Leicester High School for Girls Paper 1

IndependentGirls

20 questions

Original PDFWorked solutions in progress

Questions

1. 1
  Calculate:
  1.a
  $38 + 624 + 170$
  1.b
  $361 - 89$
  1.c
  $\rtqMathsSymbolPound 17.23 + \rtqMathsSymbolPound 6.58 + 75 \rtqMathsUnitCurrencyPence$
  1.d
  $279 \times 6$
  1.e
  $85 \div 5$
  Worked solution
  Being written
2. 2
  A box of $92$ Smarties contains only red, green and purple Smarties.
  
  If there are $37$ red Smarties and $29$ green Smarties how many purple Smarties does it contain?
  Worked solution
  Being written
3. 3
  Leyla buys a bracelet costing $\rtqMathsSymbolPound 6.49$ .
  
  If she pays with a $\rtqMathsSymbolPound 10$ note what change should she receive?
  Worked solution
  Being written
4. 4
  Jenny is given $3$ large jigsaw puzzles for Christmas which get muddled together. The first contains $496$ pieces, the second $812$ pieces and the third $984$ pieces.
  
  By rounding each of these numbers to the nearest $100$ , write down a simple sum you can do to estimate the total number of jigsaw pieces there are all together.
  Worked solution
  Being written
5. 5
  5.a
  Arrange all these numbers in order of size, writing the smallest first.
  
  $540, \rtqMathsListSeparator 452, \rtqMathsListSeparator 524, \rtqMathsListSeparator 425, \rtqMathsListSeparator 504$
  5.b
  Using any of the digits $4, \rtqMathsSpaceQuarterEm 5$ and $2$ only once in each answer, write down:
  5.b.i
  An even $2$ digit number.
  5.b.ii
  The largest $3$ digit number possible.
  5.b.iii
  The smallest $2$ digit number possible.
  Worked solution
  Being written
6. 6
  6.a
  Calculate:
  6.a.i
  $15 \times 6$
  6.a.ii
  $15 \times 60$
  6.a.iii
  $15 \times 1000$
  6.b
  What is $350 \div 10$ ?
  6.c
  A length of ribbon is $240 \rtqMathsUnit{cm}$ long. It is cut into $6$ pieces of equal length.
  
  What is the length of each piece?
  Worked solution
  Being written
7. 7
  I think of a number, multiply it by three and add $7$ . The answer is $25$ .
  
  What is the number I am thinking of?
  Worked solution
  Being written
8. 8
  8.a
  Write in figures the number “sixteen thousand, seven hundred and one”.
  8.b
  Write in words the number $8014$ .
  8.c
  Write down the number which is $100$ more than $3724$ .
  8.d
  Write down the number which is $1$ less than $1000$ .
  Worked solution
  Being written
9. 9
  In the next two questions write a number in the box which will make the statement true.
  9.a
  $4 \times \rtqMathsBoxedEmptyValueOneDigitWide = 36$
  9.b
  $\rtqMathsBoxedEmptyValueTwoDigitsWide - 13 = 32$
  Worked solution
  Being written
10. 10
  10.a
  Look at this diagram:
  Eight spokes divide the circle into equal sectors. Three separated sectors are shaded with a strong neutral fill.
  10.a.i
  What fraction is shaded?
  10.a.ii
  What fraction is unshaded?
  10.b
  Shade $\dfrac{2} {3}$ of this diagram.
  The rectangle is divided into four columns and three rows, ready for shading.
  10.c
  In an orchestra of $24$ children, $\dfrac{3} {4}$ of them are girls.
  
  How many are boys?
  10.d
  $50\%$ of the trees in a wood are fir trees.
  
  If there are $450$ trees in the wood, how many fir trees are there?
  Worked solution
  Being written
11. 11
  11.a
  Write down the names of the four shapes in this diagram.
  A curved outline marked 1 is above an upright outline marked 2. Matching slanted outlines extend left and right, with 3 on the right, and a pointed outline marked 4 is below.
  11.a.i
  Shape $1$ is a $\rtqMathsUnderlineEmptyValueLong$
  11.a.ii
  Shape $2$ is a $\rtqMathsUnderlineEmptyValueLong$
  11.a.iii
  Shape $3$ is a $\rtqMathsUnderlineEmptyValueLong$
  11.a.iv
  This diagram has a line of symmetry and so shape $4$ is a special type of triangle.
  
  Complete this statement:
  
  shape $4$ is an $\rtqMathsUnderlineEmptyValueLong$ triangle.
  11.b
  Draw all the lines of symmetry on the two diagrams below.
  11.b.i
  A plain rectangle is provided for drawing lines of symmetry.
  11.b.ii
  A plain upright isosceles triangle is provided for drawing lines of symmetry.
  11.c
  Complete the shaded shape on the diagram below to make the dotted line a line of symmetry.
  An eight-column by eight-row grid has cells twice as wide as tall. A dashed horizontal mirror line crosses the middle of the grid. A solid open outline lies above it, starting on the mirror line at the second vertical division and returning to it at the seventh.
  Worked solution
  Being written
12. 12
  12.a
  This diagram shows two angles $A$ and $B$ . One is acute and one is obtuse.
  
