Daily Practice · Higher Plus
May 1961 5-a-day
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The batch download puts all 5 tiers' May 1961 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1961A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 2nd May 1961Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 3rd May 1961Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 4th May 1961y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 5th May 1961The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 6th May 1961A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 7th May 1961On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th May 1961A block has mass 220 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th May 1961Use the iteration x(n+1) = cube root of (11x(n) + 8) with x(0) = 4. Work out x(1) to 3 decimal places.
- 10th May 1961y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 11th May 1961In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 12th May 1961The probability of winning a game is 3/5. A player expects 36 wins. How many games did they play?
- 13th May 1961A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 14th May 1961x = 82 and y = 60, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th May 1961Work out the nth term of the quadratic sequence 10, 20, 34, 52, ...
- 16th May 1961y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 64.
- 17th May 1961In a vector proof you find that vector PQ = 5a + b and vector RS = 20a + 4b. What does this show about PQ and RS?
- 18th May 1961A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 19th May 1961On 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?
- 20th May 1961A car covers 810 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st May 1961The point (2, 4) lies on y = f(x). Write down its image on y = f(x) + 2.
- 22nd May 1961A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd May 1961A cuboid measures 5 cm by 13 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th May 1961A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th May 1961A 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?
- 26th May 1961Rationalise the denominator of 56/sqrt(7), giving your answer in its simplest form.
- 27th May 1961Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 28th May 1961y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 29th May 1961A cuboid measures 13 cm by 12 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th May 1961A bag holds 4 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st May 1961On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?