Progress Check Calc Paper Practice

Progress Check

Calc Paper Practice

By Simon Homer

Finding a % of an Amount

​Change the % to a decimal and multiply by the amount

Think of every 1% as 1p. Then write it in money format as £ & p.

For example, 17% is 17p which in money format is £0.17.

Remove the £ and you're left with 0.17.

Examples ..

• 17% of 176 becomes 0.17 x 176 = 29.92​

• 12% of 864 becomes 0.12 x 864 = 103.68

• 4% of 500 becomes 0.04 x 500 = 20

Multiple Choice

Calculate 32% of 750m

• 24m

• 2.4m

• 2400m

• 240m

Multiple Choice

Find 13% of £245

• £31.85

• £33.32

• £31.75

• £42.35

Multiple Choice

Find 27% of £320

• £86.40

• £84.60

• £86.60

• £84.40

Multiple Choice

Find 81% of £64

• £51.84

• £58.14

• £54.18

• £58.18

Multiple Choice

Find 6% of £244

• £14.64

• £16.64

• £14.46

• £16.46

Rounding to Decimal Places

​5 or more let it soar, 4 or less let it rest!

Find the target number, look at the number next to it and if it's 5 or more, increase the target number by 1. If it's 4 or less, leaave the target number as it is and remove all number after it.

Examples ...

• 125.678 rounded to 2 decimal places is 125.68

• ​1.0781 rounded to 3 decimal places is 1.078

• 14.35298 rounded to 1 decimal place is 14.4​

Multiple Choice

What is 3.4550 rounded to 1 decimal place?

• 3.4
• 3.5
• 3
• 3.46

Multiple Choice

Round 134.67398 to 2 decimal places

• 134.67

• 134.700

• 134.6

• 134.68

Multiple Choice

Round 46.7863 to 3 decimal places

• 46.768

• 46.786

• 46.358

• 46786

Multiple Choice

Round 15.34792 to 3 decimal places

• 15.347

• 15.348

• 16.356

• 16.348

Changing Fractions to Decimals

​Divide the top number by the bottom number.

If there is a whole number, leave as is and just convert the fraction​

Divide the top number (numerator) by the bottom number (denominator).

Leave any whole numbers alone (2 & 3/4 for example)

​Examples ....

• 3/5 is 0.6

• 11/16 is 0.6875

• 200/57 is 3.508771

• 3 & 2/7 is 3.28571

Multiple Choice

Convert $$3\frac{4}{10}$$ into decimal.

• 3.4

• 3.04

• 3.004

Multiple Choice

1/8 as a decimal:

• .13

• .785

• .125

Multiple Choice

Convert 2/25 from a fraction to a decimal

• 2.25

• .08

• .8

Multiple Choice

Convert 13/20 to a decimal.

• .55

• .56

• .65

Reverse Percentages

​When we know the new amount but we're asked to calculate what the original amount was before a % increase/decrease was applied​

1. Assume the Original amount is 100%

2. Decide if the new amount is the result of a % increase or decrease

3. If a % increase, add to 100%, if a % decrease, take away from 100%

4. Change % to a decimal and divide new amount by this decimal

Example, a table now costs £ 270 including 20% VAT; what did it cost befor VAT was added?

1. 100% + 20% (VAT increase) = 120% which is 1.2 as a decimal

2. £270 ÷ 1.2 = £225 (so the pre VAT price was £225)

Multiple Choice

2) After fuel prices rose by 15%, a family’s annual heating bill was £1654. What would the bill have been without the price increase?

• £1438.26

• £1945.88

• £248.10

• £1500

Multiple Choice

3) The cost of a holiday, including VAT at 20% is £540. What is the pre-VAT price?

• £648

• £450

• £675

• £432.80

Multiple Choice

7) Due to falling orders a company reduces its workforce by 12% to 792. What was the original number of employees?

• 95

• 887

• 900

• 707

Multiple Choice

A jacket is in a sale with 20% off and now costs £220. What was the original cost?

• £275

• £176

• £264

• £183.33

Simplifying Fractions

​To simplify a fraction we need to find a number that divides into both the top and bottom of the fraction.​

For example, in a school of 820 children, 400 are boys; what fraction are girls?

