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HIGHER GCSE MATHS 2014
PRACTISE QUESTIONS FOR THE CALCULATOR PAPER
1 (a) Use your calculator to work out
36.28.5
5.21
Write down all the figures on your calculator display.
.....................................
(2)
(b) Write down your answer to part (a) correct to 2 decimal places.
.....................................
(1)
(c) Write down your answer to part (a) correct to 2 significant figures.
.....................................
(1)
(Total 4 marks)
___________________________________________________________________________
2) Ian invested £3500 for 3 years at 2.5% per annum simple interest.
Work out the total amount of interest Ian earned.
£ ..................................
(Total 3 marks)
___________________________________________________________________________
3. (a) Find the highest common factor (HCF) of 24 and 30
.....................................
(1)
(b) Find the lowest common multiple (LCM) of 4, 5 and 6
.....................................
(2)
( Total 3 marks)
4. (a) Express 45 as a product of its prime factors.
..............................................................
(2)
(b) Find the Highest Common Factor (HCF) of 45 and 30
.............................
(2)
(Total 4 marks)
5.
ABC and DEF are parallel lines.
BEG is a straight line.
Angle GEF = 47.
Work out the size of the angle marked x.
Give reasons for your answer.
..............................................
(Total 3 marks)
6.
6
ANB is parallel to CMD.
LNM is a straight line.
Angle LMD = 68°
(i) Work out the size of the angle marked y.
...................................°
(ii) Give reasons for your answer.
.............................................................................................................................................
.............................................................................................................................................
(3)
(Total 3 marks)
___________________________________________________________________________
7.
ABC is an isosceles triangle.
AB = AC
(a) Explain why 3x – 10 = x + 30
.....................................................................................................................................................
(1)
(b) Solve 3x – 10 = x + 30
x = ...............................
(2)
(Total 3 marks)
______________________________________________________________________________
8.
ABC is a right-angled triangle.
AC = 6 cm
AB = 13 cm
(a) Work out the length of BC.
Give your answer correct to 3 significant figures.
.......................................... cm
(3)
___________________________________________________________________________
9. Melissa is 13 years old.
Becky is 12 years old.
Daniel is 10 years old.
Melissa, Becky and Daniel share £28 in the ratio of their ages.
Becky gives a third of her share to her mother.
How much should Becky now have?
£ ..................................
(Total 4 marks)
10. Here are the first five terms of an arithmetic sequence.
17, 14, 11, 8, 5 …
(a) Find, in terms of n, an expression for the nth term of this sequence.
.....................................
(2)
(b) An expression for the nth term of another sequence is 10 − n2
(i) Find the third term of this sequence.
.....................................
(ii) Find the fifth term of this sequence.
.....................................
(2)
(Total 4 marks)
11.
Work out the total surface area of the triangular prism.
.........................................
(Total 4 marks)
12. Use your calculator to work out
034.0012.0
65tan170920
(a) Write down all the figures on your calculator display.
You must write your answer as a decimal.
.......................................................
(2)
(b) Give your answer to part (a) correct to 3 significant figures
...........................................
(1)
(Total 3 marks)
13. (a) x > −3
Show this inequality on the number line.
(2)
(b) Solve the inequality 7y + 36 8
...........................................
(2)
(Total 3 marks)
14. The diagram shows a circular pond with a path around it.
The pond has a radius of 5m.
The path has a width of 1m.
Work out the area of the path.
Give your answer correct to 3 significant figures.
............................ m2
(Total 3 marks)
15. The diagram shows a CD.
The CD is a circle of radius 6 cm.
(a) Work out the circumference of the CD.
............................... cm
(2)
CDs of this size are cut from rectangular sheets of plastic.
Each sheet is 1 metre long and 50 cm wide.
(b) Work out the greatest number of CDs that can be cut from one rectangular sheet.
.....................................
(2)
(Total 4 marks) _________________________________________________________________________________
16. The diagram shows a prism.
Work out the volume of the prism.
