Higher-Dec.pdf - Corbettmaths

1st December Higher 5-a-day

Calculate the force if the pressure is 500N/m² and the area is 20m²

Calculate an estimate of the mean.

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Simplify

�4x9y

÷6x7

Simplify

�2x5

×3x7

Using a ruler and compasses, construct the perpendicular to DE that passes through the point F.

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2nd December Higher 5-a-day

Describe fully the single transformation that maps shape B onto shape A.

The length of each diagonal is 12cm.Find the area of the square.

Find x and y

Solve, giving your answers to one decimal place.

�2x2 + 5x − 10 = 0

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Shown is a square

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3rd December Higher 5-a-day

Calculate the volume.Give your answer in terms of π

A shop is having a sale.There is a 30% discount on all TVs and 20% discount on all DVD players.

In the sale, Wilson buys a TV for £224 and a DVD player for £48.

How much would the TV and DVD player cost normally?

A radioactive substance decays with time.The mass of the substance reduces by 9% each year.

How many years will it take for 800kg of the substance to decay to a mass of less than 100kg?

Work out how many members are between 25 and 50.

Calculate an estimate of the number of members who are between 35 and 70.

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The histogram shows the distribution of the ages of the members of a cricket club.30 members are between 80 and 110.

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4th December Higher 5-a-day

Convert 4.5m² into mm²

Give your answer in standard form.

Find x

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Use your graph to find the solutions to �x2 − 3x − 4 = 2

Draw the graph �y = x2 − 3x − 4

Solve: � �x + 3y = 114x − 7y = 6

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A fish tank sprung a leak and loses 45% of its water.There is now 363 litres of water in the fish tank.

How much water was in the fish tank before the leak?

The cost of buying a coffee and a tea in a cafe is £4The cost of buying a coffee and three teas in a cafe is £7Work out the cost of buying a coffee and the cost of buying a tea.

Enlarge the triangle by scale factor −2, using centre of enlargement (−2, 6)

Work out �1634

Henry has five number cards.

�He takes two cards at random.

Work out the probability that the cards have a sum of 4.

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Estimate the median volume.

Estimate the interquartile range of the volumes.

Two clay models of the Statue of Liberty are mathematically similar.The smaller model has a height of 15cm.The larger model has a height of 20cm.The smaller model weighs 108g.Work out the weight of the larger model.

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Work out

�335

× 127

Work out

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Give your answer in standard form



Find the volume of this hemisphere

Find x and y.

Expand and simplify

�(y − 8)2

On the grid, draw the graph of

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Complete the table of values for

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Expand and simplify

�(5w + 1)(3w + 2)

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There are red, green and white sweets in a bag, in the ratio 7:4:1.

A quarter of the green sweets are removed from the bag.The green sweets that have been removed are replaced with an equal number of red and white sweets.

What is the ratio of red sweets to green sweets to white sweets now?

Gordon is building a wardrobe.

The wood costs 30% more than he had estimated.He needs 40% more wood than he had estimated.

How much more than his original estimate does the the material for the wardrobe cost?

Write down the vector for

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Write down the vector for

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Simplify � 175

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In the diagram OBDE and OAFG are parallelograms.

B is the midpoint of OG.A is the midpoint of OE.



Find x

Work out the interquartile range

A metal cylinder that has diameter 20cm and height 50cm is melted and used to create spheres of radius 4cm.

How many complete spheres can be created?

Simplify

�5x2 − 13x − 6

x2 − 9

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c = 5.34 correct to 3 significant figures.

Work out the upper bound for w.

w =c

4

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Calculate angle y

The pressure of a tyre is 34 pounds per square inch.

Given 1 pound = 0.4536 kilograms 1 inch = 2.54 centimetres

Work out the pressure in grams per square centimetre.

Kevin writes down a 5 digit number.

- It is less than 80,000.- It is a multiple of 5.- The middle digit is a prime number.

