Download JMC practise pack - NLCS Maths Department

1.
On holiday last year Phil Atterlist bought ten postcards for 10p each and ten second
class stamps at 19p each.
How much change did Phil get from £10?
A 10p
2.
D £8.10
E £9.00
B
C
D
E
Which of the following numbers is not a perfect square?
A 16
4.
C £8
Which of the following bar charts could represent the data from the pie chart below?
A
3.
B £7.10
B 36
C 64
D 80
E 100
A can of soup contains enough for three adults, or for five children. I have five cans of
soup and fifteen children to feed.
How many adults could I feed with what remains?
A 0
5.
C 5
D 6
E 15
Which of these calculations does not give the same answer as the rest?
A 2+4×2
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B 3
B (−24) ÷ (−2)
C −3 − (−15)
D 24 × (0.5)
E (−7) + 19
1
6.
The average of five consecutive integers is 10. What is the sum of the second and
fourth of these integers?
A 6
7.
B 8
C 32
D 72
E 96
B 10
C 12
D 14
E 16
B 199 × 9
C 1999
D 19 × 99
E 1999
D 9
E 10
How many prime numbers are there less than 20?
A 6
11.
E can't be sure
Which of these numbers is biggest?
A 19 × 99
10.
D 21
The sum of five consecutive even numbers is 60. What is the smallest of the five
numbers?
A 8
9.
C 20
One quarter of a number is 24. What is one third of the original number?
A 6
8.
B 10
B 7
C 8
Granny has been having a smashing time. Yesterday she had 12 cups and 10
matching saucers, but this morning she dropped a tray holding one third of the cups
and half the saucers, breaking all of those on the tray.
How many of her cups are now without saucers?
A 1
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B 3
C 4
D 5
E 6
2
12.
When written in decimal form,
What is the value of
A 0·02468
13.
1
= 0·0123456790123….
81
2
correct to six decimal places?
81
B 0·024681
C 0·024690
D 0·024691
E 0·0246914
Goldbach's conjecture, which has not been proved, states that every even number
greater than two is the sum of two primes. However, the same is not true for every odd
number.
Which of the following odd numbers is not the sum of two primes?
A 13
14.
D 53
E 73
B 2002
C 2000
D 1998
E 1996
What percentage of the large 5 × 5 square is shaded?
A 40%
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C 43
What is the value of 4002 − 2004?
A 2004
15.
B 33
B 60%
2%
C 66 3
D 75%
E 80%
3
16.
WHICH LETTER DOES NOT OCCUR MORE THAN ONCE IN THIS QUESTION −
INCLUDING THE FIVE OPTIONS?
A
17.
B
C
D
E
Humpty Dumpty sat on a wall, admiring his new digital watch which displayed hours
. when Jack and Jill set off up the hill, but
and minutes only. He noticed that it was .
. . At that
that when they later came tumbling down again his watch showed only .
point Humpty realised that he'd had his watch on upside down all the time!
How long did Jack and Jill take to go up the hill and down again?
A 40min
18.
E 4hr 30min
B 11000001
C 101000001
D 1010001
E 10100001
B 170
C 868
D 10778
E 14960
Which fraction is the odd one out?
A
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D 3hr 10min
2 × 17 + 3 × 17 + 5 × 17 equals
A 160
20.
C 2hr 20min
How is the number ten million one hundred thousand and one written?
A 1001001
19.
B 2hr 10min
1+ 4
7+4
B
20
140
C
0.2
1.4
D
1  11
7  11
E
8
56
4
21.
On a journey a certain weight of luggage is carried free, but there is a charge of £10
per kilogram for any additional luggage above this weight. Laa-laa's luggage, which
weighs a total of 50kg, is overweight and she is charged £150.
If Po's luggage weighs a total of 30kg, what will she have to pay?
A £0
22.
B £30
D £90
E £100
What is the difference between the largest and smallest of the following numbers?
