Daily Practice · Higher Plus
January 1966 5-a-day
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The batch download puts all 5 tiers' January 1966 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1966
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1966In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 5 in terms of an integer n?
- 2nd January 1966y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 3rd January 1966A cuboid measures 7 cm by 10 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th January 1966A bag holds 7 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th January 1966On 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?
- 6th January 1966Simplify sqrt(20) + sqrt(45), giving your answer in the form a sqrt(b).
- 7th January 1966Make x the subject of 6x + 4 = y(x + 4).
- 8th January 1966y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 9th January 1966The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 10th January 1966A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 11th January 1966A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 12th January 1966A rectangle is 17 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th January 1966Write 3/(x + 3) + 3/(x - 2) as a single fraction.
- 14th January 1966y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 64.
- 15th January 1966In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 16th January 1966The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
- 17th January 1966On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th January 1966Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 19th January 1966Solve 20x^2 + 29x + 6 = 0.
- 20th January 1966A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 21st January 1966In a vector proof you find that vector PQ = 4a - 5b and vector RS = 12a - 15b. What does this show about PQ and RS?
- 22nd January 1966A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
- 23rd January 1966A 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?
- 24th January 1966A block has mass 270 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th January 1966f(x) = 8x - 7. Work out the inverse function f^-1(x).
- 26th January 1966y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
- 27th January 1966A cuboid measures 4 cm by 15 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th January 1966A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th January 1966On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th January 1966x = 88 and y = 51, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st January 1966Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.