The Perse School Specimen Paper 1

IndependentCo-ed

20 questions

Original PDFWorked solutions in progress

Questions

1
Write the missing number in the space provided.

$56 \div \rtqMathsBoxedEmptyValueOneDigitWide = 8$
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2
Here is a number sequence. Write in the missing number.

$3 \rtqMathsListSeparator 6 \rtqMathsListSeparator 10 \rtqMathsListSeparator 15 \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
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3
The diagram below shows a triangle [not drawn to scale].

Calculate each of the angles marked $x$ and $y$ .
A triangle stands on a horizontal line extended to the left. Its top angle is 88 degrees. The left interior base angle is 63 degrees, the adjacent exterior angle is x, and the right interior base angle is y.
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4
Change $0.72$ to a fraction leaving your answer in its simplest form.
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5
Calculate each of the following:
1. 5.a
  $3 - 2\dfrac {5} {9}$
2. 5.b
  $2+ 4 \times \dfrac {3} {5}$
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6
My garden centre sells Summer bedding plants at $85 \rtqMathsUnitCurrencyPence$ each. I have $\rtqMathsSymbolPound 30$ to spend.

How many plants can I buy? Show your working.
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7
Write in what the two missing digits could be:

$\rtqMathsBoxedEmptyValueOneDigitWide \rtqMathsSpaceQuarterEm \rtqMathsBoxedValue{3} \rtqMathsSpaceQuarterEm \rtqMathsBoxedValue{4} + \rtqMathsBoxedEmptyValueOneDigitWide \rtqMathsSpaceQuarterEm \rtqMathsBoxedValue {9} \rtqMathsSpaceQuarterEm \rtqMathsBoxedValue{7} = 631$
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8
Brian has $7$ dominoes in a bag. He takes out one domino and finds the total of the two numbers. He then puts the domino back in the bag. His $7$ dominoes are shown below, together with a graph of his results after doing this experiment $100$ times.
A horizontal domino has one pip on the left and three pips on the right. A horizontal domino has five pips on the left and one pip on the right. A horizontal domino has six pips on the left and two pips on the right. A horizontal domino has two pips on the left and four pips on the right. A horizontal domino has five pips on the left and three pips on the right. A horizontal domino has two pips on the left and three pips on the right. A horizontal domino has three pips on the left and three pips on the right. The horizontal categories are totals 4, 5, 6, 7 and 8. Their frequencies are 21, 13, 40, 0 and 26 respectively. The vertical Frequency scale runs from 0 to 40 in steps of 5.
1. 8.a
  Explain why the total $7$ never came up.
2. 8.b
  Explain why the total of $6$ came up most often.
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9
Write in the missing numbers to each of the following:
1. 9.a
  $93 - \rtqMathsBoxedEmptyValueTwoDigitsWide - 18 = 36$
2. 9.b
  $(8 + \rtqMathsBoxedEmptyValueOneDigitWide )\times 7 =91$
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10
Which of the following fractions is closest to $\dfrac 1 4$ ?

$\dfrac {11} {40}, \rtqMathsListSeparator \dfrac {16} {60}, \rtqMathsListSeparator \dfrac {21} {80}, \rtqMathsListSeparator \dfrac {26} {100}, \rtqMathsListSeparator \dfrac {31} {120}$
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11
Susan is making a necklace of beads, using red and yellow beads in the ratio $2 \rtqMathsRatioSeparator 3$ . She has $56$ red beads altogether.
1. 11.a
  How many yellow beads will she need?
2. 11.b
  How many beads will she use altogether?
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12
The three numbers missing from these boxes are all prime numbers. Write in the missing numbers.

$\rtqMathsBoxedEmptyValueTwoDigitsWide \times \rtqMathsBoxedEmptyValueTwoDigitsWide \times \rtqMathsBoxedEmptyValueTwoDigitsWide = 385$
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Brian is looking at the schedule of TV programmes for that evening.

Time	BBC 1	Time	ITV
$5.45$	‘Neighbours’	$5.40$	News
$6.00$	News	$6.00$	Cartoons
$6.30$	Top of the Pops	$6.20$	Film
$7.10$	Sport	$8.05$	Comedy Programme
$9.25$	Drama	$9.00$	Documentary

13.a
Brian watches the film on ITV but after $\dfrac{1}{2}$ an hour he changes channel to BBC 1.

What is showing on BBC 1 when he changes channel?
13.b
The drama on BBC 1 lasts for $1 \rtqMathsUnit{hour}$ and $40 \rtqMathsUnit{minutes}$ .

At what time does it end?

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14
Make a list of all the whole numbers which leave a remainder of $7$ when divided into $46$ .
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15
The charge $\rtqMathsSymbolPound C$ made by a caterer for arranging a birthday party for $n$ people is given by the formula:

$C = 3n + 40$
1. 15.a
  What is the charge, in $\rtqMathsSymbolPound$ , for a party of $20$ people?
2. 15.b
  What is the average cost per person for a party of $20$ people?
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16
Study the graph below:
A straight line through the origin contains A at (3, 1), B at (6, 2) and C at (12, 4). The displayed horizontal scale runs from negative 1 to 13 and the vertical scale from negative 1 to about 5.5. Point D is not shown.
The co-ordinates of $A, B$ and $C$ are: $A (3 , 1) ; B (6 , 2) ; C (12 , 4)$
1. 16.a
  The value of $D$ (not shown) also lies on this line.
  
  If $D$ is $(15 , \rtqMathsSpaceQuarterEm a)$ , what is the value of $a$ ?
2. 16.b
  $E$ is another point (not shown) on this line and $E$ is $(b , \rtqMathsSpaceQuarterEm 8)$ .
  
  What is the value of $b$ ?
3. 16.c
  If $(p , \rtqMathsSpaceQuarterEm q)$ is another point on this same line, write down a relationship (equation) between $p$ and $q$ .
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17
Find the value of each of the following:
1. 17.a
  $68.9 + 9.86$
2. 17.b
  $321 - 268$
3. 17.c
  $391 \times 7$
4. 17.d
  $656 \div 8$
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18
Brian starts with $1000$ and subtracts $11$ each time. The first four numbers in his sequence are:

$1000, \rtqMathsListSeparator 989, \rtqMathsListSeparator 978, \rtqMathsListSeparator 967$

If he continues in this way, what will be the first negative number in his sequence?
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19
Find the missing numbers so that the answer is always $56$ .
Three boxed expressions are aligned on the left: 131 minus a blank, 50 percent of a blank, and 560 divided by a blank. A box above contains 17 plus a blank and a box below contains one third of a blank. Each box points to a central cloud containing equals 56.
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20
Two rectangles $ABCD$ and $PQRS$ are shown below:
Rectangle ABCD measures 5 centimetres by 3 centimetres. Square PQRS measures 2 centimetres by 2 centimetres and overlaps the upper-right corner of ABCD. The top segment from B to R is 1 centimetre. The part of ABCD outside the overlap is shaded.
$\begin{aligned} AD &= 3 \rtqMathsUnit{cm} \\\\ AB &= 5 \rtqMathsUnit{cm} \\\\ PQ &= 2 \rtqMathsUnit{cm} \\\\ PS &= 2 \rtqMathsUnit{cm} \\\\ BR &= 1 \rtqMathsUnit{cm} \end{aligned}$

Calculate the shaded area.
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Time

BBC 1

Time

ITV

5.45

‘Neighbours’

5.40

News

6.00

News

6.00

Cartoons

6.30

Top of the Pops

6.20

Film

7.10

Sport

8.05

Comedy Programme

9.25

Drama

9.00

Documentary