A 0.89
23.
C £50
B 0.9
C 0.17
D 0.72
E 0.73
In the diagram the lines PQ and SR are parallel, as are the lines PS and QT.
What is the value of x?
P
41°
83°
x°
S
Q
R
T
A 139
24.
B 138
D 98
E 97
In which of the following lists are the terms not increasing?
A
1
3
, 0.25, , 0.5
5
10
B
D
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C 124
3
4
, 0.7, ,1.5
5
5
3
4
, 0.5, , 0.9
5
5
C
E
2
7
, 0.5, , 0.9
5
10
2
10
,1.5, , 2.3
5
5
5
25.
In the sequence which begins 2, 3, 5, 10, … each number after the second is the sum
of all the previous numbers in the sequence.
What is the 10th number in the sequence?
A 47
26.
B 170
C 640
D 1280
E 2560
D 3
E 4
How many of the statements in the box are true?
Any number which is divisible by 6 is even.
Any number which is divisible by 9 is odd.
The sum of any two odd numbers is even.
The sum of any two even numbers is odd.
A 0
27.
B 1
C 2
Gill is 18 this year. She and I went to a restaurant for lunch to celebrate her birthday.
The bill for lunch for the two of us came to £25.50. Gill paid the bill by credit card and I
left a £2.50 tip in cash. We agreed to split the total cost equally.
How much did I owe Gill?
A £11
28.
C £12
D £12.50
E £13
D 1
E 4 026 042
What is the value of 2006 × 2008 − 2007 × 2007?
A −2007
29.
B £11.50
B −1
S is 25% of 60
C 0
60 is 80% of U
80 is M% of 25.
What is S + U + M?
A 100
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B 103
C 165
D 330
E 410
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30.
I have two "Spinners": one is a square, and the other is a regular pentagon. Both
spinners are spun at the same time and the two scores obtained are added together.
How many possible totals are there?
5
3
4
2
31.
3
1
A 5
2
4
B 6
C 7
1
D 8
E 9
The absorptive surface of the small intestine of a typical adult has an area of
approximately 200 square metres.
Which of the following has approximately the same area?
A a dartboard
B a table tennis table
D a golf course
32.
C a football pitch
E a tennis court
Thirty years ago Mike McNamara cycled 445.0 km in 12 hours − a new British men's
record at that time. In the same time trial Beryl Burton (who died last year) completed
446.2 km.
How much faster was Beryl Burton's average speed than Mike McNamara's (in metres
per hour)?
A 1.2
33.
B 10
C 11
D 100
E 1200
Timmy Riddle was selling toffee apples at the school fête. When I asked him what they
cost he said "One toffee apple costs the smallest amount that cannot be paid exactly
using four or fewer standard British coins".
I bought as many toffee apples as I could get for £1. How much change did I receive?
A 1p
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B 5p
C 18p
D 22p
E 24p
7
34.
Along which line should an upright mirror be placed so that the part of the square on
one side of the mirror and its reflection form an octagon?
E
A
A
35.
B
C
B
D
C
D
E
On four tests, each marked out of 100, my average was 85.
What is the lowest mark I could have scored on any one test?
A 0
36.
D 81
E 85
B 1/2
C 1/√2
D √2
E 2
Which is smallest?
A
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C 60
If x  (1/4) 1/2 , what is the value of x  x ?
A 1/4
37.
B 40
(2  3)
(4  6)
B
(2  3)
(4  6)
C
23
46
D
(2  3)
(4  6)
E
(2  3)
(4  6)
8
38.
Four wiggles are the same as three woggles; two woggles are the same as five
waggles, and six waggles are the same as one wuggle.
Which is smallest?
A 1 wuggle
39.
B 2 woggles C 3 waggles
D 4 wiggles
E two have the same value
Our ancient Ancient History teacher's copy of Homer's Odyssey cost 40p in 1974. A
similar edition today costs £5.
