Daily Practice · Higher Plus
August 1966 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1966 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1966
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1966A cuboid measures 13 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd August 1966A bag holds 6 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd August 1966A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 4th August 1966Simplify sqrt(8) + sqrt(50), giving your answer in the form a sqrt(b).
- 5th August 1966Write 4/(x + 5) + 5/(x - 2) as a single fraction.
- 6th August 1966y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 7th August 1966The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 8th August 1966A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/66. Work out r.
- 9th August 1966On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th August 1966A rectangle is 5 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th August 1966Solve 20x^2 - 23x + 6 = 0.
- 12th August 1966y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 13th August 1966In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 14th August 1966The probability of winning a game is 5/8. A player expects 65 wins. How many games did they play?
- 15th August 1966A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 16th August 1966Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 17th August 1966f(x) = 8x + 2. Work out the inverse function f^-1(x).
- 18th August 1966y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 64.
- 19th August 1966In a vector proof you find that vector PQ = 6a - 5b and vector RS = 12a - 10b. What does this show about PQ and RS?
- 20th August 1966A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 21st August 1966On 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?
- 22nd August 1966A block has mass 200 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd August 1966Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 24th August 1966A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 25th August 1966A cuboid measures 10 cm by 6 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th August 1966A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th August 1966A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 28th August 1966x = 62 and y = 48, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th August 1966Use the iteration x(n+1) = cube root of (12x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 30th August 1966y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 31st August 1966A cuboid measures 7 cm by 11 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.