• There are 420 girls out of 820 children, so our fraction is 420/820

• We can si​mplify this fraction by dividing both top and bottom by the same number. We can start by dividing them both by 2

• 420/820 > ​210/410 > 105/205; now divide by 5 to get 21/41

• ​No number will divide into both 21 & 41 so we stop at 21/41

Simplifying Fractions

​Another option is to use a calculator to divide the top by the bottom, to get a decimal (and then convert back to a fraction)​

For example, 27 out of 135 students got an A in their test; what fraction is this in it's simplest form

• Use a calculator to divide 27 by 135 = 0.2

• 0.2 is 2 tenths which as a fraction is 2/10

• 2/10 can be simplif​ied to 1/5

Multiple Choice

Simplify  9/45

• 3/15
• 5
• 4
• 1/5

Multiple Choice

If there are 12 red marbles, 16 green marbles, and 22 Blue marbles, what fraction (in its simplest form) of all the marbles are Red?

• 6/25

• 8/25

• 11/25

Multiple Choice

A politician got 486 votes out of a total of 1620? What fraction (in its simplest form) of the overall votes did they get?

• 0.3

• 486/1620

• 243/810

• 3/10

Changing a Fraction to a %

​To change a fraction to a %, divide the top number of the fraction by the bottom number, and multiply by 100.​

For example, a Gardener wants to reduce the width of their patio from 5m to 2.7m, what % reduction will this be?

• 5m take away 2.7m mea​ns the patio is being reduced by 2.3m

• ​So, 2.3m out of 5m as a fraction will be 2.3/5

• ​Change to a decimal; 2.3 ÷ 5 = 0.46

• Change to a percentage 0.46 x 100 = 46%

Multiple Choice

If you receive a 45/50 on a test , what is your percentage?

• 45%
• 80%
• 90%
• 70%

Multiple Choice

Convert the fraction 20/23 into a Percentage rounding to the nearest whole number

• 86.9%
• 86%
• 86.16%
• 87%

Using Scale to work out distances

​A scale of 1:50 means everything in Real Life is 50 times bigger than on the map/plan. etc​

For example, on an Architect's drawing the scale is 1:1200 and a building is 15cm long and 22cm wide, how long/wide (in metres) is it in real life?

• So, the real building will be 1200 bigger than the drawing dimensions

• ​15cm long on plan will be 15cm x 1200 in real life = 18,000cm

• There are 100cm in a metre so 18,000 ÷​ 100 = 180m

• 22cm wide on the plan will be 22cm x 1200​ in real life = 26400cm

• There are 100cm in a metre so 26400 ​÷​ 100 = 264m

Multiple Choice

Scale is 1cm = 8km. Hatboro and Smithville are 24cm apart on the map, what is the actual distance between the 2 cities?

• 87 km
• 216 km 
• 33 km
• 192 km

Multiple Choice

From Denver to Chicago = 3 in. If the scale is 1 in = 300 miles, find the actual distance.

• 300 miles
• 1000 miles
• 900 miles
• 600 miles

Multiple Choice

Scale: 1in.=7ft. The actual width of the backyard is 49 ft, how wide is it in the drawing?

• 14 in 
• 7 in
• 42 in
• 56 in

Multiple Choice

A model of a house was built using the scale 5 in:25 ft. If a window in the model is 1.5 in. wide, how wide is the actual window?

• 90 ft
• 7.5 ft 
• 4.5 ft
• 45 in

Mass (Weight) = Density x Volume​

Density = Mass ÷ Volume

Volume = Mass ​ ÷​ Density

​

For example, if ​the volume of a brick is 0.004m³, and the density of the brick is 800kg per m³, what is the weight of the brick?

M = (D) Density x (V) Volume​

M = 800 x 0.004 = 3.2 Kg

​

​

​

​Density/Mass/Volume

​

Multiple Choice

The mass of an object is 30 g.  The volume is 5 mL.  What is the density of this object?

• 6 g/cm
• 6 g/mL
• 6

Multiple Choice

You are given the following information: mass = 48 g; volume = 24 cm^3. What is the density of this substance? 

• 2 g/cm³
• 1,152 g/cm³
• 0.5 g/cm³
• 72 g/cm³

Multiple Choice

If a block of wood has a density of 0.6 g/cm³ and a mass of 120 g, what is its volume?

• 200 cm³
• 0.005 cm³
• 200.0 ml
• 72 ml

Multiple Choice

Find the density of a 2 cm x 2 cm x 2 cm cube with a mass of 64 g.  (Hint: find the volume first!)

• 6 cm³
• 12 g/cm³
• 128 g/cm³
• 8  g/cm³

Sharing Ratio Parts

Add up the Ratio parts and divide into the amount.

This gives you the value of 1 part of the ratio.

Multiply each Ratio part by above total.​

For example, Bob, Sue and Ahmed agree to share the bill for a meal in the ratio 2:4:1. The total meal cost is £84, how much does Sue pay?

