Daily Practice · Higher Plus
May 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1965 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1965A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd May 1965A cuboid measures 10 cm by 12 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd May 1965A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th May 1965A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 5th May 1965A rectangle is 5 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th May 1965The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 7th May 1965y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 8th May 1965A cuboid measures 5 cm by 7 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th May 1965A bag holds 4 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th May 1965On 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?
- 11th May 1965Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 12th May 1965A quadratic sequence starts 5, 19, 43, 77. Work out the second difference, and the coefficient of n^2.
- 13th May 1965y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 14th May 1965The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 15th May 1965A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 16th May 1965A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 17th May 1965A block has mass 280 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th May 1965Solve x^2 - 3x - 4 < 0.
- 19th May 1965y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 16.
- 20th May 1965In 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.
- 21st May 1965The probability of winning a game is 1/2. A player expects 50 wins. How many games did they play?
- 22nd May 1965On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 23rd May 1965x = 141 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th May 1965Write x^2 + 4x - 3 in the form (x + a)^2 + b.
- 25th May 1965A train slows steadily from 15 m/s to rest in 5 seconds. Work out its deceleration.
- 26th May 1965In a vector proof you find that vector PQ = a - 2b and vector RS = 3a - 6b. What does this show about PQ and RS?
- 27th May 1965A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 28th May 1965A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 29th May 1965A car covers 440 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 30th May 1965Work out the coordinates of the turning point of y = x^2 - 2x + 4.
- 31st May 1965y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.