Daily Practice · Higher Plus
May 1966 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1966 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1966
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1966Solve 12x^2 + 13x - 4 = 0.
- 2nd May 1966y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 3rd May 1966A cuboid measures 9 cm by 7 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th May 1966A bag holds 3 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th May 1966On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th May 1966Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.
- 7th May 1966f(x) = 4x + 11. Work out the inverse function f^-1(x).
- 8th May 1966y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 9th May 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.
- 10th May 1966A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 14/33. Work out r.
- 11th May 1966A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 12th May 1966Simplify sqrt(27) + sqrt(12), giving your answer in the form a sqrt(b).
- 13th May 1966Solve x^2 + y^2 = 625 and y = x + 17 simultaneously.
- 14th May 1966y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 81.
- 15th May 1966In 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.
- 16th May 1966The probability of winning a game is 1/5. A player expects 7 wins. How many games did they play?
- 17th May 1966On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th May 1966A rectangle is 21 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th May 1966Use the iteration x(n+1) = cube root of (12x(n) + 8) with x(0) = 3. Work out x(1) to 3 decimal places.
- 20th May 1966A train slows steadily from 15 m/s to rest in 5 seconds. Work out its deceleration.
- 21st May 1966In a vector proof you find that vector PQ = 4a - 6b and vector RS = 16a - 24b. What does this show about PQ and RS?
- 22nd May 1966A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 23rd May 1966A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 24th May 1966Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 25th May 1966Work out the nth term of the quadratic sequence 0, 14, 36, 66, ...
- 26th May 1966y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 27th May 1966A cuboid measures 8 cm by 3 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th May 1966A bag holds 5 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th May 1966On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th May 1966A block has mass 780 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 31st May 1966The point (-1, 0) lies on y = f(x). Write down its image on y = f(x - 6).