# Ratios, patterns and relations Task

**All Calculations must be shown.**

**1. **Work out these Ratios in simple whole numbers

a) 35% wool, 65% rayon Wool_rayon=?

b) ¾ cup butter, 1 ¾ cups flour Butter_Flour=?

c) 2.5 cups milk, 4.5 cups flour Milk_flour=?

d) 150ml cordial to 1 liter water Cordial_water=?

**2. **

a) “Dry cement mix used for making concrete is made by mixing sand, cement and gravel in the ratio 1:3:4. To make a total volume of 120 shovels of dry mix. How much of each ingredient should be used?

b) If you got $37.50 for 5 hours work, how much do you get for 17 hours work?

**3. **

a) We have a map scale 1:32000. How many kilometres is represented by 1cm on the map?

b) Change the scale 1.5cm to 450meters into a ratio.

**4. ** a)The drug erythromycin comes in ampoules of 100mg per 2mL.

(i) An adult patient requires 150mg. What volume of drug is needed?

(ii) A child’s dosage is 5mg per kg weight. Tanya weighs 22kg. How many millileters of dosage will she require?

b) The drug tetracycline comes in 250mg and 150mg tablets. A patient requires 550mg of tetracycline. How many whole tablets of each strength will be needed?

**5.** 250mL cleaner is made up to a 4 liter solution.

a) What volume of water was added?

b) What is the percent concentration of the solution?

**6.**

a) What is the gear ratio of these gears?

b) The large gear rotates at 60rpm. What is the speed of the small gear?

**7.** What is the mechanical advantage of the following situations?

a) A 1.8meter crowbar opening a crate. The distance to the edge of the crate is 1.6m

b) A gangplank of 14meters rises 1.2meters.

**8.** Gerry uses a 3meter plank to roll barrels up to a shelf 1.5meters above the ground.

a) What is the mechanical advantage of using the plank?

b) What fraction of effort does he make?

c) He apples 10 Newton of force. What force is applied to shift the barrels?

**9.** For the design below:

a) Draw the next three shapes in the sequence.

b) Draw up a table for the first ten shapes in the sequence, and the number of matches required to complete the shape.

c) Determine the word relationship for the sequence of outputs.

d) Determine the formula which would allow you to find the number of matches in any shape in the sequence.

e) Draw a graph of the relationship.

**10. **For the design below:

a) Draw the next three shapes in the sequence.

b) Draw up a table for the first ten shapes in the sequence, and the number of matches required to complete the shape.

c) Determine the word relationship for the sequence of outputs.

d) Determine the formula which would allow you to find the number of matches in any shape in the sequence.

e) Draw a graph of the relationship.

**11. **A student banks $200 when she starts secondary College in Grade 7. In Grade 8 she banks $250,$300 in Grade 9, and so on. She is at school for 6 years.

a) Determine a formula relating the amount deposited during a year (200,250,…) to how many years they have been saving(1,2,…).

Because the deposits are increasing, the formula for the bank balance is more complex and is not a linear relationship. Answer the following using a table.

b) What is the total amount she has banked by the time she finishes after 6 years?

c) If she continued banking in this manner after she leaves school, how many years(from the start) will it take for her balance to exceed $15,000?

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