What percentage increase is this?
A 12.5%
40.
B 1150%
C 1250%
D 12400%
E 12500%
A trapezium has parallel sides of length a and b, and height h. Sides a and b are both
decreased by 10% and the height h is increased by 10%.
What is the percentage change in the area of the trapezium?
a
h
b
A 10% decrease
B 1% decrease
D 10% increase
41.
E 30% increase
Which of the following statements is false?
A 3 + 5 × 4 = 23
D 3 + 6 × 4 = 36
JZugg
C no change
B
20 − 5 × 4 = 0
C 12 − 5 × 2 = 2
E 5 × 3 − 2 = 13
9
42.
The diagram shows two concentric circles of radii r and 2r respectively.
What is the ratio of the total shaded area to the total unshaded area?
120°
A 5:7
43.
B 7:5
C 1:1
D 2:3
Which of the following could be the graph showing the circumference C of a circle in
terms of its diameter d?
C
C
d
A
C
d
B
C
C
D
44.
E 3:2
d
C
d
d
E
In the calculation 1003 ÷ 4995 = 0.2 0 08 , the number 0.20 08 represents the recurring
decimal fraction 0.2008008008008... .
When the answers to the following calculations are arranged in numerical order, which
one is in the middle?
A 226 ÷ 1125 = 0.200 8
B
251 ÷ 1250 = 0.2008
D 1003 ÷ 4995 = 0.20 08
JZugg
C
497 ÷ 2475 = 0.20 0 8
E 2008 ÷ 9999 = 0.2 008
10
45.
What is the value of
A
46.
1
16
3
1
4
?
1
4
C 1
D 4
E 16
If I add up all the different prime factors of 1998, what answer would I get?
A 42
47.
B
4
B 43
C 48
D 116
E 1001
Five pings and five pongs are worth the same as two pongs and eleven pings.
How many pings is a pong worth?
A
48.
1
2
B 2
C 2
1
2
D 9
E can't be sure
Two square pieces of card, each 3 cm × 3 cm, are attached by a single pin to a board.
The pin passes through a point 1/3 of the way along the diagonal of each square and
the squares overlap exactly. The bottom card now remains fixed, while the top card is
rotated through 180°.
What is the area of overlap of the cards in this new position?
A 1 cm2
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B 2 cm2
C 4 cm2
D 6 cm2
E 9 cm2
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49.
A wire in the shape of an equilateral triangle with sides of length 9 cm is placed flat on
a piece of paper. A pencil is held in the hole at the centre of a disc of radius 1 cm, and
the disc is rolled all the way around the outside of the wire, and then all the way around
the inside of the wire.
What shape is drawn by the pencil?
pencil
disc
wire
A
50.
B
C
D
E
The diagram shows a right-angled isosceles triangle XYZ which circumscribes a
square PQRS.
The area of triangle XYZ is x. What is the area of square PQRS?
X
P
Y
A
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4x
9
S
B
x
2
Q
Z
R
C
4x
5
D
2x
5
E
2x
3
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51.
The Queen of Hearts had some tarts, but they were eaten. Precisely one of the
following statements about the tarts and the Knaves of Clubs, Diamonds and Spades is
true.
Which one?
A None of the three Knaves ate any tarts.
B The Knave of Clubs ate some tarts.
C Only one of the three Knaves ate any tarts.
D At least one of the Knave of Diamonds and the Knave of Spades ate no tarts.
E More than one of the three Knaves ate some tarts.
52.
A sculpture consists of a row of 2 metre rods each placed with one end resting on
horizontal ground and the other end resting against a vertical wall. The diagram shows
how the rods BT, CU, DV, … look from above. The bases of the rods B, C, D, … lie on
a straight line on the ground at 45° to the wall. The top ends of the rods T, U, V… lie on
part of a curve on the wall.
What curve is it?
T U V
B
C
D
A a straight line
53.
