Daily Practice · Higher Plus
January 1985 5-a-day
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The batch download puts all 5 tiers' January 1985 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1985On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 2nd January 1985A rectangle is 14 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd January 1985Make x the subject of 7x + 5 = y(x + 5).
- 4th January 1985y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 5th January 1985In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 6th January 1985The probability of winning a game is 3/4. A player expects 30 wins. How many games did they play?
- 7th January 1985A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 8th January 1985Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 9th January 1985Write 2/(x - 2) + 3/(x - 6) as a single fraction.
- 10th January 1985y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 36.
- 11th January 1985In a vector proof you find that vector PQ = 3a + 3b and vector RS = 6a + 6b. What does this show about PQ and RS?
- 12th January 1985A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 13th January 1985On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th January 1985A block has mass 820 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.
- 15th January 1985Solve 6x^2 + 7x - 20 = 0.
- 16th January 1985A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 17th January 1985A cuboid measures 9 cm by 11 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th January 1985A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th January 1985A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 20th January 1985x = 74 and y = 45, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st January 1985f(x) = 6x + 2. Work out the inverse function f^-1(x).
- 22nd January 1985y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 23rd January 1985A cuboid measures 11 cm by 10 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th January 1985A bag holds 3 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th January 1985On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 26th January 1985A car covers 580 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.
- 27th January 1985Solve x^2 + y^2 = 841 and y = x + 1 simultaneously.
- 28th January 1985y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 29th January 1985The 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.
- 30th January 1985A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 31st January 1985A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?