• 2 + 4 + 1 = 7

• 84 ÷ 7 = 12 (so each ratio part is worth £12)

• ​So, as Sue has 4 parts of the ratio, she will pay 4 x £12 = £48

Multiple Choice

Share 26 in the ratio 5:8

• 10:16

• 16:10

• 15:11

• 11:15

Multiple Choice

Share 40 in the ratio 3:4:1

• 2:15:20

• 20:15:5

• 15:20:5

• 5:20:15

Multiple Choice

Share 72 candles in the ratio 3 : 1 : 4

• 27 : 9 : 36 candles

• 3 : 1 : 4 candles

• 36 : 9 : 27 candles

• 9 : 27 : 36 candles

Converting between Metric Units

​10 mm = 1cm 100cm = 1m 1000m = 1km

1000g = 1Kg 1000ml = 1L​

For example, if I have 8 lots of 750g, how many Kg do I have?

• 8 x 750g = 6000g 1000g in a Kg so 6000g = 6Kg (6000 ÷ 1000)

For example, how many km is 15000cm?

• We need to go from cm to metres, and then metres to km

• 100 cm in a metre, so 15000cm ÷ 100 = 150m

• 1000m in a km, so 150m ÷ 1000 = 0.15km

Multiple Choice

Convert 6 m to cm

• 60 cm

• 600 cm

• 6000 cm

• 0.6 cm

Multiple Choice

Convert 210 mm to cm

• 2.1 cm

• 21 cm

• 210 cm

• 2100 cm

Multiple Choice

Convert 5.3 km to m

• 53 m

• 530 m

• 5300 m

• 53000 m

Multiple Choice

Convert 0.84 m to cm

• 0.084 cm

• 0.0084 cm

• 8.4 cm

• 84 cm

Multiple Choice

Convert 3000g to kg

• 0.3 kg

• 3 kg

• 30 kg

• 300 kg

Calculating with Area of Shapes

​To work out out how much one shape will fit into another we need to work out the Area for each one and then Divide​

For example, if a floor has an area of 826m², how many square tiles measuring 60cm will be needed to cover it?

• We need to work out the Area of the tile in metres (as the floor area is in metres); Area of a square is L x W

• 60cm is 0.6m so Area is 0.6 x 0.6 = 0.36m²

• Then we have to divide floor area by area of a tile

• 826 ÷ 0.36 = 2,294.4444 so we will need 2295 tiles

​

Multiple Choice

Pedro wants to scatter wildflower seeds on a plot of land that measures 25 ft by 30 ft.  How much space will he cover?

• 750 ft
• 110 ft
• 750 sq ft
• 375 sq ft

Multiple Choice

Alicia's garden is 50 square feet. Inside of her garden she plants a section of tomatoes that is 3 feet by 4 feet. How much more space does she have left in her garden to plant other crops?

• 62 square feet

• 38 square feet

• 12 square feet

• 43 square feet

Multiple Choice

Bob wants to wallpaper a wall that is 5m long and 3m wide; each roll of wallpaper is 200cm long and 80cm wide. How many rolls of wallpaper does he need to buy?

• 7 Rolls

• 8 Rolls

• 9 Rolls

• 10 Rolls

Make sure your line of best fit goes through the middle of the plotted Xs (roughly same either side of the line).

For example, using the diagram opposite, we can estimate sales on a day where the temp is 13° will be about $200

​

​Scatter Diagrams Line of Best Fit

​

Multiple Choice

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.  Use the trend line to predict how many chapters would be in a book with 140 pages. 

• 12 chapters
• 19 chapters
• 14 chapters
• 21 chapters

Multiple Choice

Mrs. Collins made a scatterplot to show the relationship between the number of absences and a student’s final exam score. Based on this scatterplot, a student with 12 absences should get approximately what score on the final exam?

• 60

• 92

• 70

• 76

Multiple Choice

Is this line an accurate line estimate of best fit for the data?

• Yes

• No

Multiply each item by the frequency.

​In the table opposite we would get ...

• 11 x 3 = 33

• 12 x 5 = 60

• 13 x 2 = 26

• 14 x 1 = 14

• 15 x 4 = 60​

​Then total the above and divide by frequency total; 193 ÷ 15 = 12.87 (to 2dp)

Mean average from Frequency Table

​

Multiple Choice

Find the mean age. You may want to write out the table with an extra column.

• 2.6

• 6.5

• 5.7

• 5.5

Multiple Choice

Find the mean number of phones. You may want to copy out the table with an extra column.

• 2.56

• 2.3

• 1.5

• 2.2

Multiple Choice

Find the mean number of pets. You may need to copy out the table with an extra column.

• 0.87

• 1.55

• 1.68

• 1.45