How many different possible numbers could Kevin have written down?

On the grid, draw the graph of � for the values of x −2 ≤ x ≤ 2

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y = − x3 − x + 2

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Find x

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Write down the coordinates of the minimum point of �y = x2 − 2x + 1

Expand and simplify

�(x − 3)3

Write down the equation of the mirror line of �y = x2 − 2x + 1

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Draw the graph �y = x2 − 2x + 1



A shop sells a “meal deal” that contains a sandwich, a drink and a snack.

There are 10 different sandwiches.There are 12 different drinks.There are 5 different snacks.

How many different “meal deals” could be bought?

The students in Year 11 were surveyed.

41% had been to France61% had been to Ireland84% had been to either Ireland or France or both countries.

Show this information on a Venn diagram.

What percentage of the students that had been to France, have also visited been to Ireland?

Factorise �8x2 − 14x + 5

Write down the equation of the line that is perpendicular to � and passes through (0, 8).

y = 6x + 1

Factorise �4y2 − 1



Find x

Show that an increase of 10% followed by an increase of 10% is equivalent to a 21% increase overall.

Show � on the Venn diagram.A′�∪ B

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Simplify �( 2)4

Shown is a sketch of �

Find the equation of the mirror line.

y = x2 − 12x + 35

Simplify �9 2 × 3 5

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Write down the exact value of Sin 180° Write down the exact value of Tan 45°

Mrs Hampton is potting plants.She is using two mathematically similar pots, the smaller is 10cm tall and the larger 14cm tall.

She has two bags of soil, each containing 30 litres of soil.

With the first bag, Mrs Hampton fills 20 small pots using all of the soil in the bag.

Calculate the height of the isosceles triangle.

Write as a single power of 5.

�58 × 57

54

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How many large pots can be filled completely using the second bag of soil?



Find x

The volume of the pyramid is 126cm³Find the height.

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Simplify

�e8

×d8

Simplify

�3a4

÷6c7

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Complete the table and histogram

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Write 16cm³ in mm³

A shape is made from a cube and a pyramid.Calculate the volume.

What is the range?

What is the interquartile range?�

Write down a vector for �

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Write down a vector for �

�ABCDEF and GHIJKL are regular hexagons with centre O.GHIJKL is an enlargement of ABCDEF, with scale factor 2.



Find angle CEF

The diagram shows a square.Two congruent triangles are shown.

Calculate the area of the shaded region.

Find the coordinates of the point where the linear graphs �and � intersect.

y = 4x + 1y = 6 − 3x

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Factorise

�5y2 + 12y − 9

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Estimate the median mark.

Calculate the volume of the cone.

Convert � to a fraction0.1 ·3 ·9

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Solve

�8(x − 2) − 3(1 − x) ≤ 9(x + 2) + 1

The line passing through (1, p) and (5, 1)

has a gradient of �

Find the value of p.

34



Cuboid A and cuboid B are similar.The surface area of cuboid A is 500cm².Work out the surface area of cuboid B.

The force, F newtons, exerted by a magnet on a metal object is inversely proportional to the square of the distance d cm.

When d = 2 cm, F = 50 N.

Express F in terms of d.

Make w the subject of

5(w − 2a) = 3w + 7

Shown is a tangent to a circle.

Find y and give a reason for your answer.

Shown is triangle RST.Angle SRT is 53°, to the nearest degree.ST is 17cm to the nearest centimetre.Work out the upper bound for the length of RS.

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The students in a class complete a puzzle.The longest time taken was 114 seconds.50% of the students completed the puzzle in under 94 seconds.The range was 52 seconds.The lower quartile was 75 seconds.The interquartile range was 30 seconds

Hannah wants to estimate the number of eels in a lake.She catches and rings 80 eels.She returns the 80 eels to the lake.Hannah then catches 30 eels.Of these 30 eels, 5 are ringed.

Work out an estimate of how many eels live in the lake.

Calculate the area of the triangle.

