Daily Practice · Higher Plus
May 1956 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1956 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1956The 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.
- 2nd May 1956A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 3rd May 1956A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 4th May 1956Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 5th May 1956Work out the nth term of the quadratic sequence 12, 22, 36, 54, ...
- 6th May 1956y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 7th May 1956In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 8th May 1956The probability of winning a game is 1/2. A player expects 30 wins. How many games did they play?
- 9th May 1956On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 10th May 1956Simplify sqrt(72) + sqrt(8), giving your answer in the form a sqrt(b).
- 11th May 1956The point (-2, 5) lies on y = f(x). Write down its image on y = f(x) - 1.
- 12th May 1956y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 13th May 1956In a vector proof you find that vector PQ = 5a + 2b and vector RS = 25a + 10b. What does this show about PQ and RS?
- 14th May 1956A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 15th May 1956A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 16th May 1956A rectangle is 5 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th May 1956Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 18th May 1956y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 36.
- 19th May 1956A cuboid measures 4 cm by 8 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th May 1956A bag holds 10 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st May 1956On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 22nd May 1956Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 23rd May 1956f(x) = 4x - 4 and g(x) = 4x + 7. Work out fg(0).
- 24th May 1956A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 25th May 1956A cuboid measures 11 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th May 1956A bag holds 5 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th May 1956A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 28th May 1956A block has mass 250 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th May 1956The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 30th May 1956y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
- 31st May 1956The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.