GCSE Mathematics

Practice Tests: Set 6

Paper 3H (Calculator)

Time: 1 hour 30 minutes

You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Instructions

Use black ink or ball-point pen.

Fill in the boxes at the top of this page with your name,
centre number and candidate number.

Answer all questions.

Answer the questions in the spaces provided

– there may be more space than you need.

Calculators may be used.

Diagrams are NOT accurately drawn, unless otherwise indicated.

You must show all your working out.

Information

The total mark for this paper is 80

The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.

Advice

Read each question carefully before you start to answer it.

Keep an eye on the time.

Try to answer every question.

Check your answers if you have time at the end.

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1.	Here is a rectangle.

The rectangle has been divided into two strips, A and B.

The strips have the same width.

of strip A is shaded.

of strip B is shaded.

The length of the rectangle is 40 cm.

What fraction of the rectangle is not shaded?

..............................................

(Total 4 marks)

___________________________________________________________________________

2.	Make w the subject of the formula P =

.................................................................................

(Total 2 marks)

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3.

A, B and C are 3 service stations on a motorway.

AB = 25 miles

BC = 25 miles

Aysha drives along the motorway from A to C.

Aysha drives at an average speed of 50 mph from A to B.

She drives at an average speed of 60 mph from B to C.

Work out the difference in the time Aysha takes to drive from A to B and the time Aysha takes to drive from B to C.

Give your answer in minutes.

.............................................. minutes

(Total 3 marks)

___________________________________________________________________________

4.	Solve the simultaneous equations

4x + 3y = –7

3x – 4y = 26

x =.......................................................

y =.......................................................

(Total 4 marks)

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5.	Toby invested £4500 for 2 years in a savings account.

He was paid 4% per annum compound interest.

(a)	How much did Toby have in his savings account after 2 years?

£ ..............................

(3)

Jaspir invested £2400 for n years in a savings account.

He was paid 7.5% per annum compound interest.

At the end of the n years he had £3445.51 in the savings account.

(b)	Work out the value of n.

...........................

(2)

(Total 5 marks)

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6.	Here is a shape.

BPC is a semicircle.

BAC is a right-angled triangle.

BC = 8 cm.

AB = 5 cm.

Work out the perimeter of the shape.

Give your answer correct to 3 significant figures.

.............................................................. cm

(Total 5 marks)

___________________________________________________________________________

7.	The diagram shows a trapezium.

All measurements on the diagram are in centimetres.

The area of the trapezium is 119 cm2

(i)	Show that	2x2 – x – 120 = 0

(ii)	Find the value of x.

Show your working clearly.

x = .......................................................

(Total 6 marks)

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8.	Here is a number line.

(a)	Write down the inequality shown on the number line.

......................................................

(1)

p is an integer.

–5 < p –2

(b)	Write down all the possible values of p.

......................................................

(2)

(c)	Solve 5y – 2 < 18

......................................................

(2)

(Total 5 marks)

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9.	There are 9 counters in a bag.

There is a number on each counter.

Kal takes at random 3 counters from the bag.

He adds together the numbers on the 3 counters to get his Total.

Work out the probability that his Total is 6.

.......................................................

(Total 5 marks)

___________________________________________________________________________

10.	The highest common factor (HCF) of 140 and x is 20.

The lowest common multiple (LCM) of 140 and x is 420.

Find the value of x.

x = ........................................................

(Total 2 marks)

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11.	A number is decreased by 15%.

The result is 323

What was the original number?

...............................................................

(Total 3 marks)

___________________________________________________________________________

12.	Each student in a group of 32 students was asked the following question.

“Do you have a desktop computer (D), a laptop (L) or a tablet (T )?”

Their answers showed that

19 students have a desktop computer

17 students have a laptop

16 students have a tablet

9 students have both a desktop computer and a laptop

11 students have both a desktop computer and a tablet

7 students have both a laptop and a tablet

5 students have all three.

(a)	Using this information, complete the Venn diagram to show the number of students in each appropriate subset.

(3)

One of the students with both a desktop computer and a laptop is chosen at random.

(b)	Find the probability that this student also has a tablet.

........................................................

(1)

(Total 4 marks)

___________________________________________________________________________

13.	The function f is defined as

(a)	Find f(8).

................................

(1)

(b)	Express the inverse function f–1 in the form f–1(x) = …

f–1(x) = ................................

(2)

The function g is defined as

(c)	Express the function gf in the form gf(x) = …

Give your answer as simply as possible.

gf(x) = ................................

(2)

(Total 5 marks)

___________________________________________________________________________

14.	The diagram shows a prism.

Triangle PQR is a cross section of the prism.

PR = 20 cm

MP = 12 cm

Angle PRQ = 30º

Angle PQR = 90º

Calculate the size of the angle that the line MR makes with the plane RQLN.

Give your answer correct to 1 decimal place.

......................................................°

(Total 5 marks)

___________________________________________________________________________

15.	A scientist is studying some rabbits.

The rabbits have a disease that kills the rabbits.

A population of 160 of these rabbits was reduced to 90 rabbits in two days.

The rabbit population is decreasing exponentially.

Work out how many of the 160 rabbits will still be alive at the end of 7 days.

.......................................................

(Total 5 marks)

___________________________________________________________________________

16.

Work out the area of the quadrilateral ABCD.

Give your answer correct to 3 significant figures.

.............................................................. cm2

(Total 6 marks)

___________________________________________________________________________

17.	y = at2 – 2at

x =2a

Express y in terms of x and a.

Give your answer in the form , where p, q, m and n are integers.

......................................................

(Total 4 marks)

___________________________________________________________________________

18.	The histogram shows information about the lifetime of some electrical components.

Lifetime (years)

Work out the proportion of the components with a lifetime of between 1 and 6 years.

..............................................................

(Total 4 marks)

___________________________________________________________________________

19.

ABCD is a parallelogram.

E is the midpoint of AB.

F is the midpoint of DC.

(a)	Prove that triangle AED is congruent to triangle CFB.

(3)

(b)	Hence, prove that DE = FB

(1)

(Total 4 marks)

TOTAL FOR PAPER IS 80 MARKS