Review: finance and economics, grade 12
Review: finance and economics, grade 12
A bike-hire shop charges 40 ₪ a day, and hires out 60 bikes a day.
For every 2 ₪ rise in the price the shop hires out 2 bikes fewer.
is the number of rises, and the revenue a day is .
Mark the parabola’s vertex on the graph.
Which price a day gives the shop the greatest revenue?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
What is the greatest revenue a day?
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/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A carpentry shop sells lamps at shekels a lamp, and sells lamps a month.
Each lamp costs the shop 20 ₪, and its fixed costs are 600 ₪ a month.
The profit a month is .
Expand the brackets and write the profit in standard form.
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/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
At which price is the profit greatest?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Solve the equation: at which prices does the shop make neither a profit nor a loss?
At which prices does it make a profit?
A bakery bakes cakes () and pies () for Friday’s sale.
A cake takes an hour in the oven, and a pie two hours; the oven has 30 free hours.
A cake needs 3 kg of flour, and a pie 2 kg; the bakery has 54 kg of flour.
The profit on a cake is 30 ₪, and on a pie 40 ₪.
Write the constraints and the objective function.
On the graph, the lines of the two constraints: , that is , and , that is (the dashed one).
Mark the corner points of the feasible region, apart from the origin.
Solve the system of equations: where do the two lines meet?
Work out the profit at each corner point.
How many cakes and how many pies should the bakery bake, and what is the profit?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
On the town map a unit is 100 m.
Branch of a chain of corner shops is at the point , and branch at the point .
What is the straight-line distance between the branches, in map units?
And how many metres is that?
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/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
The chain wants to build a warehouse exactly halfway between the branches.
At which point?
A straight street runs between the branches.
On the graph board, write the street’s equation, and the equation of the street parallel to it through the petrol station .
An avenue whose equation is crosses the street between the branches.
Solve the system of equations: where is the junction?
A factory has 600 workers.
The monthly salary is normally distributed: the mean is 8000 ₪, and the standard deviation 1200 ₪.
What percent of the workers earn between 6800 ₪ and 10,400 ₪?
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How many workers earn more than 10,400 ₪?
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What is the standard score of a worker who earns 9800 ₪?
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The factory gives a grant to the 16% of the workers with the lowest salaries.
Up to which salary is the grant given?
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/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A machine fills one-kilogram bags of sugar.
The weight is normally distributed: the mean is 1000 grams, and the standard deviation 5 grams.
A bag whose weight is more than two standard deviations from the mean leaves the production line.
Between which weights does a bag stay on the line?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
About how many bags out of 4000 leave the line?
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/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A bag weighs 1012 grams.
What is its standard score?
Does it leave the line?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power