End of year B

These two sheets are equivalent, the sets of ten questions swapped so that 11-20 come first on this one (because so many pupils failed to finish).


11.Solve these:

5x – 3 = 10 – 2x;
2(x + 5) = 7 – x;
4x + 5 = 9x – 6


12. These are the first few terms of a sequence: 9, 13, 17, 21, 25, ...

Write down a rule for the next term

Find a formula for the nth term

Find the 100th term

Find the formula for the sequence which starts 25, 21, 17, 13, 9, ...

What is the 100th term of this second series?


13. Write these numbers,           57903,         179939,                7932,

to the nearest ten;   to the nearest hundred;      to two significant figures in standard form


14. Fred wants more than 70% in the next test. There are 60 questions, 60 marks. How many must he get right?


15. To convert Centigrade to Fahrenheit you must multiply by 9, divide by 5 and add 32.

Convert  (i)     5ºC to ºF                             (ii)    100ºC to ºF

        (iii)       Find what  -40º F is in ºC


16. Write these in order, smallest first:    4/3,  0.785,  √2,  0.950,   6/7


17. There are three otherwise identical cars of different colours. How many different ways can they be parked in three adjacent spaces and facing the same way?


18. A cuboid tank has a base of 25x45cm and is 60 cm deep. Find its volume in cm³ and in litres. If 50 litres of water are added to the cuboid, to what depth is it filled?


19. Write examples of events which describe probabilities of: impossible, certain, likely, unlikely, even (or evens).

Write the probability that a pair of fair dice, when thrown, will 
(a) show the same value,
(b) have scores that add to seven


20. Simplify these:

(a) p + p + p + p                         (b) 3p + 4p + 5p                         (c)  4p + 5q + 2p + q

(d) 24x – 35y – 9x – 13y            (e)  53z – 43w – 29z + 31w          (f)  x² – y²











NON-CALCULATOR QUESTIONS


1. Write these ratios in their simplest form.

(a)   6 minutes to one hour

(b)   75p to £3

(c)    3 inches to a yard

(d)   350 ml to 7 litres

(e)    15 minutes to three hours


2. Work out these:

a)    37 x 100

b)    4000 / 25

c)   50 000 / 100

d)   √49

e)     4.202 x 100

Put these in order, smallest first:  0.28, 0.208, 0.020800, 0.0028, 0.802


3. Draw a grid (rapidly) that is 4 by 6 squares. Fill in (hatch) 5/12 of it. Shade an eighth of the whole.


4. (a) Write the prime factors of 84.         (b) Find the highest common factor of 84 and 56. (c) Find the lowest common multiple of 84 and 56. [no calculator!!]


5. Draw the triangle ABC with vertices (1, 2), (3, 2) and (3, 5).    –3<x<10, -4<y<10

(a) Reflect ABC in the line x=5            (b) Rotate ABC about (1,1) through 90º clockwise


6. Indicate the number of lines of symmetry and order of rotational symmetry for each of:

    (a) a rhombus     (b) an ellipse      (c) a parallelogram      (d) a kite.


7. Draw accurately a triangle with angles of 60º and 55º and a side of 11cm between them. Use a protractor. 

    Bisect the new angle using compasses. 

    Measure the shortest side to the nearest millimetre.


8. A car hire company uses the formula y = 30x + 12 to work out the cost £y of hiring a car for x complete days. Find the cost of hiring a car for 1, 5 and 10 days. Draw the graph of y = 3x + 12. Use 0<x<10 and 0<y<100 (one unit per square in x, ten in y).
Another company charges £35 per day. Draw this (and label it) on the same graph. After how many days does the first company become the cheaper one?


9. Gaynor is using the formula p2 + 6p + 5 to fill in a table of values. Fill in the missing numbers to complete her table.

p                 0   1     2        3          4                                  10                            

p2                     1    4                                                       100                  144     169  

6p                    6   12                                          48           60

p2+6p+5    5  12   21                                         117        165                                      285  


10. A measurement of 12 metres is given to the nearest metre. What are the smallest and largest lengths in millimetres that could be described as being 12 metres?

© David Scoins 2017