Daily Practice · Higher Plus
September 1969 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1969 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1969
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1969A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd September 1969In a vector proof you find that vector PQ = 3a + 4b and vector RS = 6a + 8b. What does this show about PQ and RS?
- 3rd September 1969A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 4th September 1969A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 5th September 1969Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 6th September 1969Solve 4x^2 + 8x + 3 = 0.
- 7th September 1969y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 8th September 1969A cuboid measures 7 cm by 9 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th September 1969A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th September 1969On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 11th September 1969Simplify sqrt(75) + sqrt(108), giving your answer in the form a sqrt(b).
- 12th September 1969f(x) = 7x - 9. Work out the inverse function f^-1(x).
- 13th September 1969y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 14th September 1969A 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.
- 15th September 1969A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th September 1969A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 17th September 1969A rectangle is 11 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th September 1969Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 19th September 1969y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 16.
- 20th September 1969The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 21st September 1969A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 22nd September 1969On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd September 1969Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 24th September 1969Use the iteration x(n+1) = cube root of (9x(n) + 4) with x(0) = 1. Work out x(1) to 3 decimal places.
- 25th September 1969A train slows steadily from 31 m/s to rest in 10 seconds. Work out its deceleration.
- 26th September 1969In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 27th September 1969The probability of winning a game is 1/4. A player expects 30 wins. How many games did they play?
- 28th September 1969A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 29th September 1969A block has mass 700 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th September 1969Work out the nth term of the quadratic sequence 7, 11, 19, 31, ...