Daily Practice · Higher Plus
October 1956 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1956 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1956A block has mass 410 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd October 1956Work out the coordinates of the turning point of y = x^2 - 4x - 6.
- 3rd October 1956y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 4th October 1956In 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.
- 5th October 1956The probability of winning a game is 1/5. A player expects 14 wins. How many games did they play?
- 6th October 1956A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 7th October 1956x = 70 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th October 1956Simplify (x^2 - 10x + 24)/(x - 4).
- 9th October 1956y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 25.
- 10th October 1956In a vector proof you find that vector PQ = 2a + 6b and vector RS = 10a + 30b. What does this show about PQ and RS?
- 11th October 1956A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 12th October 1956On 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?
- 13th October 1956A car covers 330 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.
- 14th October 1956In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 15th October 1956A train slows steadily from 27 m/s to rest in 4 seconds. Work out its deceleration.
- 16th October 1956A cuboid measures 13 cm by 3 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th October 1956A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th October 1956A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 19th October 1956Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 20th October 1956Make x the subject of 2x + 6 = y(x + 6).
- 21st October 1956y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 22nd October 1956A cuboid measures 6 cm by 7 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd October 1956A bag holds 7 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th October 1956On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th October 1956Simplify sqrt(18) + sqrt(98), giving your answer in the form a sqrt(b).
- 26th October 1956Write 5/(x + 4) + 4/(x + 6) as a single fraction.
- 27th October 1956y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 28th October 1956The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 29th October 1956A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 30th October 1956A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 31st October 1956A rectangle is 7 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.