End of year A


1.  Write these ratios in their simplest form.

   a)  16 minutes to one hundred seconds   b)   75 € (euros) to 3 cents

   c)  3 feet to a chain (22yards)                   d)   500cm³ to 5 litres

2.  Demonstrate that you know these conversions by stating

   a) the number of metres in a mile       b) how many grammes make a pound

   c) the number of litres in a gallon        d) the number of lives in a cat

3.  Work out these (sans calculator)

a) 37 x 53       b) 6500 / 40       c) 50 million / 100 thousand

d) √121 / 100  e) 5.73 x 42.23 + 4.27 x 42.23

Put these in order, smallest first:  0.37, 0.703, 0.030700, 0.0037, 0.307

4. Using squared paper such as in your exercise book draw a 10x12 rectangle. Shade //// 3/8 of this. Shade \\\\\\ 3/4 of what is left.

5.    a) Write the prime factors of 12.         b) Find the highest common factor of 12 and 54.

       c) Find the lowest common multiple of 12 and 54. (sans calculator)

Questions such as 6 to 9 woudl usually have a diagram in test conditions.

6.   Draw any simple asymmetric shape on a set of axes. Such as an F or a P.

  a) Reflect it about a vertical axis, giving the equation of that axis. Such as x = 6

  b) Rotate it about the origin through 120º clockwise.

7. Draw a pair of mutually perpendicular axes. Draw any sort of curve joining (0,3) to (5,0). Now reflect what you have drawn on both axes so your completed figure fits all four quadrants.   

8.  Draw accurately a line of length 12cm. Using straight edge and compasses bisect your line. Find a point on your bisector that is 5cm from the line. Construct an  angle of 60º from this point and measure where the line created meets your original line. Write the enclosed length on your drawing to two significant figures.

9.  A telephone bill has a fixed, or standing charge and a variable, or traffic, charge based on the level of usage. The total bill from company A, £y, is calculated by a formula such as y = 25 + 40x  where x is the hours of use in a month.

Write down the size of the bill for not using the phone at all, and for accidentally leaving it on for a whole day (and otherwise not using it).

Draw the graph of y = 25 + 40x  and label it A.  Use ten units per square in x, and ten in y.

Company B charges according to the formula y = 45x - 5 per month.

Draw this (and label it) on the same graph. When are the bills ever equal?

10.    Write these figures as stated:        a) thirty thousand and fifty six in figures

    b)    467 907 to 3 sig.fig.                      c)  0.005 689 367  in Std Form to 3 s.f.

    d)    756 million in Standard Form        e)  three eighths as a decimal


11. Solve these:   12x – 13 = 47 – 3x;       3(y - 5) = 7 + y;             z + 5 = 7z – 6

12. These are the first few terms of a sequence: 21, 19, 15, 11, 7, ...

Write down a)  the next two terms            b)  a rule for the next term

   c)  Find a formula for the nth term         d)  Find the 100th term

   e)  Find the formula for the sequence which starts 121, 119, 115, 111, 17, ...

   f)  What is the 100th term of this series?

13. Calculate, writing the answer in standard form  (5 sig.fig will do)

    a) 236    b)  0.0005612    c)  3.4x104 x 2.06x10-3

14. What is the probability of:    a) the school being closed next Wednesday

    b)  Throwing a five with a fair die       c) picking an Ace from a full shuffled pack.

15. Two hundred sweets are divided among three friends in the ratio 1:2:5. How many sweets are there in each pile? Can you sketch (i.e. very fast and rough) a pie chart for this?

16. Write these in order, smallest first:    4/5,  0.85,  √0.7,  0.805,   6/7

The remaining questions begin to stretch away from any internal exam. The third sheet of this sort will look at topics you are expected to be able to do that are (only) in the NFER tests.

17. I have three jobs to do: A, B and C. If order matters, list the order in which the jobs can be tackled. If there were four jobs, how many ways would there be?

18. A large rectangular-based tank has dimensions 5 by 8m and is 3m deep. Find its volume in m3 and in litres. If the tank is filled with sand at a rate of half a cubic metre per second (which is pretty fast, sand is 1.3 to 2.1 tonnes per cubic metre), how long will it take to fill it?

19. If I use different bases, then nineteen is written 100112 in binary and 2034 and 238.

Write twenty five in the same way (in base two, four and eight).

Convert 347 back to base ten (called denary).

20. You are supposed to know that   x2 – y2 = (x+y) (x-y)  and   (x+y)2 = x2 + 2xy + y2

Using these, and preferably not using a calculator except perhaps to check, do:

   a)  512 – 492   b) 1512 – 1492            c) (40 + 5)2

   d) (300 - 1)2     e)  expand (3x - y)2     f)  factorise 16x2 – 25y2

Not covered: ratio, mean, median, values in formulae, probability on selections, nets

© David Scoins 2017