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Draw a box plot to show this information

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Calculate the perimeter of this sector.

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�2x2 + 7x + 2 = 0



Matt invests some money at 5% compound interest per annum for four years.After four years, Matt has £48620.25 in the bank.

How much did he invest originally?

Two pyramids are mathematically similar.Pyramid A has a surface area of 20cm²Pyramid B has a surface area of 320cm²The height of pyramid A is 2cmWork out the height of pyramid B.

Find y.

Solve

6y² + 17y − 39 = 0

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Solve

�

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23

x − 3y = 7

12

x − 7y = 10

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22nd December Higher 5-a-day

Aoife truncates a number, y to 1 decimal place.

Her result is 3.8

Write down the error interval for y

A tree grows 22% each year.When planted, it is 20cm tall.

How long will it take the tree to grow to at least a height of 5m?

Find the size of y.

Work out the bearing of B from A. Work out the bearing of A from B.

Simplify

�c9

÷5c

Simplify

�8x3y

×y6

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23rd December Higher 5-a-day

If a student passes the final exam or retake, they receive a certificate.

Work out the probability that a student receives a certificate.

The line L passes through the points (−4, 0) and (2, −2)The line M passes through the points (3, 8) and (2, 2)

Are the lines L and M perpendicular?Show your workings

Find the area of ABC.

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A college course consists of 8 weeks of teaching with a final exam at the end of the course

If a student fails the final exam, they have one opportunity to retake the exam.The probability of a student passing thefinal exam is �The probability of a student passing the retake is �

Complete the tree diagram

78

23

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Factorise

�2x2 + x − 1



Each side of a regular hexagon has a side length of 3.2cm to 1 decimal place.

Write down the error interval for the perimeter of the hexagon.

Shown are two mathematically similar cuboids.The volume of cuboid A is 30cm³Find the volume of cuboid B.

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Simplify

�7x2 − 4x − 3

x2 − 1

Simplify

�(16x4)12

Find the length of the hypotenuse. Give your answer as a surd.

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Calculate the surface area of the prism.

Make x the subject

�y =x + 11x − 5

Solve

�3y2 + 4y − 15 = 0

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Find �

f (x) = 1 − cosx

f (60)

Work out the reciprocal of the cube root of �8−2



Find y.

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Draw a histogram to show this information.

Which of the following is the odd one out?

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Solve �x2 = 50 − 5x

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Find x

The area of the sector is 3m².Find x.

Find the size of Cos x

Solve �x2 + x = 12

x is � of y

x is � of z

Write down the ratio of x : y : z

35

23

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Shown is a right angled triangle.

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A circular plaque of diameter 10cm is cut from a square piece of metal with side length 10cm.

What percentage of the metal is wasted?

The region labelled R satisfies three inequalities.

State the three inequalities

The areas of two mathematically similar shapes are in the ratio 49 : 81The length of the smaller shape is 24.5cmWork out the length of the larger shape.

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Write as a single power of 2

�(22)3 × 4

16



Write down the equation of a line perpendicular to y = 2x − 3

A rectangular garden is 5m longer than it is wide. The area of the garden is 600m²Calculate the width and length of the garden.

Make a the subject

Estimate � 3 70

Simplify � 800

�s = ut +12

at2



The weight of a bag of potatoes is 18kg, correct to the nearest kg.

Write down the lower bound for weight of the bag of potatoes.

Write down the upper bound for weight of the bag of potatoes.

� and �

Write down an inequality for �

−1 ≤ c ≤ 10 −4 ≤ d ≤ − 2

d − c

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Show � on the Venn diagram.A ∩ B′�

Match each graph to the correct relationship.

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a is 40% more than b.b : c = 9 : 2

Write the ratio a : c

Find in terms of a and b

AB

EA


�x2 + 5x + 1 = 0

Simplify

�x2 − 2x − 83x2 + 7x + 2

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Simplify � 6 × 10


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