, ….. 2n+2b) 3, 6, 9, 12, …. 3nc) 1, 5, 9, 13, ….. 4n-3d) 10, 7, 4, ….. 13-3ne) 20, 24, 28, ….. 4n+16

Plot linear graphs

• And use words like gradient and intercept

Plot these points

Plot these points

Plot these points

Plot these points

Plot these points

Plot these points

Plot these points

Which point could sit on either line?

Plot these points

Plot these points

Name your line

Plot these points

Girls name a line to the left of your line

Plot these points

Boys name a line above your line

Plot linear graphs

Complete the table and plot y=4x+1

x -1 0 1 2

y 1 9

Percentages without a calculator

£50

10%

35%25%

60%

20%

100%1%

3%

98%

Percentages without a calculator

£50

10%

35%25%

60%

20%

100%1%

3%

98%£5

£0.50 £50

£10

£30£12.50

£17.50

£1.50

£49

URGENT NEWS FLASH

URGENT NEWS FLASH

Maths exam markers today have announced

that probability questions must be

answered as a fraction

Maths exam markers today have announced

that probability questions must be

answered as a fraction

URGENT NEWS FLASH

Or a decimal....Or a decimal....

URGENT NEWS FLASH

Or a percentage....Or a percentage....

URGENT NEWS FLASH

Or as a word if they give you words to

choose from....

Or as a word if they give you words to

choose from....

URGENT NEWS FLASH

But neverBut never

URGENT NEWS FLASH

Ever....Ever....

URGENT NEWS FLASH

EVER......EVER......

URGENT NEWS FLASH

As a ratioAs a ratio

Write a probability..

• With a fraction• Or a decimal• Or a percentage

Volume of a prism

• What is the surface area of a cuboid with dimensions 10 cm, 8 cm and 5 cm.

5 cm

10 cm8 cm

Find the volume and surface area of this prism

4cm

5cm

14cm

Find the volume of this prism

2m

1.5m