...................................................cm3
(Total 3 marks)
___________________________________________________________________________
17. The exchange rate in London is £1 = €1.14
The exchange rate in Paris is €1 = £0.86
Elaine wants to change some pounds into euros.
In which of these cities would Elaine get the most euros?
You must show all of your working.
.....................................
(Total 3 marks)
18. Bill’s weight decreases from 64.8 kg to 59.3 kg.
Calculate the percentage decrease in Bill’s weight.
Give your answer correct to 3 significant figures.
..............................................%
(Total 3 marks)
___________________________________________________________________________
19. In a sale the normal price of a book is reduced by 10%.
The sale price of the book is £4.86
Calculate the normal price of the book.
..............................................%
(Total 3 marks)
___________________________________________________________________________
20. The table shows some information about the ages, in years, of 60 people.
Age (in years) Frequency
0 to 9 6
10 to 10 13
20 to 29 12
30 to 39 9
40 to 49 7
50 to 59 3
60 to 69 10
(a) Write down the modal class.
.....................................
(1)
Luke says
“The median lies in the class 30 to 39”
Luke is wrong.
(b) Explain why.
.....................................................................................................................................................
.....................................................................................................................................................
(1)
(c) On the grid, draw a frequency polygon for the information in the table.
(2)
(Total 4 marks)
21. The temperature (T °C) at noon at a seaside resort was recorded for a period of 60 days.
The table shows some of this information.
Temperature (T °C) Number of days
10 < T 14 2
14 < T 18 8
18 < T 22 14
22 < T 26 23
26 < T 30 9
30 < T 34 4
Calculate an estimate for the mean temperature at noon during these 60 days.
Give your answer correct to 3 significant figures.
.................................°C
(Total 4 marks)
22. –2 n < 5
n is an integer.
(a) Write down all the possible values of n.
..........................................................................
(2)
(b) Solve the inequality 4x + 1 > 11
..........................................................................
(2)
(Total 4 marks)
___________________________________________________________________________
23. (a) Write 82 500 000 in standard form.
...............................................................
(1)
(b) Work out (5.2 10–7
) (2.8 10–9
)
Give your answer in standard form.
...............................................................
(2)
(Total 3 marks)
___________________________________________________________________________
24.
ABC is a right-angled triangle.
AC = 8 m.
Angle CAB = 37.
Calculate the length of AB. Give your answer correct to 3 significant figures
................................. m
(Total 3 marks)
___________________________________________________________________________
25.
LMN is a right-angled triangle.
MN = 9.6 cm.
LM = 6.4 cm.
Calculate the size of the angle marked x.
Give your answer correct to 1 decimal place.
..............................................................
(Total 3 marks)
__________________________________________________________________________
26. Liam invests £6200 for 3 years in a savings account.
He gets 2.5% per annum compound interest.
How much money will Liam have in his savings account at the end of 3 years?
£ ..............................................................
(Total 3 marks)
___________________________________________________________________________
27. The equation
x3 – 6x = 72
has a solution between 4 and 5
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show all your working.
x = ..............................................
(Total 4 marks)
___________________________________________________________________________
28. Change 9 cm2 to mm
2.
............................ mm2
(Total 2 marks)
___________________________________________________________________________
29. The histogram shows information about the times, in minutes, that some passengers had
to wait at an airport.
Work out the percentage of the passengers who had to wait for more than one hour.
..........................................
(Total 3 marks)
30. The table and histogram give some information about the weights of parcels received at a
post office during one day.
(a) Use the histogram to complete the frequency table.
Weight (w) kg Frequency
0 < w 2 40
2 < w 3
3 < w 4 24
4 < w 5 18
5 < w 8
(2)
(b) Use the table to complete the histogram.
(2)
(Total 4 marks)
31. y is directly proportional to the square of x.
When x = 3, y = 36.
Find the value of y when x = 5.
..........................................
