Daily Practice · Higher Plus
January 1962 5-a-day
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The batch download puts all 5 tiers' January 1962 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1962
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1962A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 2nd January 1962On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd January 1962A rectangle is 8 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th January 1962A quadratic sequence starts 3, 13, 31, 57. Work out the second difference, and the coefficient of n^2.
- 5th January 1962y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 6th January 1962In 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.
- 7th January 1962The probability of winning a game is 1/8. A player expects 2 wins. How many games did they play?
- 8th January 1962A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 9th January 1962Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 10th January 1962Solve x^2 - 4 > 0.
- 11th January 1962y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 9.
- 12th January 1962In a vector proof you find that vector PQ = 2a - 4b and vector RS = 10a - 20b. What does this show about PQ and RS?
- 13th January 1962A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 14th January 1962On 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?
- 15th January 1962A block has mass 520 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th January 1962Write x^2 + 14x - 2 in the form (x + a)^2 + b.
- 17th January 1962A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 18th January 1962A cuboid measures 15 cm by 7 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th January 1962A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th January 1962A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 21st January 1962x = 65 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd January 1962Work out the coordinates of the turning point of y = x^2 - 6x - 6.
- 23rd January 1962y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 24th January 1962A cuboid measures 7 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th January 1962A bag holds 4 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th January 1962On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th January 1962A car covers 890 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th January 1962Simplify (x^2 - 13x + 42)/(x - 7).
- 29th January 1962y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 30th January 1962The 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.
- 31st January 1962A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.