  Complete the statement below with the letter $A$ or $B$ .
  A sloping ray rises to the right from a point on a horizontal straight line. The obtuse angle on the left is labelled A and the acute angle on the right is labelled B.
  The acute angle is $\rtqMathsUnderlineEmptyValueMedium$
  
  The obtuse angle is $\rtqMathsUnderlineEmptyValueMedium$
  12.b
  How many degrees are there in a right angle?
  Worked solution
  Being written
13. 13
  Using the letters $\text{N}$ for North, $\text{S}$ for South, $\text{E}$ for East and $\text{W}$ for West, name the eight points on this compass. $\text{North} \rtqMathsSpaceQuarterEm (\text{N})$ has been marked for you.
  Four straight lines meet at one centre to form eight equal compass spokes. The upward spoke is labelled N.
  Worked solution
  Being written
14. 14
  
  IMPOSSIBLE
  
  UNLIKELY
  
  EVENS
  
  LIKELY
  
  CERTAIN
  
  Which of the above words best describes the following probabilities:
  14.a
  If I buy a national Lottery ticket today I will win the jackpot prize with it.
  14.b
  I will know the correct answer to the sum $2+ 2 =$
  14.c
  The next baby born at the Leicester Royal Infirmary is a boy.
  Worked solution
  Being written
15. 15
  This temperature chart shows the temperature taken at $6 \rtqMathsUnit{hour}$ intervals one day in January.
  The chart titled Temperature One Day in January plots four readings: minus 7 degrees Celsius at Midnight, minus 4 at 6:00 AM, 8 at Noon and 5 at 6:00 PM. Straight line segments join the four filled points. The vertical scale runs from minus 8 to 10 degrees Celsius.
  15.a
  What is the temperature at midnight?
  15.b
  What was the rise in temperature between $6 \rtqMathsTimeAm$ and noon?
  15.c
  Show the time $1800 \rtqMathsUnit{hours}$ in this clock face.
  A circular analogue clock face has the hour numbers 1 to 12 and a filled centre point. It has no hands, ready for the requested time to be drawn.
  Worked solution
  Being written
16. 16
  Part of the TV programme schedule for Saturday morning is shown below.
  
  $8.25$ Rugrats
  $8.50$ Smart Guy
  $9.15$ Live and Kicking
  $12.10$ BBC News; Weather
  16.a
  For how many minutes does the programme Smart Guy last?
  16.b
  Carla wants to record Live and Kicking. She thinks that the $180 \rtqMathsUnit{minute}$ tape she has will be long enough.
  
  How many spare minutes will be left on the tape after recording Live and Kicking?
  Worked solution
  Being written
17. 17
  17.a
  Measure the dimensions of this rectangle giving your answers to the nearest whole centimetre.
  
  length $\rtqMathsUnderlineEmptyValueLong \rtqMathsSpaceQuarterEm \text{cm}$
  
  breadth $\rtqMathsUnderlineEmptyValueLong \rtqMathsSpaceQuarterEm \text{cm}$
  
  An unlabelled rectangle is shown with a width visibly greater than its height.
  17.b
  Using these answers, calculate the perimeter of the rectangle above.
  17.c
  Calculate the area of the rectangle above. Write down the units of your answer.
  Worked solution
  Being written
18. 18
  Write down the next two numbers in the following sequences:
  18.a
  $7, \rtqMathsListSeparator 14, \rtqMathsListSeparator 21, \rtqMathsListSeparator 28, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  18.b
  $3, \rtqMathsListSeparator 6, \rtqMathsListSeparator 12, \rtqMathsListSeparator 24, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  18.c
  $50, \rtqMathsListSeparator 41, \rtqMathsListSeparator 33, \rtqMathsListSeparator 26, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  Worked solution
  Being written
19. 19
  Look carefully at this number pattern:
  
  $\begin{aligned} \text{Line 1}: 1 \times 1 + 3 &= 4 \\\\ \text{Line 2}: 2 \times 2 + 5 &= 9 \\\\ \text{Line 3}: 3 \times 3 + 7 &= 16 \end{aligned}$
  19.a
  Write down the next two lines of the pattern.
  
  $\begin{aligned} \text{Line 4}: \rtqMathsBoxedEmptyValueTwoDigitsWide \times \rtqMathsBoxedEmptyValueTwoDigitsWide + \rtqMathsBoxedEmptyValueTwoDigitsWide &= \rtqMathsBoxedEmptyValueTwoDigitsWide \\\\ \text{Line 5}: \rtqMathsBoxedEmptyValueTwoDigitsWide \times \rtqMathsBoxedEmptyValueTwoDigitsWide + \rtqMathsBoxedEmptyValueTwoDigitsWide &= \rtqMathsBoxedEmptyValueTwoDigitsWide \end{aligned}$
  19.b
  The numbers in the final column are special numbers. What is the name of these special numbers?
  Worked solution
  Being written
20. 20
  Hannah has $4$ pieces of string of lengths $1 \rtqMathsUnit{m}, 2 \rtqMathsUnit{m}, 3 \rtqMathsUnit{m}$ and $5 \rtqMathsUnit{m}$ .
  
  She can join them together to make other lengths e.g. to make $4 \rtqMathsUnit{m}$ she can use $1 \rtqMathsUnit{m} + 3 \rtqMathsUnit{m}$ .
  
  She can use two or more pieces each time.
  20.a
  Which pieces should she use to make the following lengths?
  20.a.i
  $7 \rtqMathsUnit{m}$
  20.a.ii
  $9 \rtqMathsUnit{m}$
  20.b
  What is the longest length she can make?
  Worked solution
  Being written

$8.25$	Rugrats
$8.50$	Smart Guy
$9.15$	Live and Kicking
$12.10$	BBC News; Weather