Daily Practice · Higher Plus
January 1955 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1955 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1955A cuboid measures 8 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd January 1955A 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?
- 3rd January 1955On 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?
- 4th January 1955Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 5th January 1955The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 6th January 1955A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 7th January 1955The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 8th January 1955A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 9th January 1955A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 10th January 1955A block has mass 280 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th January 1955A quadratic sequence starts 7, 19, 35, 55. Work out the second difference, and the coefficient of n^2.
- 12th January 1955y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 13th January 1955In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 14th January 1955The probability of winning a game is 4/5. A player expects 56 wins. How many games did they play?
- 15th January 1955On 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?
- 16th January 1955x = 41 and y = 22, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th January 1955Solve x^2 - 11x + 24 > 0.
- 18th January 1955y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 19th January 1955In a vector proof you find that vector PQ = 3a + 5b and vector RS = 6a + 10b. What does this show about PQ and RS?
- 20th January 1955A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 21st January 1955A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 22nd January 1955A car covers 630 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd January 1955Write x^2 - 16x - 4 in the form (x + a)^2 + b.
- 24th January 1955y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 81.
- 25th January 1955A cuboid measures 11 cm by 6 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th January 1955A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th January 1955On 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?
- 28th January 1955Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.
- 29th January 1955Work out the coordinates of the turning point of y = x^2 + 10x + 12.
- 30th January 1955A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 31st January 1955A cuboid measures 10 cm by 6 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.