Daily Practice · Higher Plus
October 1962 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1962 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1962
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1962Use the iteration x(n+1) = cube root of (5x(n) + 2) with x(0) = 2. Work out x(1) to 3 decimal places.
- 2nd October 1962y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 36.
- 3rd October 1962In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 4th October 1962The probability of winning a game is 1/4. A player expects 12 wins. How many games did they play?
- 5th October 1962On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th October 1962A car covers 450 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 7th October 1962Work out the nth term of the quadratic sequence -8, -8, -6, -2, ...
- 8th October 1962A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 9th October 1962In a vector proof you find that vector PQ = 6a - 5b and vector RS = 12a - 10b. What does this show about PQ and RS?
- 10th October 1962A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 11th October 1962A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 12th October 1962Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.
- 13th October 1962The point (4, -5) lies on y = f(x). Write down its image on y = -f(x).
- 14th October 1962y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 15th October 1962A cuboid measures 8 cm by 13 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th October 1962A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th October 1962On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th October 1962Simplify sqrt(75) + sqrt(147), giving your answer in the form a sqrt(b).
- 19th October 1962Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 20th October 1962y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 21st October 1962A cuboid measures 6 cm by 13 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd October 1962A bag holds 6 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd October 1962A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 24th October 1962A rectangle is 12 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th October 1962f(x) = 3x + 8 and g(x) = 3x - 5. Work out fg(6).
- 26th October 1962y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 49.
- 27th October 1962The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 28th October 1962A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 29th October 1962On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th October 1962Expand and simplify (5 + sqrt(11))(5 - sqrt(11)).
- 31st October 1962The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.