GCSE, 9-1 H, C2/3 online exam

Instructions


Q1 - Quadratic Sequence

Find an expression for the nth term of this sequence for 1, 4, 13, 28, 49

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Q2 Compound Interest

£2500 is invested at 3.6% compound interest per annum.
How many years will it take for the investment to more than double


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Q3 Mean and speed

Henry measured how far some snails could crawl in 20 minutes.

Distance (cm)No. of snails
30 <t ≤ 34 4
34 <t ≤ 38 7
38 <t ≤ 42 16
42 <t ≤ 46 5
46 <t ≤ 50 2

a) Write down the modal class interval

b) Calculate an estimate for the mean distance to 1 decimal place.

c) Estimate the speed of the fastest snails.
Give your answer in metres per hour.

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Q4 Calculation

a) Find the value of (3.9 – 0.36) + 3√6.7


David says √6 = √2 + √4 ,  Jess says √6 = √2 × √3.

b) Who is right?
Explain your answer

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Q5 Circle

A circular wheel has a radius of 36cm.

The wheel rolls for 8 revolutions.

How far will it travel
Give your answer to the nearest 10cm

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Q6 Angles
exterior angles

A 12 sided £1 coin was placed next to a 7 sided 50p coin.

Work out the angle x to 1 decimal place


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Q7 Stem and Leaf

Speed signs were placed near a school to tell drivers to drive more slowly.
The stem-and-leaf diagrams show the speed of 19 cars before and after the sign was added.

stem leaf

How many mph did the median speed before and after fall by?

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Q8 Equation

Solve the equation:
a)   linear equation


b) Complete the square for 3y2 – 60y + 220


c) Hence solve 3y2 – 60y + 220 = 0 leaving your answer in surd form

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Q9 Iteration

a) Show that the equation x2 – 5x + 2 = 0 has a root between x = 4 and x = 5

b) Show that the equation x2 – 5x + 2 = 0 can be arranged to give x = √(5x – 2)

c) Use the iteration xn+1 = √(5xn – 2), with x0 = 5 , to find a solution to the equation
Give your answer correct to 1 decimal point.


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Q10 Volume

A jug is partly filled with liquid.

A regular 3-D shape with dimensions shown in centimetres, is dropped into the jug.

volume

a) What will be the new height of the liquid on the jug scale

b) What is the volume of the 3-D shape?
Give your answer in standard form in m3

c) The mass of the 3-D shape is 0.227kg
What is its density in grams per cm3

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Q11 Graphs, equation line

Jane started an internet business selling socks.

In method 1, postage was £5 for any number of socks and socks cost £3 a pair.

a) Draw a line on the graph to represent this information

graph

b) What is the equation of this line?

In method 2, she decided to increase the price of socks by ⅓ with free postage.

c) Draw a new line on the graph for method 2 and use your graph to work out how many pairs of socks cost the same for both methods

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Q12 Box plot

40 batteries were tested to see how long they lasted.
This information is shown on the cumulative frequency garph below.

Use the graph to make a boxplot for the batteries. Show the values for median and quartiles.

cumulative frequency
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Q13 Algebra

a) Expand    (5z – 3)2


b) Factorise   10a3 – 15a2


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Q14 Transformation

a) Rotate the shape A, 90° anti-clockwise about centre (– 1, 1)
Label the shape B

transformation - rotation

b) Reflect shape B in the line x = 1. Label it C.

c) Describe the transformation from shape C to shape A


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Q15 Pythagoras and Bearings
pythagoras

A school S is directly 500m north of my house H

A cafe C is directly 600m East of my house H

a) How far is it from the school S to the cafe C?

Give your answer to the nearest metre


b) What is the bearing of the school from the cafe to 1 decimal place.


c) A tree T is directly West of my house. The distance from the tree to the school is 801m.

How far is the tree from my house. Give your answer to 2 significant figures.


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Q16 Speed and distance

Poppy's house is 20 miles from David's house.

