Daily Practice · Higher Plus
September 1966 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1966 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1966
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1966A bag holds 3 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd September 1966On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 3rd September 1966A car covers 790 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.
- 4th September 1966Work out the nth term of the quadratic sequence 14, 26, 44, 68, ...
- 5th September 1966y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 6th September 1966The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 7th September 1966A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 8th September 1966A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 9th September 1966Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 10th September 1966The point (2, 3) lies on y = f(x). Write down its image on y = f(x) - 3.
- 11th September 1966y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 16.
- 12th September 1966In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 13th September 1966The probability of winning a game is 4/5. A player expects 40 wins. How many games did they play?
- 14th September 1966On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th September 1966Simplify sqrt(12) + sqrt(12), giving your answer in the form a sqrt(b).
- 16th September 1966Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 17th September 1966A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.
- 18th September 1966In a vector proof you find that vector PQ = 6a - 3b and vector RS = 18a - 9b. What does this show about PQ and RS?
- 19th September 1966A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 20th September 1966A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 21st September 1966A rectangle is 23 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd September 1966f(x) = 2x + 8 and g(x) = 3x - 8. Work out fg(-1).
- 23rd September 1966y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 24th September 1966A cuboid measures 10 cm by 10 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th September 1966A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th September 1966On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th September 1966Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 28th September 1966The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 29th September 1966y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 30th September 1966A cuboid measures 9 cm by 10 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.