C a circle
D a sine curve
E a quartic curve
Which of the following straight lines should be omitted to leave four lines which
determine a square?
A y+x=3
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B a parabola
B y=x−1
C y+x=1
D y=x+1
E y+x=2
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54.
The year 2004 had the units digit equal to twice the thousands digit.
How many years after 2004 does this first happen again?
A 10
55.
B 36
C 220
D 1002
E 2004
The trunk of a monkey-puzzle tree has diameter 40 cm. As a protection from fire, the
trunk of the tree has a bark which makes up 19% of its volume.
On average, roughly how thick is the bark of the trunk?
A 0.4 cm
56.
B 1.2 cm
C 2 cm
D 2.8 cm
E 4 cm
The factorial of n, written n!, is defined by n! = 1 × 2 × 3 × … × (n − 2) × (n − 1) × n.
Which of the following values of n provides a counterexample to the statement:
“If n is a prime number, then n! + 1 is also a prime number”?
A 1
57.
B 2
C 3
D 4
E 5
The sculpture 'Cubo Vazado' [Emptied Cube] by the Brazilian artist Franz Weissmann
is formed by removing cubical blocks from a solid cube to leave the symmetrical shape
shown.
If all the edges have length 1, 2 or 3 units, what is the surface area of the sculpture in
square units?
A 36
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B 42
C 48
D 54
E 60
14
58.
2
4
and
. Each term after the second term is
3
5
the average (mean) of the two previous terms. What is the fifth term in the sequence?
The first two terms of a sequence are
A
59.
5
34
B
1
2
C
10
13
D
3
4
E
10
11
Beatrix has a 24-hour digital clock on a glass table-top next to her desk. When she
looked at the clock at 13:08, she noticed that the reflected display also read 13:08, as
shown.
How many times in a 24-hour period do the display and its reflection give the same
time?
A 12
60.
B 36
C 48
D 72
E 96
Tickets for a school play cost £3 for adults and £1 for children. The total amount
collected from ticket sales was £1320. The play was staged in a hall seating 600, but
the hall was not completely full.
What was the smallest possible number of adults at the play?
A 358
61.
C 360
If a = b − c, b = c − d and c = d − a, then
A 1
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B 359
B
1
2
C 0
D 361
E 362
a b c d
equals
  
b c d a
D –
1
2
E –1
15
62.
A cube is inscribed in a sphere of diameter 1m.
What is the surface area of the cube?
A 2 m2
63.
B 3 m2
C 4 m2
D 5 m2
E 6 m2
The two-digit by two-digit multiplication on the right has lots of gaps, but most of them
can be filled in by logic (not by guesswork).
Which digit must go in position *?
–
4
–
×
–
–
–
8
–
8
–
0
–
4
A 1
64.
B 3
C 5
D 7
E 9
Seventy pupils (37 boys and 33 girls) are divided into two groups, with forty pupils in
Group I and thirty pupils in Group II.
How many more boys are there in Group I than there are girls in Group II?
A 4
65.
B 7
C 8
E more information needed
1 )....(1+ 1 ) equal to an
When exactly is the value of the product (1+ 1 )(1+ 1 )(1+ 4
n
2
3
integer?
A when n is odd
B when n is even
D always
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D 9
C when n is a multiple of 3
E never
16
66.
The diagram shows a circle with circumference 1 being rolled around an equilateral
triangle with sides of length 1.
How many complete turns does the circle make as it rolls once around the triangle
without slipping?
A 3
67.
C 0
n2 – 9
are integers?
n –1
D 4
E 8
B 0.312
C 0.42
D 1.0
E 1.5
What is the sum of the six marked angles?
A 1080°
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B −4
E 51
2
D 5
What is the value of 0.1 + 0.2 + 0.3 × 0.4?
A 0.24
69.
C 4
What is the sum of the values of n for which both n and
A −8
68.
B 31
2
B 1440°
C
1620°
D 1800°
E
more information needed
17