(Total 4 marks)
32. y is inversely proportional to the positive square root of x.
When x = 25, y = 1.6
a) Calculate the value of y when x = 49.
b) Calculate the value of x when y = 1
..........................................
(Total 6 marks)
___________________________________________________________________________
33. The table shows some expressions.
a, b, c and d represent lengths.
and 2 are numbers that have no dimensions.
c2(b + d) a
2 c
2
3
3
c
ba a
2 b
c
da32 d2 2a + b2
Tick () the boxes underneath the three expressions which could represent volumes.
(Total 3 marks)
________________________________________________________________________________
34. There are three secondary schools in Banley.
The table shows the number of students in each of these schools.
Adis College Greslow High Fripp School
750 700 900
Germaine takes a sample of 50 students stratified by school.
Work out the number of students from Greslow High in the sample.
............................................
(Total 2 marks)
________________________________________________________________________________
35.
In triangle PQR,
PQ = 10.5 cm,
PR = 8.3 cm.
angle QPR = 62.
(a) Calculate the area of triangle PQR.
Give your answer correct to 3 significant figures.
...............................cm2
(2)
(b) Calculate the length of QR.
Give your answer correct to 3 significant figures.
................................cm
(3)
(Total 5 marks)
36.
PQRS is a trapezium.
PQ is parallel to SR.
Angle PSR = 90°.
Angle PRS = 62°.
PQ = 14 cm.
PS = 8 cm.
(a) Work out the length of PR.
Give your answer correct to 3 significant figures.
............................... cm
(3)
(b) Work out the length of QR.
Give your answer correct to 3 significant figures.
............................... cm
(4)
(Total 7 marks)
___________________________________________________________________________
37.
AC = 8 cm.
AB = 3 cm.
DE = 19 cm.
Angle ABC = angle CBD = angle BDE = 90°.
Angle BDC = 50°.
(a) Calculate the length of CD.
Give your answer correct to 3 significant figures.
............................................ cm
(4)
(b) Calculate the length of CE.
Give your answer correct to 3 significant figures.
............................................ cm
(3)
(Total 7 marks)
38. The diagram shows a solid hemisphere of radius 8 cm.
Work out the total surface area of the hemisphere.
Give your answer correct to 3 significant figures.
............................. cm2
(Total 3 marks)
39. The diagram shows a sector of a circle with centre O.
The radius of the circle is 8 cm.
PRS is an arc of the circle.
PS is a chord of the circle.
Angle POS = 40°
Calculate the area of the shaded segment.
Give your answer correct to 3 significant figures.
............................. cm2
(Total 5 marks)
40. Steve measured the length and the width of a rectangle.
He measured the length to be 645 mm correct to the nearest 5 mm.
He measured the width to be 400 mm correct to the nearest 5 mm.
Calculate the lower bound for the area of this rectangle.
Give your answer correct to 3 significant figures.
............................ mm2
(Total 3 marks)
41. The diagram below shows a large rectangle of length (2x + 6) cm and width x cm.
A smaller rectangle of length x cm and width 3 cm is cut out and removed.
The area of the shape that is left is 100 cm2.
(a) Show that 2x2 + 3x − 100 = 0
(3)
(b) Calculate the length of the smaller rectangle.
Give your answer correct to 3 significant figures.
............................................ cm
(4)
(Total 7 marks)
42. Prove that
(2n + 3)2 – (2n – 3)
2 is a multiple of 8
for all positive integer values of n.
(Total 3 marks)
___________________________________________________________________________
43. Solve 3x2 – 4x – 2 = 0
Give your solutions correct to 3 significant figures.
.................................................................................
(Total 3 marks)
44.
The diagram shows a triangle ABC.
LMNB is a parallelogram where
L is the midpoint of AB,
M is the midpoint of AC,
and N is the midpoint of BC.
Prove that triangle ALM and triangle MNC are congruent.
You must give reasons for each stage of your proof.
(Total 3 marks)