David drove 10 miles @ 30mph.

How fast will he have to drive the remaining distance to average 40mph for the trip.

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Q17 Venn Diagram
venn

Look at the Venn diagram for two sets.

a) Shade the region that represents P(A' B')

A' means NOT A


In a maths test for trainee teachers there was a mental part and a calculator part.
In a group of trainee teachers everyone passed at least one part.

85% passed the mental part and 90% passed the calculator part.

b) Show this information on a Venn diagram.

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Q18 Exchange rate

Laura changed £250 into Euros. There was a fee of 1% and the exchange rate was £1 : €1.14

a) How much will she get to the nearest €?

She spent some euros and had €45 left. She exchanged that back into pounds.
There was no fee and the exchange rate was €1.15 : £0.76

b) How much will she get to the nearest £?


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Q19 Ratio

Matt had 3 piles of penny coins.

In the 1st pile there was 49p, in the 2nd pile was 14p and in the 3rd pile was 35p.

What is the ratio for the money in the three piles.

Give your answer in its simplest form.

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Q20 Error interval, bounds

The perimeter of a square is 52 cm to the nearest centimetre.

a) Work out the error interval of the length, l, of a side of this square.

The distance d between two points was 19.7 cm to the nearest mm.

b) Write down the error interval for the distance, d cm.

c) Henry ran 100m in 12.6 sec. both correct to 1 dp.
Find the Upper and Lower Bound for his speed.

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Q21 Two way table

90 students were asked what subjects they liked - Art, PE or Drama.

42 of the 90 students were boys.
12 of the girls liked Drama.
6 boys liked Art.

⅔ of the 39 students who liked PE were boys.

Work out the total number of students who liked Art.

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Q22 Equation line

Look at this line

equation line

Find the equation of another line that is perpendicular to the line shown and passes through the point (1 , 1)

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Q23 LCM

What is the lowest common multiple of 56 and 72


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Q24 Mode, mean and range

The modal age of three boys was 7 and the mean of their ages was 9

The age range of three girls was 7 and the mode of their ages was 7

Who was the oldest, a boy or a girl? Show your working.


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Q25 Calculation

Calculate the value of

3.25 – 2.09  / 3.25 – 2.092

a) Write down your full calculator display

b) Give your answer to three significant figures.

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Q26 Standard form

The mass of the planet Venus is 4.869 × 1024 kg

The mass of the Sun is 408 000 times the mass of Venus.

Work out the mass of the Sun.
Give your answer in standard form correct to 3 significant figures.

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Q27 Sectors
circle circumference

Look at the two sectors?

a) Which has the largest area? Show your working.

b)Which had the largest perimeter?
Show your working.

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Q28 Inversely proportional

The time T (hours), required to build a brick wall is inversely proportional to the number of men M laying bricks.

When 6 men are laying bricks the wall takes 4 hours to build.

a) Find the time taken if 8 men were building the wall.

b) If it took ¾ hour to build the wall how many men would there be?


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Q29 Bearings

1. A plane flies for 200 km on a bearing of 255° from Luton to Cardiff airport.
It lands at Cardiff and then takes off again flying for 225 km on a bearing of 15° to Manchester airport. It then flew back to Luton.
a) Draw luton as a cross at the middle right of a piece of paper. Then using a protractor and ruler make a scale drawing with 25 km = 1 cm.
b) Estimate the bearing and distance (km) from Manchester to Luton.


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Q30 Roots and turning points

Look at this graph of a quadratic equation.

turning points

a) Estimate the roots for x

b) Estimate the co-ordinates of the turning point of the curve


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Q31 Trig ratios

a) Write the exact value of Cosine 30° [1]

b) Write the exact value of Sine 45° [1]

c) Write the exact value of Tan 60° [1]


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Q32 Squared cubic reciprocal graphs

a) Sketch the graph y = x4

b) Sketch the graph y = x5

c) Sketch the graph y = 1/x


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